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1. The document discusses key fluid properties including density, viscosity, vapor pressure, and specific gravity. It also covers different systems of units used to describe fluid mechanics. 2. Viscosity is defined as the property of a fluid that causes resistance to layers of fluid moving past one another. Shear stress develops between layers due to differences in flow velocity. 3. Vapor pressure is the pressure at which a liquid will boil and is a function of temperature, with boiling occurring when vapor pressure equals the atmospheric pressure.

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FLUID MECHANICS & MACHINERY - CE3391

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UNIT-I FLUID PROPERTIES AND FLOW CHARACTERISTICS

PRE REQUEST DISCUSSION

Unit I broadly deal with units and dimensions, properties of fluids and applications
of control volume of continuity equation, energy equation, and momentum equation.

Man’s desire for knowledge of fluid phenomena began with his problems of water
supply, irrigation, navigation, and waterpower.
Matter exists in two states; the solid and the fluid, the fluid state being commonly
divided into the liquid and gaseous states. Solids differ from liquids and liquids from
gases in the spacing and latitude of motion of their molecules, these variables being large

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in a gas, smaller in a liquid, and extremely small in a solid. Thus it follows that
intermolecular cohesive forces are large in a solid, smaller in a liquid, and extremely

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small in a gas.

DIFFERENCES BETWEEN SOLIDS AND FLUIDS

The differences between the behaviors of solids and fluids under an applied force
are as follows:
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i. For a solid, the strain is a function of the applied stress, providing that the elastic
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limit is not exceeded. For a fluid, the rate of strain is proportional to the applied
stress.
ii. The strain in a solid is independent of the time over which the force is applied and, if
the elastic limit is not exceeded, the deformation disappears when the force is
removed. A fluid continues to flow as long as the force is applied and will not
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recover its original form when the force is removed.

FLUID MECHANICS
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Fluid mechanics is that branch of science which deals with the behavior of
fluids (liquids or gases) at rest as well as in motion. Thus this branch of science deals with
the static, kinematics and dynamic aspects of fluids. The study of fluids at rest is called fluid
statics. The study of fluids in motion, where pressure forces are not considered, is called
fluid kinematics and if the pressure forces are also considered for the fluids in motion, that
branch of science is called fluid dynamics.

1.1 UNITS AND DIMENSIONS.

The word dimensions are used to describe basic concepts like mass, length, time,
temperature and force.Units are the means of expressing the value of the dimension
quantitatively or numerically.

Example - Kilogram, Metre, Second, Kelvin, Celcius.

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The four examples are the fundamental units; other derived units are

Density = mass per unit volume = kg/m3

Force = mass x acceleration = kg.m/s2 = Newton or N

Pressure = force per unit area = N/m2 =Pascal or Pa
Other unit is ‘ bar’ ,
where 1 bar =1 X105 Pa =100 Kpa = 0.1 Mpa
Work = force x distance = Newton x metre = N.m==J or Joule

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Power = work done per unit time= J/s = Watt or W
Term Dimension Unit

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Area L*L m2
Volume L*L*L m3
Velocity L* T-1 m/s
Acceleration L*T-2 m/s2
Force M*L*T-2 N
Pressure M*L-1*T-2 N/m2 = Pa
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Work M*L2*T-2 Nm =J
Power M*L2*T-3 J/s =W
M*L-3 kg/m3
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Density
Viscosity M*L-1*T-1 kg/ms = N s/m2
Surface Tension M*T-1 N/m

Quantity Representative symbol Dimensions

Angular velocity  t-1

Area A L2

Density  M/L3

Force F ML/t2

Kinematic
 L2/t
viscosity

Linear velocity V L/t

Linear acceleration A L/t2

Mass flow rate m. M/t

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Power P ML2/t3

Pressure P M/Lt2

Sonic velocity C L/t

Shear stress  M/Lt2

Surface tension  M/t2

Viscosity  M/Lt

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Volume V L3

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Dimensions:
Dimensions of the primary quantities:
Fundamental
Symbol
dimension
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Length L
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Mass M

Time T
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Temperature T
Dimensions of derived quantities can be expressed in terms of the fundamental dimensions.
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1.1.1 SYSTEM OF UNITS

1. CGS Units

2. FPS Units

3. MKS Units

4. SI Units

1.2 FLUID PROPERTIES

1 Density or Mass density:

Density or mass density of a fluid is defined as the ratio of the mass of a fluid to its

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volume. Thus mass per unit volume of a is called density.

2. Specific weight or weight density:

Specific weight or weight density of a fluid is the ratio between the weight of a
fluid to its volume. The weight per unit volume of a fluid is called weight density.

3. Specific Volume:

Specific volume of a fluid is defined as the volume of a fluid occupied by a unit mass
or volume per unit mass of a fluid

4.Specific Gravity:

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Specific gravity is defined as the ratio of the weight density of a fluid to the weight

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density of a standard fluid.

1.3 VISCOSITY

Viscosity is defined as the property of a fluid which offers resistance to the

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movement of one layer of fluid over adjacent layer of the fluid. When two layers of
a fluid, a distance ‘dy’ apart, move one over the other at different velocities, say u
and u+du as shown in figure. The viscosity together with relative velocity causes a
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shear stress acting between the fluid layers

The top layer causes a shear stress on the adjacent lower layer while the
lower layer causes a shear stress on the adjacent top layer. This shear stress is
proportional to the rate of change of velocity with respect to y.
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1.4 VAPOUR PRESSURE

The pressure at which a liquid will boil is called its vapor pressure. This
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pressure is a function of temperature (vapor pressure increases with
temperature). In this context we usually think about the temperature at which boiling
occurs. For example, water boils at 100oC at sea-level atmospheric pressure (1 atm
abs). However, in terms of vapor pressure, we can say that by increasing the
temperature of water at sea level to 100 oC, we increase the vapor pressure to the
point at which it is equal to the atmospheric pressure (1 atm abs), so that boiling
occurs. It is easy to visualize that boiling can also occur in water at temperatures
much below 100oC if the pressure in the water is reduced to its vapor pressure. For
example, the vapor pressure of water at 10oC is 0.01 atm.

1.4.1 CAVITATION

Cavitation(flashing of the liquid into vapour) takes place when very low
pressures are produced at certain locations of a flowing liquid. Cavitation results

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in the formation of vapour pockets or cavities which are carried away from the
point of origin and collapse at the high pressure zone.

1.5 COMPRESSIBILITY

Compressibility is the reciprocal of the bulk modulus of elasticity, K which is

defined as the ratio of compressive stress to volumetric strain.

Compressibility is given by = 1/K

1.6 SURFACE TENSION

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Surface tension is defined as the tensile force acting on the surface of a liquid in
contact with a gas or on the surface between two two immiscible liquids such that the
contact surface behaves like a membrane under tension.

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1.A soap bubble 50 mm in diameter contains a pressure (in excess of atmospheric) of 2

bar. Find the surface tension in the soap film.
Data:
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Radius of soap bubble (r) = 25 mm = 0.025 m

p = 2 Bar = 2 x 105 N/m2

Formula:
Pressure inside a soap bubble and surface tension () are related by,
p = 4/r
Calculations:
 = pr/4 = 2 x 105 x 0.025/4 = 1250 N/m

1.7 CAPILLARITY
Capillarity is defined as a phenomenon of rise or fall of a liquid surface in a small
tube relative to the adjacent general level of liquid when the tube is held vertically in the
liquid. The rise of liquid surface is known as capillary rise while the fall of the liquid
surface is known as capillary depression.

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It is expressed in terms of cm or mm of liquid. Its value depends upon the specific weight of
the liquid, diameter of the tube and surface tension of the liquid.

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1.Water has a surface tension of 0.4 N/m. In a 3 mm diameter vertical tube if the liquid
rises 6 mm above the liquid outside the tube, calculate the contact angle.
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Data:
Surface tension = 0.4 N/m
Dia of tube (d) = 3 mm = 0.003 m
Capillary rise (h) = 6 mm = 0.006 m
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Formula:
Capillary rise due to surface tension is given by
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h = 4cos(gd), where  is the contact angle.

Calculations:
cos() = hgd/(4) = 0.006 x 1000 x 9.812 x 0.003 / (4 x 0.4) = 0.11
Therfore, contact angle  = 83.7o

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1.8 CONCEPT OF CONTROL VOLUME

A specified large number of fluid and thermal devices have mass flow in and
out of a system called as control volume.

1.8.1 CONTINUITY EQUATION

Concepts

The continuity equation is governed from the principle of conservation of

mass.It states that the mass of fluid flowing through the pipe at the cross-section
remains constants,if there is no fluid is added or removed from the pipe.

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Let us make the mass balance for a fluid element as shown below: (an open-faced cube)

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This is the continuity equation for every point in a fluid flow whether steady or unsteady ,
compressible or incompressible.
For steady, incompressible flow, the density is constant and the equation simplifies to

For two dimensional incompressible flow this will simplify still further to

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1.8.2 EULER'S EQUATION OF MOTION

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This is known as Euler's equation, giving, in differential form the relationship between p, v,
 and elevation z, along a streamline for steady flow.
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1.8.3 BERNOULLI EQUATION

Concepts
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Bernoulli’s Equation relates velocity, pressure and elevation changes of a fluid in motion. It
may be stated as follows “ In an ideal incompressible fluid when the flow is steady and
continuous the sum of pressure energy, kinetic energy and potential energy is constant
along streamline”

--> 1

This is the basic from of Bernoulli equation for steady incompressible inviscid flows. It
may be written for any two points 1 and 2 on the same streamline as

--> 2

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The contstant of Bernoulli equation, can be named as total head (ho) has different values on
different streamlines.

