Mrs. Bhujadi P. N.

Assistant Professor,
MES’s College of Pharmacy,Sonai
Tal- Newasa, Dist- Ahmednagar 414105
Syllabus
 Contens
• Fluid properties
• Reynolds experiment
• Manometer
• Orificemeter
• Venturimeter
• Pitot tube
• Rotameter
• Current flow meter
 Fluid Flow
• Mention fluid properties such as viscosity,
compressibility and surface tension offluids.
• Hydrostatics (Fluidstatics) influencing
fluid flow.
• Fluid dynamics‐ Bernoulli’s theorem,
flowof fluids in pipes, laminar and
turbulentflow.
THE PROPERTIES OF
FLUIDS
• VISCOSITY
• SURFACE TENSION
• COMPRESSIBILITY
 VISCOSITY
• Viscosity is a measure of a fluid's resistance to flow.

• It describes the internal friction of a moving fluid.

• A fluid with large viscosity resists motion because its

molecular makeup gives it a lot of internal friction.

• A fluid with low viscosity flows easily because its

molecular makeup results in very little frictionwhen
it is in motion.
 SURFACE
TENSION
"Surface tension is a contractive tendency
of the surface of a fluid that allows it to
resist an externalforce."
 FLUID
FLOW
• A fluid is a substance that continually deforms (flows)
under an applied shear stress.

• Fluids are a subset of the phases of matter and include

liquids, gases.

• Fluid flow may be defined as the flow of substances

that do not permanently resistdistortion.

• The subject of fluid flow can be divided intofluid

static's and fluid dynamics.
 FLUID
• Fluid static's deals with the fluids at rest in equilibrium.
•
STATICS
Behaviour of liquid atrest.
• Nature of pressure it exerts and the variation of pressure at
different layers.
• Pressure differences between layers ofliquids.
• Consider a column of liquid with two openings Which are
provided at the wall of the vessel at different height

• The rate of flow through these openings are different due to

the pressure exerted at the different heights are
different

• Consider a stationary column the pressure P is acting on

the surface of the fluid, column is maintained at constant
pressure by applying pressure

• The force acting below and above the point 1 are evaluated

• Substituting the force with pressure x area of cross

section in the above equation
Pressure at point 2 xArea= (Pressure on the surface area x surface area)

Pressure at point 1 xArea (Pressure on the surface area x surface area)

P1S = P2S + height x volume x density x g

P1S = P2S + volume x density x g
= P2S + height x area x density x g

P1S = P2S + h1 S ρ g

Since surface area issame

P1 = P + h1 ρ g

Pressure acting on point 2 may be written as

P2 = P + h2 ρ g

Difference in the pressure is--

P2 - P1 = g (Ps + h2 ρ ) – ( Ps + h1 ρ) g

ΔP = (Ps + h2 ρ – Ps - h1 ρ ) g

ΔP = Δ h ρ g [F=Volume.ρ g]
 FLUID DYNAMICS

• Fluid dynamics deals with the study of fluids in motion

• This knowledge is important for liquids, gels, ointments which will

change their flow behaviour when exposed to different stress
conditions
 Importanc
e
Identification of type of flow is important in
• Manufacture of dosage forms
• Handling of drugs foradministration

The flow of fluid through a pipe can be viscous or turbulent

and it can be determined by Reynolds number Reynolds
number have no unit
 Reynolds
• Glass tube Experiment
is connected to
reservoir of water, rate offlow
of water is adjusted by a valve.

• A reservoir of colored solution

is connected to one end of the
glass tube with help of nozzle.

• Colored solution is introduced

into the nozzle as fine stream
through jettube.
 TYPES OF FLOW
• Laminar flow is one in which • When velocity of the water is
the fluid particles move in layers increased the thread of the colored
or laminar with onelayer sliding water disappears and mass of the
with other water gets uniformlycolored

• There is no exchange of fluid • There is complete mixing of the

particles from one layer toother solution and the flow of the fluid is
called as Turbulent flow
• Avg velocity = 0.5Vmax
• Avg velocity = 0.8Vmax
• Re < 2000
• Re >4000
The velocity at which the fluid changes from laminar flow to turbulent flow
that velocity is called as critical velocity
 REYNOLDS NUMBER
In Reynolds experiment the flow conditions are affected by
•Diameter of pipe
•Average velocity
•Density of liquid
•Viscosity of the fluid
This four factors are combined in one way as Reynolds number

 Inertial forces are due to mass and the velocity of the fluid
particles trying to diffuse the fluid particles

 viscous force if the frictional force due to the viscosity of the

fluid which make the motion of the fluid in parallel.
• At low velocities the inertial forces are less when
compared to the frictionalforces

• Resulting flow will be viscous innature

• Other hand when inertial forces arepredominant

the fluid layers break up due to the increase in
velocity hence turbulent flow takesplace.

