•16/03/2024

• Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology

Objectives
Students will be able to:
FLUID MECHANICS  Classify flow conditions (Inviscid vs. Viscous,
Incompressible vs. Compressible and Steady vs.
CLB 11003 Unsteady).
Fluid Flow in Pipes and Conduits  Identify the characteristics of laminar flow and turbulent
flow.
 Solve problems of conservation of mass using continuity
Ahmad Azahari Hamzah equation.
Section of Chemical Engineering Technology
 Derive and apply the Bernoulli’s equation in measuring flow.
UNIKL – MICET
 Understand the different flow rate measurement techniques.
 Identify major and minor losses.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Ideal vs Real fluid Viscous vs. Inviscid Regions of Flow

 Ideal / perfect fluid – the concept of a
 Flows in which frictional
frictious fluid that can flow in the absence of effects are significant.
all frictional effects. They are usually close
to solid surfaces.

 For real fluid, all the frictional effects will be

considered.  Regions where viscous
(frictional) forces are
small compared to
inertial or pressure
forces.
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Compressible vs. Incompressible Flow Compressible vs. Incompressible Flow

 Depend on the level of variation of density
during flow.
 A flow is incompressible if the density remains
nearly constant.
– Ma < 0.3 : Incompressible
 Liquid flows are typically incompressible.
– Ma < 1 : Subsonic
 Gas flows are often compressible, especially – Ma = 1 : Sonic
for high speeds. – Ma > 1 : Supersonic
 Mach number, Ma is a good indicator of – Ma >> 1 : Hypersonic
whether or not compressibility effects are
important.
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology

Steady vs. Unsteady Flow

 Steady implies no change at a point with time.
 During steady flow, fluid properties can
change from point to point within a device, but
at any fixed point they remain constant
 Uniform implies no change with location over a
specified region.
 Unsteady is the opposite of steady.
 Unsteady flows may appear steady if “time-
averaged”
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Laminar vs. Turbulent Flow Reynolds's experiment

 Laminar: highly ordered
fluid motion with smooth
streamlines.

 Transitional: a flow that

contains both laminar
and turbulent regions

 Turbulent: highly
disordered fluid motion
characterized by velocity
fluctuations and eddies.
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Laminar vs. Turbulent Flow Laminar vs. Turbulent Flow

 Laminar flow: A thin filament of dye injected into
a laminar flow appears as a single line. There is
no dispersion of dye throughout the flow,
except the slow dispersion due to molecular
motion.
 Turbulent flow: If a dye filament injected into a
turbulent flow, it disperses quickly throughout
the flow field; the line of dye breaks up into
myriad entangled threads of dye.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Laminar Flow Turbulent Flow

Flow in sink

Flow in sink

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Turbulent Flow Turbulent Flow

Wake around submarine

Volcano eruption Water stream

Tornado
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Reynolds number Reynolds number

 To determine whether flow is laminar or turbulent.
Re < 2300  laminar
2300 ≤ Re ≤ 4000  transitional
Where:
Re > 4000  turbulent
 Re depends upon  = density, kgm-3
– Pipe roughness u = average velocity , ms-1
– Vibrations
– Upstream fluctuations, disturbances (valves, d = diameter of the pipe, m
elbows, etc. that may disturb the flow)
 = fluid viscosity, kgm-1s-1
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Reynolds number Reynolds number

For non-round pipes, define A = 0.15 * 0.4 = 0.06 m2

the hydraulic diameter, Dh P = 0.15 + 0.15 + 0.4 = 0.7 m

Dh = 4A/P
* Don’t count free surface, since it does not contribute to
A = cross-section area friction along pipe walls!