--> 3

The total head may be regarded as the sum of the piezometric head h* = p/g + z and the
kinetic head v2/2g.

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Bernoullie equation is arrived from the following assumptions:

1. Steady flow - common assumption applicable to many flows.

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2. Incompressible flow - acceptable if the flow Mach number is less than 0.3.
3. Frictionless flow - very restrictive; solid walls introduce friction effects.
4. Valid for flow along a single streamline; i.e., different streamlines may have
different ho.
5. No shaft work - no pump or turbines on the streamline.
6. No transfer of heat - either added or removed.
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Range of validity of the Bernoulli Equation:
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Bernoulli equation is valid along any streamline in any steady, inviscid,
incompressible flow. There are no restrictions on the shape of the streamline or on the
geometry of the overall flow. The equation is valid for flow in one, two or three dimensions.

Modifications on Bernoulli equation:

Bernoulli equation can be corrected and used in the following form for real cases.
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APPLICATIONS

1.Venturimeter.

2.Orificemeter

3.Pitot Tube

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1.9 MOMENTUM EQUATION

Net force acting on fluid in the direction of x=Rate of change of momentum in x

direction

=Mass per sec×Change in velocity

p1A1-p2A2×cosθ-Fx=ρQ(v2cosθ-v1)

Fx=ρQ(v1-v2cosθ)-p2A2cosθ+p1A1

Similarlt,the momentum in y-direction is

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-p2A2sinθ+Fy=ρQ(v2sinθ-0)

Fy=ρQv2sinθ+p2A2 sinθ

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Resultant force acting on the bend,

Fr=√Fx²+Fy²

GLOSSARY
Quantity
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Mass in Kilogram Kg
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Length in Meter M

Time in Second s or as sec

Temperature in Kelvin K

Mole gmol or simply as mol

Derived quantities:
Quantity Unit

Force in Newton (1 N = 1 kg.m/s2) N

Pressure in Pascal (1 Pa = 1 N/m2) N/m2

Work, energy in Joule ( 1 J = 1 N.m) J

Power in Watt (1 W = 1 J/s) W

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REVIEW QUESTIONS

PART A

1. Define compressibility of a fluid.

2. What is viscosity? What is the cause of it in liquids and gases.
3. What is the effect of temperature on viscosity of water and that of air?
4. Explain about capillarity.
5. Distinguish between fluid and solid.
6. Define (a) Dynamic viscosity and (b) Kinematic viscosity.

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7. Define (a) Surface tension (b) Capillarity
8. What is a real fluid? Give examples.

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9. Define cavitation.
10. Define Viscosity
11. Define the following fluid properties:
12. Density, weight density, specific volume and specific gravity of a fluid.
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PART B
1. (a) What are the different types fluids? Explain each type. (b) Discuss the
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thermodynamic properties of fluids

2. (a) One litter of crude oil weighs 9.6 N. Calculate its Specific weight, density and
specific weight.
(b) The Velocity Distribution for flow over a flat plate is given by u=(2/3)y-y2, Where u
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is the point velocity in meter per second at a distance y meter above the plate.
Determine the shear stress at y=0 and y=15 cm. Assume dynamic viscosity as 8.63
poises
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3. (a) A plate, 0.025 mm distant from a fixed plate, moves at 50 cm/s and requires a force
of 1.471 N/ m2 to maintain this speed. Determine the fluid viscosity between plates in
the poise.
(b) Determine the intensity of shear of an oil having viscosity =1.2 poise and is used for
lubrication in the clearance between a 10 cm diameter shaft and its journal bearing. The
clearance is 1.0 mm and Shaft rotates at 200 r.p.m

4. (a) Two plates are placed at a distance of 0.15mm apart. The lower plate is fixed while
the upper plate having surface area 1.0 m2 is pulled at 0.3 nm/s. Find the force and
power required to maintain this speed, if the fluid separating them is having viscosity
1.5 poise.
(b) An oil film of thickness 1.5 mm is used for lubrication between a square plate of
size 0.9m *0.9m and an inclined plane having an angle of inclination 200 . . The weight
of square plate is 392.4 N and its slides down the plane with a uniform velocity of 0.2
m/s. find the dynamic viscosity of the oil.

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5. (a) Assuming the bulk modulus of elasticity of water is 2.07 x10 6 kN/m2 at standard
atmospheric condition determine the increase of pressure necessary to produce one
percent reduction in volume at the same temperature
(b) Calculate the capillary rise in glass tube pf 3mm diameter when immersed in
mercury, take the surface tension and angle of contact of mercury as 0.52 N/m and 1300
respectively. Also determine the minimum size of the glass tube, if it is immersed in
water, given that the surface tension of water is 0.0725 N/m and Capillary rise in tube is
not exceed 0.5mm

6. (a) Calculate the pressure exerted by 5kg of nitrogen gas at a temperature of 100 C.
Assume ideal gas law is applicable.
(b) Calculate the capillary effect in glass tube 5mm diameter, when immersed in (1)
water and (2) mercury. The surface tension of water and mercury in contact with air are

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0.0725 N/m and 0.51 N/m respectively. The angle of contact of mercury of mercury is
130.

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7. (a) Explain all three Simple manometers with neat sketch.
(b) Explain Differential manometer With Neat sketch.

8. A U-tube differential manometer is connected two pressure pipes A and B.Pipe A

contains Carbon tetrachloride having a specific gravity 1.594 under a pressure of 11.772
N/ Cm2 . The pipe A lies 2.5 m above pipe B. Find the difference of pressure measured
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by mercury as a fluid filling U-tube
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UNIT -II FLOW THROUGH CIRCULAR CONDUITS

PRE REQUEST DISCUSSION

Unit II has an in dept dealing of laminar flow through pipes, boundary layer
concept, hydraulic and energy gradient, friction factor, minor losses, and flow through pipes
in series and parallel.

Boundary layer is the region near a solid where the fluid motion is affected by the
solid boundary. In the bulk of the fluid the flow is usually governed by the theory of ideal
fluids. By contrast, viscosity is important in the boundary layer. The division of the problem
of flow past an solid object into these two parts, as suggested by Prandtl in 1904 has proved

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to be of fundamental importance in fluid mechanics.

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This concept of hydraulic gradient line and total energy line is very useful in the
study of flow This concept of hydraulic gradient line and total energy line is very useful in
the study of flow of fluids through pipes. f fluids through pipes.

2.1 HYDRAULIC GRADIENT AND TOTAL ENERGY LINE

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1.Hydraulic Gradient Line
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It is defined as the line which gives the sum of pressure head (p/w)
and datum head (z) of a flowing fluid in a pipe with respect to some reference line or it is
the line which is obtained by joining the top of all vertical ordinates, showing the pressure
head (p/w) of a flowing fluid in a pipe from the centre of the pipe. It is briefly
written as H.G.L (Hydraulic Gradient Line).
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2.Total Energy Line

It is defined as the line which gives the sum of pressure head, datum head and
kinetic head of a flowing fluid in a pipe with respect to some reference line. It is also
defined as the line which is obtained by joining the tops of all vertical ordinates
showing the sum of pressure head and kinetic head from the centre of the pipe. It is briefly
written as T.E.L (Total Energy Line).

2.2 BOUNDARY LAYER

Concepts

The variation of velocity takes place in a narrow region in the vicinity of solid boundary.
The fluid layer in the vicinity of the solid boundary where the effects of fluid friction i.e.,
variation of velocity are predominant is known as the boundary layer.

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2.2.1 FLOW OF VISCOUS FLUID THROUGH CIRCULAR PIPE

For the flow of viscous fluid through circular pipe, the velocity distribution across a
section, the ratio of maximum velocity to average velocity, the shear stress distribution and
drop of pressure fora given length is to be determined. The flow through circular pipe will
be viscous or laminar, if the Reynold’s number is less than 2000.

2.2.2 DEVELOPMENT OF LAMINAR AND TURBULENT FLOWS IN CIRCULAR

PIPES

1.Laminar Boundary Layer

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At the initial stage i.e, near the surface of the leading edge of the plate, the thickness of
boundary layer is the small and the flow in the boundary layer is laminar though the main

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stream flows turbulent. So, the layer of the fluid is said to be laminar boundary layer.

2.Turbulent Boundary Layer

The thickness boundary layer increases with distance from the leading edge in the
down-stream direction. Due to increases in thickness of boundary layer, the laminar
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boundary layer becomes unstable and the motion of the fluid is disturbed. It leads to a
transition from laminar to turbulent boundary layer.
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2.2.3 BOUNDARY LAYER GROWTH OVER A FLAT PLATE

Consider a continuous flow of fluid along the surface of a thin flat plate with its sharp
leading edge set parallel to the flow direction as shown in figure 2.7.The fluid approaches
the plate with uniform velocity U known as free stream velocity at the leading edge. As
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soon as the fluid comes in contact the leading edge of the plate,its velocity is reduced to
zero as the fluid particles adhere to the plate boundary thereby satisfying no-slip condition.
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2.3 FLOW THROUGH CIRCULAR PIPES-HAGEN POISEUILLE’S EQUATION

Due to viscosity of the flowing fluid in a laminar flow,some losses of head take place.The
equation which gives us the value of loss of head due to viscosity in a laminar flow is
known as Hagen-Poiseuille’s law.