 If Re < 2000 the flow is said to be laminar

 If Re > 4000 the flow is said to be turbulent

 If Re lies between 2000 to 4000 the flow

change between laminar toturbulent
 APPLICATIONS
• Reynolds number is used to
predict the nature of theflow
• Stocks law equation ismodified
to include Reynolds number to
study the rate ofsedimentation
in suspension
When velocity isplotted against the
distance from the wall following
conclusions can be drawn
• The flow of fluid in the middle of
the pipe is faster then the fluid
near to thewall
• At the actual surface of the pipe –
wall the velocity of the fluid is
zero
 BERNOULLI'S THEOREM
• When the principles of the law of energy is applied to the
flow of the fluids the resulting equation is a Bernoulli's
theorem

• Consider a pump working under isothermal conditions

between points A andB

• Bernoulli's theorem statement, "In a steady state the total

energy per unit mass consists of pressure, kinetic
and potential energies are constant.
B
Pum
p
Kinetic energy = u2 /2g
Pressure energy = Pa /ρAg

Friction energy
=F
A
• At point A one kilogram of liquid is assumed to be entering at point A,

Pressure energy = Pa /gρA

Where Pa = Pressure at point a

g = Acceleration dueto gravity
ρ A = Density of theliquid

• Potential energy of a body is defined as the energy possessed by the body by the
virtue of its position

Potential energy = XA

• Kinetic energy of a body is defined as the energy possessed by the body by virtue
of its motion,

kinetic energy = UA2 /2g

Total energy at point A = Pressure energy + Potential

energy + K. E Total energy at point A = PaV

+ XA + UA2 / 2g
• According to the Bernoulli's theorem the total energy at point A is
constant

Total energy at point A = PAV +XA + (UA2 /2g) =Constant

• After the system reaches the steady state, whenever one kilogram
of liquid enters at point A, another one kilogram of liquid leaves at
point B

Total energy at point B = PBV +XB + U 2 /2g

B

PAV +XA + (UA2 /2g) + Energy added by thepump

= PBV +XB + (UB2 /2g)

• V is specific volume and it is reciprocal of density.

Theoretically all kinds of the energies involved in fluid flow should be

accounted, pump has added certain amount of energy.
• During the transport, some energy is converted to
heat due to frictionalForces
Energy loss due to friction in the
line = F Energy added by pump =
W

PA /ρ A + XA + UA2 / 2g – F + W = PB /ρ B +XB
+UB2 / 2g

This equation is called as Bernoulli's

 ENERGY LOSS
• According to the law of conversation of energy,
energy balance have to be properly calculated
• Fluids experiences energy losses in several ways
while flowing through pipes, theyare
Frictional losses
Losses in thefitting
Enlargement losses
Contraction losses
 Application of
BERNOULLI'S
THEOREM
• Used in the measurement of rate of fluid flow
using flowmeters

• It applied in the working of the centrifugal

pump, in this kinetic energy is converted in to
pressure.
 Fluid Flow and Pressure
measurements
• Pressure measurement‐
– Classification of manometers,
– simple manometer/
– Utube manometer and modifications (Differential/inclined),
– Bourdon gauge
• Measurement of flow‐
– Classification of flowmeters,
– venturimeter,
– orificemeter,
– pitot tube,
– rotameter
– current flow meters
 MANOMETERS
• Manometers are the devices usedfor
measuring the pressure difference

• Different type of manometersare there they

are
1)Simple manometer
2)Differential manometer
3)Inclined manometer
 SIMPLE MANOMETER
• This manometer is the
most commonly used
one

• It consists of a glass U
shaped tube filled with a
liquid A- of density ρA kg
/meter cube and above Athe
arms are filled with liquid B of
densityρB

• The liquid A and B are immiscible

and the interference can be seen
clearly

• If two different pressures are

applied on the two arms the
• Let pressure at point1
will be P1 Pascal's and
point 5 will be P2
Pascal's