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p1-p2=32μUL/D²

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=128μQL/πD4

This equation is called as Hargen-Poiseuille equation for laminar flow in the circular pipes.

2.4 DARCY’S EQUATION FOR LOSS OF HEAD DUE TO FRICTION IN PIPE

A pipe is a closed conduit through which the fluid flows under pressure.When the
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fluid flows through the piping system,some of the potential energy is lost due to friction.
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hƒ=4ƒLv²/2gD

2.5 MOODY’S DIAGRAM

Moody’s diagram is plotted between various values of friction factor(ƒ),Reynolds

number(Re) and relative roughness(R/K) as shown in figure 2.6.For any turbulent flow
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problem,the values of friction factor(ƒ) can therefore be determined from Moody’s

diagram,if the numerical values of R/K for the pipe and Rе of flow are known.
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The Moody’s diagram has plotted from the equation

1/√ ƒ-2.0 log10(R/K)=1.74-2.0 log10[1+18.7/(R/K/Re/ ƒ)]

Where,R/K=relative roughness

ƒ=friction factor and Re=Reynolds number.

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2.6 CLASSIFICATION OF BOUNDARY LAYER THICKNESS
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1. Displacements thickness(δ*)

2. Momentum thickness(θ)

3. Energy thickness(δe)
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2.7 BOUNDARY LAYER SEPARATION

The boundary layer leaves the surface and gets separated from it. This phenomenon is
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known as boundary layer separation.

2.8 LOSSESS IN PIPES

When a fluid flowing through a pipe, certain resistance is offered to the flowing fluid,
it results in causing a loss of energy.

The loss is classified as:

1. Major losses
2. Minor losses

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2.8.1 Major Losses in Pipe Flow

The major loss of energy is caused by friction in pipe. It may be computed by Darcy-
weisbach equation.

Minor Losses in Pipe Flow

The loss of energy caused on account of the change in velocity of flowing fluid is called
minor loss of energy.

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2.9 FLOW THOUGH PIPES IN SERIES AND PARALLEL

Pipes in Series

The pipes of different diamers and lengths which are connected with one
another to form a single pipeline.

Pipes in Parallel

When a main pipeline divides into two or more parallel pipes which
again join together to form a single pipe and continuous as a main line

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GLOSSARY

HGL –Hydraulic gradient line

TEL – Total energy line.

Applications

1. To find out friction factor in the flow through pipe.

2. To find out the losses in losses in the pipes.

REVIEW QUESTIONS

PART A

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1.Mention the general characteristics of laminar flow.
2. Write down the Navier-stokes equation.

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3. Write down the Hagen-Poiseuille equation for laminar flow.
4. What are energy lines and hydraulic gradient lines?
5. What is a siphon? What is its application?
6. What is hydraulic Mean Depth or hydraulic radius?
7. Write the Darcy weishbach and Chezy’s formulas.
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8. Where the Darcy weishbach and Chezy’s formulas are used?
9. What are the losses experienced by fluid when it is passing
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through a pipe?
10.Write the equation of loss of energy due to sudden enlargement.
11.What do you mean by flow through parallel pipes?
12.What is boundary layer?

PART-B
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1. (a) Derive an expression for the velocity distribution for viscous flow through a circular
pipe.
(b) A main pipe divides into two parallel pipes, which again forms one pipe. The length
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and diameter for the first parallel pipe are 2000m and 1m respectively, while the length
and diameter of second parallel pipe are 2000 and 0.8 m respectively. Find the rate of
flow in each parallel pipe, if total flow in the main is 3 m³/s. The coefficient of friction
for each parallel pipe is same and equal to 0.005.

2. (a)Two pipes of 15 cm and 30 cm diameters are laid in parallel to pass a total discharge
of 100 liters/ second. Each pipe is 250 m long. Determine discharge through each pipe.
Now these pipes are connected in series to connect two tanks 500 m apart, to carry same
total discharge. Determine water level difference between the tanks. Neglect minor
losses in both cases, f=0.02 fn both pipes.
(b) A pipe line carrying oil of specific gravity 0.85, changes in diameter from 350 mm
at position 1 to 550 mm diameter to a position 2, which is at 6 m at a higher level. If the
pressure at position 1 and 2 are taken as 20 N/cm2 and 15 N/ cm2 respectively and
discharge through the pipe is 0.2 m³/s. determine the loss of head.

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3. Obtain an expression for Hagen- Poisulle flow. Deduce the condition of maximum
velocity.

4. A flat plate 1.5 m X 1.5 m moves at 50 km / h in a stationary air density 1.15 kg/ m³. If
The coefficient of drag and lift are 0.15 and 0.75 respectively, determine (i) the lift force
(ii) the drag force (iii) the resultant force and (iv) the power required to set the plate in
motion.

5 (a). The rate of flow of water through a horizontal pipe is 0.3 m³/s. The diameter of the
pipe is suddenly enlarged from 25 cm to 50 cm. The pressure intensity in the smaller
pipe is 14N/m².
Determine (i) Loss of head due to sudden enlargement. (ii) Pressure intensity in the
large

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pipe and (iii) Power lost due to enlargement.
(b) Water is flowing through a tapering pipe of length 200 m having diameters 500 mm

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at the upper end and 250 mm at the lower end, the pipe has a slope of 1 in 40. The rate
of flow through the pipe is 250 lit/ sec. the pressure at the lower end and the upper end
are 20 N/cm² and 10 N/cm² respectively. Find the loss of head and direction of flow.

6. A horizontal pipe of 400 mm diameter is suddenly contracted to a diameter of 200 mm.

The pressure intensities in the large and small pipe is given as 15 N/cm² and 10 N/cm²
respectively. Find the loss of head due to contraction, if Cc=0.62, determine also the
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rate of flow of water.
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7. Determine the length of an equivalent pipe of diameter 20 cm and friction factor 0.02
for a given pipe system discharging 0.1m³/s. The pipe system consists of the following:
(i) A 10 m line of 20 cm dia with f=0.03
(ii) Three 90º bend, k=0.5 for each
(iii) Two sudden expansion of diameter 20 to 30 cm
(iv) A 15 m line of 30 cm diameter with f=0.025 and
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(v) A global valve, fully open, k=10.

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UNIT-III DIMENSIONAL ANALYSIS

DIMENSIONAL ANALYSIS

PRE REQUEST DISCUSSION

Unit III deals with dimensional analysis,models and similitude,and application of

dimensionless parameters.

Many important engineering problems cannot be solved completely by theoretical or

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mathematical methods. Problems of this type are especially common in fluid-flow, heat-
flow, and diffusional operations. One method of attacking a problem for which no
mathematical equation can be derived is that of empirical experimentations.

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For example, the pressure loss from friction in a long, round, straight, smooth pipe
depends on all these variables: the length and diameter of the pipe, the flow rate of the
liquid, and the density and viscosity of the liquid. If any one of these variables is changed,
the pressure drop also changes. The empirical method of obtaining an equation relating
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these factors to pressure drop requires that the effect of each separate variable be
determined in turn by systematically varying that variable while keep all others constant.
The procedure is laborious, and is difficult to organize or correlate the results so obtained
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into a useful relationship for calculations.

There exists a method intermediate between formal mathematical development and a

completely empirical study. It is based on the fact that if a theoretical equation does exist
among the variables affecting a physical process, that equation must be dimensionally
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homogeneous. Because of this requirement it is possible to group many factors into a

smaller number of dimensionless groups of variables. The groups themselves rather than the
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separate factors appear in the final equation.

Concepts

Dimensional analysis drastically simplifies the task of fitting experimental data to

design equations where a completely mathematical treatment is not possible; it is also useful
in checking the consistency of the units in equations, in converting units, and in the scale-up
of data obtained in physical models to predict the performance of full-scale model. The
method is based on the concept of dimension and the use of dimensional formulas.

Dimensional analysis does not yield a numerical equation, and experiment is

required to complete the solution of the problem. The result of a dimensional analysis is
valuable in pointing a way to correlations of experimental data suitable for engineering use.

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3.1 METHODS OF DIMENSIONAL ANALYSIS

If the number of variables involved in a physical phenomenon are known, then the
relation among the variables can be determined by the following two methods.

1.Rayleigh’s method

2. Buckingham’s π theorem

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3.1.1Rayleigh’s method
This method is used for determining the expression for a variable which depends upon

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maximum three or four variables only. If the number of independent variables
becomes more than four then it is very difficult to find the expression for the dependent
variable.

3.1.2 Buckingham’s π theorem.

If there are n variables (independent and dependent variables) in a physical
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phenomenon and if these variables contain m fundamental dimensions (M, L, T), then the
variables are arranged into (n-m) dimensionless numbers. Each term is called Buckingham’s
π theorem.
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Applications

 It is used to justify the dependency of one variable with the other.

 Usually this type of situation occurs in structures and hydraulic machines.
 To solve this problem efficiently, an excellent tool is identified called dimensional
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analysis.
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AP
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3.2 SMILITUDE –TYPES OF SIMILARITIES

Similitude is defined as the similarity between the model and its prototype in
every respect, which means that the model and prototype are completely similar. Three
types of similarities must exist between the model and prototype.

Concepts

Whenever it is necessary to perform tests on a model to obtain information that

cannot be obtained by analytical means alone, the rules of similitude must be applied.
Similitude is the theory and art of predicting prototype performance from model
observations

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1. Geometric similarity refers to linear dimensions. Two vessels of different sizes are
geometrically similar if the ratios of the corresponding dimensions on the two scales are the

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same. If photographs of two vessels are completely super-impossible, they are
geometrically similar.

2.Kinematic similarity refers to motion and requires geometric similarity and the same
ratio of velocities for the corresponding positions in the vessels.
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3.Dynamic similarity concerns forces and requires all force ratios for corresponding
positions to be equal in kinematically similar vessels.
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SIGNIFICANCE

The requirement for similitude of flow between model and prototype is that the
significant dimensionless parameters must be equal for model and prototype

3.3 DIMENSIONLESS PARAMETERS

Since the inertia force is always present in a fluid flow, its ratio with each of the
other forces provides a dimensionless number.
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1. Reynold’s number
2. Froud’s number
3. Euler’s number
4. Weber’s number
5. Mach’s number

Applications of dimensionless parameters

1. Reynold’s model law

2. Froud’s model law
3. Euler’s model law
4. Weber’s model law
5. Mach’s model law

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Important Dimensionless Numbers in Fluid Mechanics:

Dimensionless
Symbol Formula Numerator Denominator Importance
Number
Fluid flow
Reynolds Inertial involving
NRe Dv/ Viscous force
number force viscous and
inertial forces
Froude Inertial Gravitational Fluid flow with
NFr u2/gD
number force force free surface

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Inertial Fluid flow with
Weber number NWe u2D/ Surface force
force interfacial forces

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Local Gas flow at high
Mach number NMa u/c Sonic velocity
velocity velocity
Drag Total drag Flow around
CD FD/(u2/2) Inertial force
coefficient force solid bodies
Flow though
w/(u2/2)
Friction factor f
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closed conduits
Flow though
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Pressure Pressure closed conduits.
CP p/(u2/2) Inertial force
coefficient force Pressure drop
estimation
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3.4 MODEL ANALYSIS.

PRE REQUEST DISCUSSION

Present engineering practice makes use of model tests more frequently

than most people realize. For example, whenever a new airplane is designed, tests are made
not only on the general scale model but also on various components of the plane. Numerous
tests are made on individual wing sections as well as on the engine pods and tail sections

Models of automobiles and high-speed trains are also tested in wind tunnels to
predict the drag and flow patterns for the prototype. Information derived from these model
studies often indicates potential problems that can be corrected before prototype is built,
thereby saving considerable time and expense in development of the prototype.

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Concepts

Much time, mony and energy goes into the design construction and eradication of
hydraulic structures and machines.

To minimize the chances of failure, it is always desired that the tests to be performed
on small size models of the structures or machines. The model is the small scale replica of
the actual structure or machine. The actual structure or machine is Called prototype.

Applictions

1. Civil engineering structures such as dams, canals etc.

2. Design of harbor, ships and submarines

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3. Aero planes, rockets and machines.
4. Marine engineers make extensive tests on model shop hulls to predict the drag of the

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ships

GLOSSARY

The three friction factor problems:

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The friction factor relates six parameters of the flow:

1. Pipe diameter
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2. Average velocity
3. Fluid density
4. Fluid viscosity
5. Pipe roughness
6. The frictional losses per unit mass.
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Therefore, given any five of these, we can use the friction-factor charts to find the sixth.
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Most often, instead of being interested in the average velocity, we are interested in the
volumetric flow rate Q = (/4)D2V

The three most common types of problems are the following:

Type Given To find

1 D, k, , , Q hf

 D, k, , , hf Q

 k, , hf, Q D

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Generally, type 1 can be solved directly, where as types 2 and 3 require simple trial and
error.

Three fundamental problems which are commonly encountered in pipe-flow calculations:

Constants: rho, mu, g, L

1. Given D, and v or Q, compute the pressure drop. (pressure-drop problem)

2. Given D, delP, compute velocity or flow rate (flow-rate problem)
3. Given Q, delP, compute the diameter D of the pipe (sizing problem)

REVIEW QUESTIONS

1. Define Dimensional Analysis

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2. What you meant by fundamental and derived units?
3. Define dimensionally homogeneous equation.

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4. What are the methods of dimensional analysis?
5. State Buckingham’s Π theorem
6. What you meant by Repeating variables
7. What is dimensionless number?
8. Check the dimensional homogeneity for the equation V=u+at
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PART-B
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1) Check the dimensional homogeneity for the equation V = u + ft.

2) Determine the dimension of the following quantities:

i) Discharge
ii) Kinematic viscosity
iii) Force and
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iv) Specific weight.

3) Find an expression for the drag force on smooth sphere of diameter D, moving with
uniform velocity v, in fluid density and dynamic viscosity .

4) Efficiency of a fan depends on the density , the dynamic viscosity of the fluid ,
the angular velocity , diameter D of the rotor and the discharge Q. Express in
terms of dimensional parameters.

5) The resistance force R of a supersonic plane during flight can be considered as

dependent upon the length of the aircraftl, velocity v, air viscosity , air density
and bulk modulus of air K. Express the functional relationship between these
variables and the resisting force.

6) A partially submerged body is towed in water. The resistance R to its motion

depends on the density , the viscosity of water, length l of the body, velocity v of

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the body and acceleration due to gravityg. Show that the resistance to motion can be
expressed in the form
R = L2v2 , .

7) The pressure drop ∆p in a pipe of diameter D and length l depends on the density
and viscosity of fluid flowing, mean velocity v of flow and average height of
protuberance t. Show that the pressure drop can be expressed in the form p =
v2 , , .

8) Find the expression for the drag force on smooth sphere of diameter D moving with

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uniform velocity v in fluid density and dynamic viscosity .

9) The efficiency of a fan depends on the density , the dynamic viscosity , angular

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velocity , diameter D of the motor and the discharge Q. Express the efficiency
in terms of dimensional parameters.

10) The pressure difference p in a pipe of diameter D and length l due to turbulent flow
depends on the velocity v, viscosity , density and roughness K. Using
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Buckingham’s -theorem, obtain an expression for p.
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ST

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UNIT-IV PUMPS

PRE REQUEST DISCUSSION

Basic concepts of rot dynamic machines, velocity triangles for radial flow and axial
flow machines, centrifugal pumps, turbines and Positive displacement pumps and rotary
pumps its performance curves are discussed in Unit IV.

The liquids used in the chemical industries differ considerably in physical and chemical
properties. And it has been necessary to develop a wide variety of pumping equipment.

The two main forms are the positive displacement type and centrifugal pumps.

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the former, the volume of liquid delivered is directly related to the displacement of
the piston and therefore increases directly with speed and is not appreciably influenced by

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the pressure. In this group are the reciprocating piston pump and the rotary gear pump, both
of which are commonly used for delivery against high pressures and where nearly constant
delivery rates are required.

The centrifugal type depends on giving the liquid a high kinetic energy which is then
converted as efficiently as possible into pressure energy.
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4.1 HEAD AND EFFICIANCES
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1. Gross head
2. Effective or Net head
3. Water and Bucket power
4. Hydraulic efficiency
5. Mechanical efficiency
6. Volume efficiency
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7. Overall efficiency
Concepts
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A pump is a device which converts the mechanical energy supplied into hydraulic energy by
lifting water to higher levels.

4.2 CENTRIFUGAL PUMP

Working principle
If the mechanical energy is converted into pressure energy by means of centrifugal
force acting
on the fluid, the hydraulic machine is called centrifugal pump. The centrifugal pump
acts as a reversed of an inward radial flow reaction turbine

4.2.3 Performance Characteristics of Pumps

The fluid quantities involved in all hydraulic machines are the flow rate (Q) and the
head (H), whereas the mechanical quantities associated with the machine itself are the
power (P), speed (N), size (D) and efficiency ( ). Although they are of equal importance,
the emphasis placed on certain of these quantities is different for different pumps. The

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output of a pump running at a given speed is the flow rate delivered by it and the head
developed. Thus, a plot of head and flow rate at a given speed forms the fundamental
performance characteristic of a pump. In order to achieve this performance, a power input is
required which involves efficiency of energy transfer. Thus, it is useful to plot also the
power P and the efficiency  against Q.
Over all efficiency of a pump ( ) = Fluid power output / Power input to the shaft = gHQ /
P
Type number or Specific speed of pump, nS = NQ1/2 / (gH)3/4 (it is a dimensionless number)

Centrifugal pump Performance

In the volute of the centrifugal pump, the cross section of the liquid path is greater than in
the impeller, and in an ideal frictionless pump the drop from the velocity V to the lower
velocity is converted according to Bernoulli's equation, to an increased pressure. This is the

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source of the discharge pressure of a centrifugal pump.

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If the speed of the impeller is increased from N1 to N2 rpm, the flow rate will increase from
Q1 to Q2 as per the given formula:

The head developed(H) will be proportional to the square of the quantity discharged, so that
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The power consumed(W) will be the product of H and Q, and, therefore

These relationships, however, form only the roughest guide to the performance of
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centrifugal pumps.