• The pressure at point2

can be written as

=P1+ (m + R )ρB g

since ΔP = Δ h ρ g (m + R ) = distance
from 3 to5
• Since the points 2 and 3 are at same
height the pressure

Pressure at 3 =P1+ (m + R )ρB g

• Pressure at 4 is less than pressure at

point 3 by R ρAg

• Pressure at 5 is still lessthan

pressure at point 4 bymρB g

• This can be summarise as

P1 + (m + R) ρ B g - RρA g - mρ B g=

P2 ΔP= P1-P2=R (ρ A- ρ B )g
 Application
• Pressure difference can be determinedby
measuring R

• Manometers are use in measuring flow of

fluid.
 DIFFERENTIAL
MANOMETERS
• These manometers are suitable for measurement of small pressure
differences

• It is also known as two – Fluid U- tube manometer

• It contains two immiscible liquids A and B having nearly same

densities

• The U tube contains of enlarged chambers on both limbs,

• Using the principle of simple manometer the pressure differences

can be written as

ΔP=P1 –P2 =R (ρc – ρA) g

• ΔP=P1 –P2 =R (ρc – ρA) g

• Hence smaller the

difference between ρc
and ρA larger will be R
 INCLINED TUBE
•
MANOMETERS
Many applications require
accurate measurement of low
pressure such as drafts and
very low differentials, primarily
in air and gasinstallations.

• In these applications the

manometer is arrangedwith
the indicating tube inclined,

• This enables the measurement

of small pressure changes with
increased accuracy.

PA –PB = g R (ρA - ρB) sinα

 MEASUREMENT OF
RATE OF FLOW OF
FLUIDS
• Methods of measurementare
 Direct weighing or measuring
 Hydrodynamic methods
• Orifice meter
• Venturi meter
• Pitot meter
• Rotameter
 Direct displacement meter
• Disc meters
• Current meter
 DIRECT WEIGHING
OR MEASURING
• The liquid flowing through a pipe is collected
for specific period at any point and weighed or
measured, and the rate of flow can be
determined.

• Gases can not be determined by this method

 ORIFICE
METER
• Principle Variable head meter
 Orifice meter is a thin plate
containing a narrow andsharp
aperture.

 When a fluid stream is allowed

to pass through a narrow
constriction the velocity of
the fluid increase
compared to up stream

 This results in decrease in

pressure head and the
difference in the pressuremay
be read from amanometer
 Applicatio
ns
• Velocity at either of the point A and B can be
measured.

• Volume of liquid flowing per hour can be

determined by knowing area of cross section.
 VENTURI METER
Variable head meter
• Principle
– When fluid is allowed to
pass through narrow
venturi throat then
velocity of fluidincreases
and pressure decreases
– Difference in upstream
and downstream
pressure head can be
measured by using
Manometer

Uv = Cv √ 2g .ΔH
 Why Venturi meter if
Orifice meter is
• available?
Main disadvantage of orifice meter is power loss due to
sudden contraction with consequent eddies on other
side of orifice plate.

• We can minimize power loss by gradual contraction of pipe

• Ventury meter consist of two tapperd(conical section)

inserted in pipeline

• Friction losses and eddies can be minimized by this

arrangement.
 Pitot
Insertion
tube meter
• Principle
• According to Bernoulli's therom
Total energy at any point =Pressure energy + Potential energy + K. E
U0 = C 0 √ 2g ΔH ........ΔH= Difference in pressure head
ΔH = U2 /2g ........U= Velocity at point ofincertion
 ROTAMET
Variable
ER area meter
• Principl
e– In this device a stream of water
enters Transparent tapered tube
and strikes the movingplummet

– During fluid flow plummet riseor

fall

– As a result,annular space
(area) between plummet
and tapperd tube may
increase or decrease,
depending on variation of flow
rate.

– Head across annulus is equalto

weight of plummet.
• Use
– To measure flow rate of gasas
well as liquid

– Easy to use andallow direct visual

inspection
 CURRENT FLOW
•
METER
Construction
• It has a propeller which is
rotated when water hits it and
is connected to magnetswhich
actuates recorders when the
propeller rotates.

• The velocity of waterincreases

the propeller rotation.

• The number of rotationsare

measured and correlated to
velocity of fluid using the
formula:
V = a + bN
-where N is the rotation of the propeller (revs per sec)
-a and b are coefficients determined by calibration in an experimental