4.2.4 Characteristic curves

Pump action and the performance of a pump are defined interms of their
characteristic curves. These curves correlate the capacity of the pump in unit volume per
unit time versus discharge or differential pressures. These curves usually supplied by pump
manufacturers are for water only.

These curves usually shows the following relationships (for centrifugal pump).

 A plot of capacity versus differential head. The differential head is the difference in
pressure between the suction and discharge.
 The pump efficiency as a percentage versus capacity.
 The break horsepower of the pump versus capacity.
 The net poisitive head required by the pump versus capacity. The required NPSH for
the pump is a characteristic determined by the manufacturer.

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Centrifugal pumps are usually rated on the basis of head and capacity at the point of
maximum efficiency.

4.3 RECIPROCATING PUMPS

Working principle

If the mechanical energy is converted into hydraulic energy (or pressure energy) by
sucking
the liquid into a cylinder in which a piston is reciprocating (moving backwards and
forwards), which
exerts the thrust on the liquid and increases its hydraulic energy (pressure energy), the pump

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is known as reciprocating pump

Main ports of a reciprocating pump

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1.A cylinder with a piston, piston rod, connecting rod and a crank, 2. Suction pipe

3.Delivery pipe, 4. Suction valve and 5.Delivery valve.

Slip of Reciprocating Pump

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Slip of a reciprocating pump is defined as the difference between the theoretical discharge
and the actual discharge of the pump.
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4.3.1Characteristic Curves Of Reciprocatring Pumps

1.According to the water being on contact with one side or both sides of the piston
(i.) Single acting pump (ii.) Double-acting pump
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2.According to the number of cylinders provided

(i.) Single acting pump (ii.) Double-acting pump (iii.) Triple-acting pump
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Reciprocating pumps Vs centrifugal pumps

The advantages of reciprocating pumps in general over centrifugal pumps may be

summarized as follows:

1. They can be designed for higher heads than centrifugal pumps.

2. They are not subject to air binding, and the suction may be under a pressure less
than atmospheric without necessitating special devices for priming.
3. They are more flexible in operation than centrifugal pumps.
4. They operate at nearly constant efficiency over a wide range of flow rates.

The advantages of centrifugal pumps over reciprocating pumps are:

1. The simplest centrifugal pumps are cheaper than the simplest reciprocating pumps.
2. Centrifugal pumps deliver liquid at uniform pressure without shocks or pulsations.

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3. They can be directly connected to motor derive without the use of gears or belts.
4. Valves in the discharge line may be completely closed without injuring them.
5. They can handle liquids with large amounts of solids in suspension.

4.4 Rotary Pumps

The rotary pump is good for handling viscous liquids, nut because of the close
tolerances needed, it can not be manufactured large enough to compete with centrifugal
pumps for coping with very high flow rates.
Rotary pumps are available in a variety of configurations.
 Double lobe pump
 Trible lobe pumps
 Gear pump

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 Gear Pumps


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 Spur Gear or External-gear pump

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External-gear pump (called as gear pump) consists essentially of two

intermeshing gears which are identical and which are surrounded by a closely fitting
casing. One of the gears is driven directly by the prime mover while the other is
allowed to rotate freely. The fluid enters the spaces between the teeth and the casing
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and moves with the teeth along the outer periphery until it reaches the outlet where it
is expelled from the pump.

External-gear pumps are used for flow rates up to about 400 m 3/hr working
against pressures as high as 170 atm. The volumetric efficiency of gear pumps is in
the order of 96 percent at pressures of about 40 atm but decreases as the pressure
rises.

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4.4.1 Internal-gear Pump

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The above figure shows the operation of a internal gear pump. In the
internal-gear pump a spur gear, or pinion, meshes with a ring gear with internal
teeth. Both gears are inside the casing. The ring gear is coaxial with the inside of the
casing, but the pinion, which is externally driven, is mounted eccentrically with
respect to the center of the casing. A stationary metal crescent fills the space
between the two gears. Liquid is carried from inlet to discharge by both gears, in the
spaces between the gear teeth and the crescent.
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4.4.2 Lobe pumps
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In principle the lobe pump is similar to the external gear pump; liquid flows into the
region created as the counter-rotating lobes unmesh. Displacement volumes are formed
between the surfaces of each lobe and the casing, and the liquid is displaced by meshing of
the lobes. Relatively large displacement volumes enable large solids (nonabrasive) to be
handled. They also tend to keep liquid velocities and shear low, making the pump type
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suitable for high viscosity, shear-sensitive liquids.

Two lobe pump Three lobe pump

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The choice of two or three lobe rotors depends upon solids size, liquid viscosity, and
tolerance of flow pulsation. Two lobe handles larger solids and high viscosity but pulsates
more. Larger lobe pumps cost 4-5 times a centrifugal pump of equal flow and head.

4.3 Selection of Pumps

The following factors influence the choice of pump for a particular operation:

1. The quantity of liquid to be handled: This primarily affects the size of the pump and
determines whether it is desirable to use a number of pumps in parallel.
2. The head against which the liquid is to be pumped. This will be determined by the
difference in pressure, the vertical height of the downstream and upstream reservoirs
and by the frictional losses which occur in the delivery line. The suitability of a

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centrifugal pump and the number of stages required will largely be determined by
this factor.

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3. The nature of the liquid to be pumped. For a given throughput, the viscosity largely
determines the frictional losses and hence the power required. The corrosive nature
will determine the material of construction both for the pump and the packing. With
suspensions, the clearance in the pump must be large compared with the size of the
particles.
4. The nature of power supply. If the pump is to be driven by an electric motor or
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internal combustion engine, a high-speed centrifugal or rotary pump will be
preferred as it can be coupled directly to the motor.
5. If the pump is used only intermittently, corrosion troubles are more likely than with
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continuous working.

Applications

The handling of liquids which are particularly corrosive or contain abrasive solids in
suspension, compressed air is used as the motive force instead of a mechanical pump.
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REVIEW QUESTIONS
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PART A

1.What is meant by Pump?

2. Mention main components of Centrifugal pump.
3. What is meant by Priming?
4. Define Manometric head.
5. Define Manometric efficiency
6. Define Mechanical efficiency.
7. Define overall efficiency.
8. Give the range of specific speed for low, medium, high speed
radial flow.
9. Define speed ratio, flow ratio.
10.Mention main components of Reciprocating pump.
11.Define Slip of reciprocating pump. When the negative slip does
occur?

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PART-B

1. Write short notes on the following (1) Cavitations in hydraulic machines their causes,
effects and remedies. (2) Type of rotary pumps.

2. Draw a neat sketch of centrifugal pump and explain the working principle of the
centrifugal pump.

3. Draw a neat sketch of Reciprocating pump and explain the working principle of single
acing and double acting Reciprocating pump.

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4. A radial flow impeller has a diameter 25 cm and width 7.5 cm at exit. It delivers 120
liters of water per second against a head of 24 m at 1440 rpm. Assuming the vanes block
the flow area by 5% and hydraulic efficiency of 0.8, estimate the vane angle at exit.

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Also calculate the torque exerted on the driving shaft if the mechanical efficiency is
95%.

5. Find the power required to drive a centrifugal pump which to drive a centrifugal pump
which delivers 0.04 m3 /s of water to a height of 20 m through a 15 cm diameter pipe
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and 100 m long. The over all efficiency of the pump is 70% and coefficient of friction is
0.15 in the formula hf=4flv2/2gd.
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6. A Centrifugal pump having outer diameter equal to 2 times the inner diameter and
running at 1200 rpm works against a total head of 75 m. The Velocity of flow through
the impeller is constant and equal to 3 m/s. The vanes are set back at an angle of 30º at
out let. If the outer diameter of impeller is 600 mm and width at outlet is 50 mm.
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Determine (i) Vane angle at inlet (ii) Work done per second on impeller
(iii) Manometric efficiency.
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7. The diameter and stroke of a single acting reciprocating pump are 200 mm and 400 mm
respectively, the pump runs at 60 rpm and lifts 12 liters of water per second through a
height of 25 m. The delivery pipe is 20m long and 150mm in diameter. Find (i)
Theoretical power required to run the pump. (ii) Percentage of slip. (iii) Acceleration
head at the beginning and middle of the delivery stroke.

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UNIT V TURBINES

PRE REQUEST DISCUSSION

Hydraulic Machines are defined as those machines which convert either

hydraulic energy (energy possessed by water) into mechanical energy (which is
further converted into electrical energy) or mechanical energy into hydraulic energy.
The hydraulic machines, which convert the hydraulic energy into mechanical energy, are
called turbines.

Turbines are defined as the hydraulic machines which convert hydraulic energy into
mechanical energy. This mechanical energy is used in running an electric generator which is

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directly coupled to the shaft of the turbine. Thus the mechanical energy is converted
into electrical energy. The electric power which is obtained from the hydraulic energy
(energy of water) is known as Hydro- electro power.

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In our subject point of view, the following turbines are important and will be
discussed one by one.

1. Pelton wheel

2. Francis turbine
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3. Kaplan turbine
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Concept

Turbines are defined as the hydraulic machines which convert hydraulic energy into
mechanical energy. This mechanical energy is used in running an electric generator which is
directly coupled to the shaft of the turbine
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FLUID TYPES OF TURBINE

Water Hydraulic Turbine

Steam Steam Turbine

Froen Vapour Turbine
Gas or air Gas Turbine
Wind Wind Mills

5.1 CLASSIFICATION OF HYDRAULIC TURBINES

1. According to the action of the water flowing

2. According to the main direction of flow of water

3. According to the head and quality of water required

4. According to the specific speed

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5.2 HEAD AND EFFICIANCES OF PELTON WHEEL

1. Gross head
2. Effective or Net head
3. Water and Bucket power
4. Hydraulic efficiency
5. Mechanical efficiency
6. Volume efficiency
7. Overall efficiency

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5.3 IMPULSE TURBINE

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In an impulse turbine, all the energy available by water is converted into kinetic
energy by passing a nozzle. The high velocity jet coming out of the nozzle then impinges on
a series of buckets fixed around the rim of a wheel.

5.4 Tangential Flow Turbine, Radial And Axial Turbines

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1. Tangential flow turbine

In a tangential flow turbine, water flows along the tangent to the path of runner. E.g. Pelton
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wheel

2. Radial flow turbine

In a radial flow turbine, water flows along the radial direction and mainly in the plane
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normal to the axis of rotation, as it passes through the runner. It may be either inward radial
flow type or outward radial flow type.
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3. Axial flow turbine

In axial flow turbines, water flows parallel to the axis of the turbine shaft. E.g. kaplan
turbine

4. Mixed flow turbine

In a mixed flow turbine, the water enters the blades radiallsy and comes out axially and
parallel to the turbine shaft .E.g. Modern Francis turbine.

In our subject point of view, the following turbines are important and will be discussed one
by one

1. Pelton wheel
2. Francis turbine
3. Kaplan turbine
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5.5 PELTON WHEEL OR PELTON TURBINE

The Pelton wheel is a tangential flow impulse turbine and now in common use.
Leston A Pelton, an American engineer during 1880,develops this turbines. A pelton
wheel consists of following main parts.

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1. Penstock
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2. Spear and nozzle

3. Runner with buckets

4. Brake nozzle

5. Outer casing

6. Governing mechanism

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5.5.1 VELOCITY TRIANGLES, WORKDONE, EFFICIENCY OF PELTON

WHEEL INLET AND OUTLET VECTOR DIAGRAMS

Let V = Velocity of the jet

u = Velocity of the vane (cups) at the impact point u
= DN/ 60

where D = Diameter of the wheel corresponding to the impact point

= Pitch circle diameter.
At inlet the shape of the vane is such that the direction of motion of the jet and the
vane is the same.
i.e., Ȑ = 0, ș = 0

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Relative velocity at inlet Vr = V —u

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Hydraulic efficiency
This is the ratio of the work done per second per
head at inlet to the turbine.

Energy head at inlet = V2/2g

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Condition for maximum hydraulic efficiency
For a given jet velocity for efficiency to be maximum, word done should be
maximum
Work done per second per N of water
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Hence for the condition of maximum hydraulic efficiency, the peripheral speed of
the turbine should reach one half the jet speed.

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5.6 SPECIFIC SPEED

[ The speed of any water turbine is represented by N rpm. A turbine has speed,
known as specific speed and is represented by N
‘ Specific speed of a water turbine in the speed at which a geometrically similar
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turbine would run if producing unit power (1 kW) and working under a net head of
1 m. Such a turbine would be an imaginary one and is called specific turbine.
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5.7 FRANCIS TURBINE

Francis turbine is an inward flow reaction turbine. It is developed by the American engineer
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James B. Francis. In the earlier stages, Francis turbine had a purely radial floe runner. But the
modern Francis turbine is a mixed flow reaction turbine in which the water enters the runner
radially at its outer periphery and leaves axially at its centre. This arrangement provides larger
discharge area with prescribed diameter of the runner. The main parts such as

1. Penstock

2. Scroll or Spiral Casing

3. Speed ring or Stay ring

4. Guide vanes or Wickets gates

5. Runner and runner blades

6. Draft tube
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5.8 KAPLAN TURBINE

A Kaplan turbine is an axial flow reaction turbine which was developed by Austrian
engineer V. Kaplan. It is suitable for relatively low heads. Hence, it requires a large quantity of
water to develop large power. The main parts of Kaplan turbine, they are

1. Scroll casing

2. Stay ring

3. Guide vanes

4. Runner

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5. Draft tube

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5.9 PERFORMANCE OF TURBINES

Turbines are often required to work under varying conditions of head, speed, output and gate
opening. In order to predict their behavior, it is essential to study the performance of the turbines
under the varying conditions. The concept of unit quantities and specific quantities are required to

 The behavior of a turbine is predicted working under different conditions.

 Comparison is made between the performance of turbine of same type but of different
sizes.
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 The performance of turbine is compared with different types.

5.10 DRAFT TUBE

The pressure at the exit of the runner of a reaction turbine is generally less than atmospheric
pressure. Thus the water at the exit of the runner cannot be directly discharged to the tail race. A
pipe o gradually increasing area is used for discharging water form the exit of the turbine to the tail
race. This pipe of gradually increasing area is called a draft tube.

5.11 SPECIFIC SPEED

Homologus units are required in governing dimensionless groups to use scaled models in
designing turbomachines, based geometric similitude.

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Specific speed is the speed of a geometrically similar turbine, which will develop unit
power when working under a unit head. The specific speed is used in comparing the different types

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of turbines as every type of turbine has different specific speed. In S.I. units, unit power is taken as
one Kw and unit as one meter.

5.12 GOVERNING OF TURBINES

All the modern hydraulic turbines are directly coupled to the electric generators. The
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generators are always required to run at constant speed irrespective of the variations in the load. It
is usually done by regulating the quantity of water flowing through the runner in accordance with
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the variations in the load. Such an operation of regulation of speed of turbine runner is known as
governing of turbine and is usually done automatically by means of a governor.

Applications

1. To produce the power by water.

GLOSSARY
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HP –Horse power
KW- Kilo watts

REVIEW QUESTIONS

1.Define hydraulic machines.

2. Give example for a low head, medium head and high head turbine.
3. What is impulse turbine? Give example.
4. What is reaction turbine? Give example.
5. What is axial flow turbine?
6. What is the function of spear and nozzle?
9. Define gross head and net or effective head.
7.Define hydraulic efficiency.
8.Define unit speed of turbine.
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9.Define specific speed of turbine.
10.Give the range of specific speed values of Kaplan , Francis turbine
and pelton wheels
11.Define unit discharge.
12.Define unit power.
13.What is a draft tube? In which type of turbine it is mostly used?
14.Write the function of draft tube in turbine outlet.

PART B

1. Obtain en expression for the work done per second by water on the runner of a pelton wheel.
Hence derive an expression for maximum efficiency of the pelton wheel giving the relationship
between the jet speed and bucket speed.

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2. (a) A pelton wheel is having a mean bucket diameter of 1 m and is running at 1000 rpm. The
net head on the pelton wheel is 700 m. If the side clearance angle is 15º and discharge through

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nozzle is 0.1 m³/s, find (1) power available at nozzle and (2) hydraulic efficiency of the turbine.
Take Cv=1 (b) A turbine is to operate under a head of 25 m
at 200 rpm. The discharge is 9 m³/s. If the efficiency is 90% determine, Specific speed of the
machine, Power generated and type of turbine.

3. A pelton turbine is required to develop 9000 KW when working under a head of 300 m the
impeller may rotate at 500 rpm. Assuming a jet ratio of 10 And an overall efficiency of 85%
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calculate (1) Quantity of water required. (2) Diameter of the wheel (3) Number of jets (4)
Number and size of the bucket vanes on the runner.
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4. An Outward flow reaction turbine has internal and external diameters of the runner as 0.5 m and
1.0 m respectively. The turbine is running at 250 rpm and rate of flow of water through the
turbine is 8 m³/s. The width of the runner is constant at inlet and out let and is equal to 30 cm.
The head on the turbine is 10 m and discharge at outlet6 is radial, determine (1) Vane angle at
inlet and outlet. (2) Velocity of flow at inlet and outlet.
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5. The Nozzle of a pelton Wheel gives a jet of 9 cm diameter and velocity 75 m/s. Coefficient of
velocity is 0.978. The pitch circle diameter is 1.5 m and the deflection angle of the bucket is
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170º. The wheel velocity is 0.46 times the jet velocity. Estimate the speed of the pelton wheel
turbine in rpm, theoretical power developed and also the efficiency of the turbine.

6. (a)A turbine is to operate a head of a 25 m at 200 rpm; the available discharge is 9 m³/s
assuming an efficiency of 90%. Determine (1) Specific speed (2) Power generated (3)
Performance under a head of 20 m (4) The type of turbine. ) (b) A vertical reaction
turbine under 6m head at 400 rpm the area and diameter of runner at inlet are 0.7 m² and 1m
respective the absolute and relative velocities of fluid entering are 15ºand 60º to the tangential
direction. Calculate hydraulic efficiency.

7. A Francis turbine has an inlet diameter of 2.0 m and an outlet diameter of 1.2m. The width of
the blades is constant at 0.2 m. The runner rotates at a speed of 250 rpm with a discharge of 8
m³/s .The vanes are radial at the inlet and the discharge is radially outwards at the outlet.
Calculate the angle of guide vane at inlet and blade angle at the outlet.

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REFERENCE BOOKS

1.Modi P.N. and Seth, S.M. "Hydraulics and Fluid Mechanics

2.Bansal, R.K., Fluid Mechanics and Hydraulics Machines,

3. G.K.Vijayaraghavan Fluid Mechanics and Machinery

Key contributors to Fluid Mechanics

Archimedes 287 - 212 BC Greek philosopher

Pascal 1623 - 1662 French philosopher
Newton, Issac 1642 - 1727 Bristish mathematician

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Bernoulli, Daniel 1700 - 1782 Swiss mathematician
Euler, Leonhard 1707 - 1783 Swiss mathematician

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Hagen, Gotthilf 1797 - 1884 German engineer
Poiseuille, Jean Louis 1799 - 1869 French physiologist
Darcy, Henry 1803 - 1858 French engineer
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Froude, William 1810 - 1879 British naval architect
Stokes, George 1819 - 1903 Bristish mathematician
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Reynolds, Osborne 1842 - 1912 British academic

Buckingham, Edgar 1867 - 1940 American physicist
Prandtl, Ludwig 1875 - 1953 German engineer
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Moody, Lewis 1880 - 1953 American engineer

von Karman, Theodore 1881 - 1963 Hungarian engineer
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Blasius, Heinrich 1883 - 1970 German academic

Nikuradse, Johann 1894 - 1979 German engineer
White, Cedric 1898 - British engineer
Colebrook, Cyril 1910 - British engineer
Source: Fluid Principles, Alan Vardy, McGraw Hill

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QUESTION BANK

UNIT- I
FLUID PROPERTIES AND FLOW CHARACTERISTICS
PART – A
1. Define fluids.
Fluid may be defined as a substance which is capable of flowing. It has no definite shape
of its own, but confirms to the shape of the containing vessel.

2. What are the properties of ideal fluid?

Ideal fluids have following properties
i)It is incompressible
ii) It has zero viscosity
iii) Shear force is zero

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3. What are the properties of real fluid?
Real fluids have following properties

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i)It is compressible
ii) They are viscous in nature
iii) Shear force exists always in such fluids.

4. Explain the Density

Density or mass density is defined as the ratio of the mass of the fluid to its volume.
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Thus mass per unit volume of a fluid is called density. It is denoted by the
symbol (ρ).
Density = Mass of the fluid (kg)
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Volume of the fluid (m3)

5. Explain the Specific weight or weight density

Specific weight or weight density of a fluid is the ratio between the weight of a fluid
to its volume. Thus weight per uint volume of a fluid is called weight density and is
denoted by the symbol (W).
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(W) = Weight of the fluid = Mass x Acceleration due to gravity

Volume of fluid Volume of fluid
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W = pg

6. Explain the Specific volume

Specific volume of a fluid is defined as the volume of the fluid occupied by a unit
Mass or volume per unit mass of a fluid is called specific volume.
Specific volume = Volume = m3 = 1
Mass kg p

7. Explain the Specific gravity

Specific gravity is defined as the ratio of weight density of a fluid to the weight
density of a standard fluid. For liquid, standard fluid is water and for gases, it is
air.
Specific gravity = Weight density of any liquid or gas
Weight density of standard liquid or gas

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8.Define Viscosity.
It is defined as the property of a liquid due to which it offers resistance to the movement of
one layer of liquid over another adjacent layer.

9. Define kinematic viscosity.

It is defined as the ratio of dynamic viscosity to mass density. (m²/sec)

10. Define Relative or Specific viscosity.

It is the ratio of dynamic viscosity of fluid to dynamic viscosity of water at
20°C.
11. State Newton's law of viscosity and give examples.
Newton's law states that the shear stress ( ) on a fluid element layer is directly
proportional to the rate of shear strain. The constant of proportionality is called co-
efficient of viscosity.

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r = μ du
dy

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12. Give the importance of viscosity on fluid motion and its effect on temperature.
Viscosity is the property of a fluid which offers resistance to the movement of one
layer of fluid over another adjacent layer of the fluid. The viscosity is an important
property which offers the fluid motion.
The viscosity of liquid decreases with increase in temperature and for gas it
Increases with increase in temperature.
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13. Explain the Newtonian fluid
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The fluid which obeys the Newton's law of viscosity i.e., the shear stress is directly
proportional to the rate of shear strain, is called Newtonian fluid.
r=μ du
dy

14. Explain the Non-Newtonian fluid

The fluids which does not obey the Newton's law of viscosity i.e., the shear stress is
not directly proportional to the ratio of shear strain, is called non-Newtonian fluid.
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15. Define compressibility.

Compressibility is the reciprocal of bulk modulus of elasticity, k which is defined as
the ratio of compressive stress to volume strain.
k = Increase of pressure
Volume strain
Compressibility 1 = Volume of strain
k Increase of pressure

16. Define surface tension.

Surface tension is defined as the tensile force acting on the surface of a liquid in
Contact with a gas or on the surface between two immiscible liquids such that
contact surface behaves like a membrane under tension.

17. Define Capillarity.

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Capillary is a phenomenon of rise or fall of liquid surface relative to the
adjacent general level of liquid.

18. What is cohesion and adhesion in fluids?

Cohesion is due to the force of attraction between the molecules of the same liquid.
Adhesion is due to the force of attraction between the molecules of two different
Liquids or between the molecules of the liquid and molecules of the solid boundary
surface.

19. State momentum of momentum equation?

It states that the resulting torque acting on a rotating fluid is equal to the rate
of change of moment of momentum.

20. What is momentum equation

It is based on the law of conservation of momentum or on the momentum principle

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It states that,the net force acting on a fluid mass is equal to the change in
momentum of flow per unit time in that direction.

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21. What is Euler's equation of motion
This is the equation of motion in which forces due to gravity and pressure are taken into
consideration. This is derived by considering the motion of a fluid element along a stream
line.

22. What is venturi meter?

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Venturi meter is a device for measuring the rate of fluid flow of a flowing fluid through a
pipe. It consisits of three parts.
a. A short converging part b. Throat c.Diverging part.
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It is based on the principle of Bernoalli's equation.

23. What is an orifice meter?

Orifice meter is the device used for measuring the rate of flow of a fluid through a pipe. it
is a cheaper device as compared to venturi meter. it also works on the priniciple as that of venturi
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meter. It consists of a flat circular plate which has a circular sharp edged hole called orifice.

24. What is a pitot tube?

Pitot tube is a device for measuring the velocity of a flow at any point in a pipe or a channel.
It is based on the principle that if the velocity of flow at a point becomes zero, the pressure there is
increased due to the conversion of kinetic energy into pressure energy.
. What are the types of fluid flow?
Steady & unsteady fluid flow
Uniform & Non-uniform flow
One dimensional, two-dimensional & three-dimensional flows
Rotational & Irrotational flow

25. State the application of Bernouillie’s equation ?

It has the application on the following measuring devices.
1.Orifice meter.
2.Venturimeter.
3.Pitot tube.

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11. Define displacement thickness

Displacement thickness (S*) is defined as the distances, measured perpendicular to the
boundary of the solid body, by which the boundary should be displaced to compensate for the
reduction inflow rate on account of boundary layer formation.

12. What is momentum thickness?

Momentum thickness (0) is defined as the distance, measured perpendicular to the boundary
of the solid body, by which the boundary should be displaced to compensate for the reduction in
momentum of flowing fluid on account of boundary layer formation.

13.Mention the general characteristics of laminar flow.

• There is a shear stress between fluid layers
• ‘No slip’ at the boundary

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• The flow is rotational
• There is a continuous dissipation of energy due to viscous shear

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14. What is Hagen poiseuille’s formula ?
P1-P2 / pg = h f = 32 µUL / _gD2
The expression is known as Hagen poiseuille formula .
Where P1-P2 / _g = Loss of pressure head U = Average velocity
µ = Coefficient of viscosity D = Diameter of pipe
L = Length of pipe
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15.What are the factors influencing the frictional loss in pipe flow ?
Frictional resistance for the turbulent flow is
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i. Proportional to vn where v varies from 1.5 to 2.0 . ii.

Proportional to the density of fluid .
iii. Proportional to the area of surface in contact . iv.
Independent of pressure .
v. Depend on the nature of the surface in contact .
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16. What is the expression for head loss due to friction in Darcy formula ?
hf = 4fLV2 / 2gD
Where f = Coefficient of friction in pipe L = Length of the pipe
D = Diameter of pipe V = velocity of the fluid

17. What do you understand by the terms

a) major energy losses , b) minor energy losses
Major energy losses : -
This loss due to friction and it is calculated by Darcy weis bach formula and
chezy’s formula .
Minor energy losses :- This is
due to
i. Sudden expansion in pipe .ii. Sudden contraction in pipe .
iii. Bend in pipe .iv. Due to obstruction in pipe .

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18. Give an expression for loss of head due to sudden enlargement of the pipe :

he = (V1-V2)2 /2g
Wherehe = Loss of head due to sudden enlargement of pipe .
V1 = Velocity of flow at section 1-1
V2 = Velocity of flow at section 2-2

19.Give an expression for loss of head due to sudden contraction :

hc =0.5 V2/2g
Where hc = Loss of head due to sudden contraction .
V = Velocity at outlet of pipe.

20. Give an expression for loss of head at the entrance of the pipe
hi =0.5V2/2g
where hi = Loss of head at entrance of pipe .

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V = Velocity of liquid at inlet and outlet of the pipe .

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There are two methods of dimensional analysis. They are,
a. Rayleigh - Retz method
b. Buckingham's theotem method.
Nowadays Buckingham's theorem method is only used.

2. Describe the Rayleigh's method for dimensional analysis.

Rayleigh's method is used for determining the expression for a variable which depends upon
maximum three or four variables only. If the number of independent variables becomes more than
four, then it is very difficult to find the expression for dependent variable.

3. What do you mean by dimensionless number

Dimensionless numbers are those numbers which are obtained by dividing the inertia force
by viscous force or gravity force or pressure force or surface tension or elastic force. As this is a
ratio of one force to other force, it will be a dimensionless number.

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4. Name the different forces present in fluid flow
Inertia force

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Viscous force
Surface tension force
Gravity force
5. State Buckingham’s Π theorem
It states that if there are ‘n’ variables in a dimensionally homogeneous equation and if
these variables contain ‘m’ fundamental dimensions (M,L,T), then they are grouped into
(n-m), dimensionless independent Π-terms.
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6. State the limitations of dimensional analysis.
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1. Dimensional analysis does not give any due regarding the selection of variables.
2.The complete information is not provided by dimensional analysis.
3.The values of coefficient and the nature of function can be obtained only by
experiments or from mathematical analysis.

7. Define Similitude
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Similitude is defined as the complete similarity between the model and

prototype.
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8. State Froude’s model law

Only Gravitational force is more predominant force. The law states ‘The Froude’s
number is same for both model and prototype’

9.What are the similarities between model and prototype?

(i) Geometric Similarity
(ii) Kinematicc Similarity
(iii) Dynamic Similarity

10.Define Weber number.

It is the ratio of the square root of the inertia force to the surface tension force.

PART-B
100 V.P.KRISHNAMURTHY – AP/MECH 2015 - 16

UNIT-IV
PUMPS
PART – A (2 Marks)
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1. What is meant by Pump?

A pump is device which converts mechanical energy into hydraulic energy.

2. Define a centrifugal pump

If the mechanical energy is converted into pressure energy by means of centrifugal force
cutting on the fluid, the hydraulic machine is called centrifugal pump.

3. Define suction head (hs).

Suction head is the vertical height of the centre lines of the centrifugal pump above the
water surface in the tank or pump from which water is to be lifted. This height is also called
suction lift and is denoted by hs.

4. Define delivery head (hd).

The vertical distance between the center line of the pump and the water surface in the tank
to which water is delivered is known as delivery head. This is denoted by hd.

5. Define static head (Hs).

The sum of suction head and delivery head is known as static head. This is represented by
'Hs' and is written as,
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Hs = hs+ hd

6. Mention main components of Centrifugal pump.

i) Impeller ii) Casing
iii) Suction pipe,strainer & Foot valve iv) Delivery pipe & Delivery valve

7. What is meant by Priming?

The delivery valve is closed and the suction pipe, casing and portion of the delivery
pipe upto delivery valve are completely filled with the liquid so that no air pocket is
left. This is called as priming.

8. Define Manometric head.

It is the head against which a centrifugal pump work.

9. Describe multistage pump with

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a. impellers in parallel b. impellers in series. In multi stage centrifugal pump,
a. when the impellers are connected in series ( or on the same shaft) high head can be
developed.

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b. When the impellers are in parallel (or pumps) large quantity of liquid can be discharged.

10.. Define specific speed of a centrifugal pump (Ns).

The specific speed of a centrifugal pump is defined as the speed of a geometrically circular
pump which would deliver one cubic meter of liquid per second against a head of one meter. It is
denoted by 'Ns'.
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11. What do you understand by characteristic curves of the pump?
Characteristic curves of centrifugal pumps are defined those curves which are plotted from
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the results of a number of tests on the centrifugal pump.

12. Why are centrifugal pumps used sometimes in series and sometimes in parallel?
The centrifugal pumps used sometimes in series because for high heads and in
parallel for high discharge
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13.Define Mechanical efficiency.

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t is defined as the ratio of the power actually delivered by the impeller to the power
supplied to the shaft.

14. Define overall efficiency.

It is the ratio of power output of the pump to the power input to the pump.

15. Define speed ratio, flow ratio.

Speed ratio: It is the ratio of peripheral speed at outlet to the theoretical velocity of jet
corresponding to manometric head.
Flow ratio: It is the ratio of the velocity of flow at exit to the theoretical
velocity of jet corresponding to manometric head.

16.. Mention main components of Reciprocating pump.

# Piton or Plunger
# Suction and delivery pipe
# Crank and Connecting rod
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17.. Define Slip of reciprocating pump. When the negative slip does occur?
The difference between the theoretical discharge and actual discharge is called slip of
the pump.
But in sometimes actual discharge may be higher then theoretical discharge, in such a
case coefficient of discharge is greater then unity and the slip will be negative called
as negative slip.

18. What is indicator diagram?

Indicator diagram is nothing but a graph plotted between the pressure head in the
cylinder and the distance traveled by the piston from inner dead center for one
complete revolution of the crank
19. What is meant by Cavitations?
It is defined phenomenon of formation of vapor bubbles of a flowing liquid in a region
where the pressure of the liquid falls below its vapor pressure and the sudden

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UNIT-V
TURBINES
PART – A

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1. Define hydraulic machines.

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Hydraulic machines which convert the energy of flowing water into mechanical energy.

2. Give example for a low head, medium head and high head turbine.
Low head turbine – Kaplan turbine
Medium head turbine – Modern Francis turbine
High head turbine – Pelton wheel
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3. What is impulse turbine? Give example.
In impulse turbine all the energy converted into kinetic energy. From these the turbine
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will develop high kinetic energy power. This turbine is called impulse turbine. Example:
Pelton turbine

4. What is reaction turbine? Give example.

In a reaction turbine, the runner utilizes both potential and kinetic energies. Here
portion of potential energy is converted into kinetic energy before entering into the turbine.
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Example: Francis and Kaplan turbine.

5. What is axial flow turbine?

In axial flow turbine water flows parallel to the axis of the turbine shaft. Example:
Kaplan turbine

6. What is mixed flow turbine?

In mixed flow water enters the blades radially and comes out axially, parallel to the turbine
shaft. Example: Modern Francis turbine.

7. What is the function of spear and nozzle?

The nozzle is used to convert whole hydraulic energy into kinetic energy. Thus the nozzle
delivers high speed jet. To regulate the water flow through the nozzle and to obtain a good jet
of water spear or nozzle is arranged.

8. Define gross head and net or effective head.

Gross Head: The gross head is the difference between the water level at the reservoir
and the level at the tailstock.
Effective Head: The head available at the inlet of the turbine.
129 V.P.KRISHNAMURTHY – AP/MECH 2015 - 16

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9. Define hydraulic efficiency.
It is defined as the ratio of power developed by the runner to the power supplied by the water
jet.

10. Define mechanical efficiency.

It is defined as the ratio of power available at the turbine shaft to the power developed
by the turbine runner.

11. Define volumetric efficiency.

It is defied as the volume of water actually striking the buckets to the total water supplied
by the jet.

12. Define over all efficiency.

It is defined as the ratio of power available at the turbine shaft to the power available
from the water jet.

P
13. Define the terms
(a) Hydraulic machines (b) Turbines (c) Pumps.

AP
a. Hydraulic machines:
Hydraulic machines are defined as those machines which convert either hydraulic energy
into mechanical energy or mechanical energy into hydraulic energy.
b. Turbines;
The hydraulic machines which convert hydraulic energy into mechanical energy are called
turbines.
R
c. Pumps:
The hydraulic Machines which convert mechanical energy into hydraulic energy are called
pumps.
CO

14. What do you mean by gross head?

The difference between the head race level and tail race level when no water is flowing is
known as gross head. It is denoted by Hg.
U

15. What do you mean by net head?

Net head is also known as effective head and is defined as the head available at the inlet of
te turbine. It is denoted as H
ST

16. What is draft tube? why it is used in reaction turbine?

The pressure at exit of runner of a reaction turbine is generally less than the atmospheric
pressure. The water at exit cannot be directly discharged to tail race. A tube or pipe of gradually
increasing area is used for discharging water from exit of turbine to tail race. This tube of
increasing area is called draft tube.

17. What is the significance of specific speed?

Specific speed plays an important role for selecting the type of turbine. Also the
performance of turbine can be predicted by knowing the specific speed of turbine.

18.. What are unit quantities?

Unit quantities are the quantities which are obtained when the head on the turbine is unity.
They are unit speed, unit power unit discharge.

19. Why unit quantities are important

130 V.P.KRISHNAMURTHY – AP/MECH 2015 - 16

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If a turbine is working under different heads, the behavior of turbine can be easily known
from the values of unit quantities.

20. What do you understand by characteristic curves of turbine?

Characteristic curves of a hydraulic turbine are the curves, with the help of which the exact
behavior and performance of turbine under different working conditions can be known.

21. Define the term 'governing of turbine'.

Governing of turbine is defined as the operation by which the speed of the turbine is kept
constant under all conditions of working. It is done by oil pressure governor.

22. What are the types of draft tubes?

The following are the important types of draft tubes which are commonly used.
a. Conical draft tubes

P
b. Simple elbow tubes
c. Moody spreading tubes and
d. Elbow draft tubes with circular inlet and rectangular outlet.

AP
R
CO
U
ST

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