P = wetted perimeter
 Dh = 4A / P = 4*0.06/0.7 = 0.34 m

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Check your understanding Check your understanding

Oil flow through a pipe 25 mm in diameter at a
velocity of 6 m/s. Determine whether the flow will
be laminar or turbulent assuming that the viscosity
of oil is 1.30 x 10-3 kgm-1s-1 and its S.G 0.9.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Check your understanding Conservation of Mass

Water is flowing in a pipe of 15 mm diameter. Mass, m is a conserved
property, and it cannot be
What is the maximum velocity it can have to created or destroyed during
ensure laminar flow if the value of absolute a process.
viscosity is 1.002 x 10-3 N.sm-2.
Principle: the net mass
transfer to or from a control
volume during a time interval
t is equal to the net change
(increase or decrease) in the
total mass within the control
volume during t.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology

Conservation of Mass

or

min – mout = Δmsystem

or in rate form

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Mass and Volume Flow Rates Mass and Volume Flow Rates
 The amount of mass flowing through a cross section  The volume of the fluid flowing through a cross
per unit time is called the mass flow rate (kg/s) and is section per unit time is called the volume flow rate
expressed as (m3/s) and is given by:

 The mass and volume flow rates are related by:

where
 = density, kg/m3
u = average velocity, m/s
Q = volume flow rate of the fluid, m3/s
where
A = cross-sectional area, m2
 = specific volume, m3/kg

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Continuity Equation Continuity Equation

 Conservation of mass principle for steady-
flow devices is expressed as Steady incompressible flow:

Steady flow:

Steady incompressible flow (single stream):

Steady flow (single stream):

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Continuity Equation Continuity Equation

 For pipes of constant
diameter and  For pipes with variable diameter,m is still the same
incompressible flow due to conservation of mass, but u1 ≠ u2
– uavg stays the same D1
down the pipe, even if
the velocity profile D2
uavg uavg changes u1

o Why? Conservation m u2 m
of Mass
2

1
same same
same
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Check your understanding Conservation of Energy

Water flowing at the rate of 10 gal/min in pipe
having an inside diameter of 0.0525 m.
Calculate the Reynolds Number if  = 8.007 x
10-4 Pa.s. Given  H2O = 996 kg/m3.

Energy cannot be created or destroyed;

it can only change forms.
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Conservation of Energy Conservation of Energy

Esys = Emec
Total energy Total energy Change in the =  changes in flow, kinetic and potential
entering the - leaving the = total energy of energies
system system the system
Emec

Flow Kinetic Potential

Energy Energy Energy

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Conservation of Energy Conservation of Energy

Mechanical energy can be defined as the form of
energy that can be converted to mechanical work
completely .

 Mechanical energy change of a fluid during

incompressible flow becomes
gz

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Conservation of Energy Conservation of Energy

Mechanisms of Energy Transfer

 Falling rock, picks up speed

as PE is converted to KE.
 If air resistance is neglected,
PE + KE = constant

Heat Transfer, Q
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Conservation of Energy Conservation of Energy

Mechanisms of Energy Transfer
Mechanisms of Energy Transfer
Wout
Eout=Qout+Wout
Qout

SYSTEM
ENERGY

Qin
W in
Ein=Qin+Win
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Conservation of Energy Bernoulli Equation

 Bernoulli equation is an approximate relation
Work in, W=2kJ between pressure, velocity, and elevation,
 Valid in regions of steady, incompressible flow
 Viscous effects are negligibly small compared to
Heat out, Q=5kJ inertial, gravitational, and pressure effects.

Heat in, Q=10kJ

ΔE= Qin + Win - Qout
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Derivation of Bernoulli Equation Derivation of Bernoulli Equation

 Consider the motion of a fluid particle in a The significant forces
flow field in steady flow. acting in the s-direction
are the pressure (acting
 Applying Newton’s second law in the s on both sides) and the
direction on a particle moving along a component of the
streamline gives weight of the particle in
the s-direction.

(4.1)
The forces acting on a fluid
particle along a streamline.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Derivation of Bernoulli Equation Derivation of Bernoulli Equation

 Therefore, equation 4.1 becomes,
 Canceling dA and simplified gives
(4.2)
(4.4)

 Substituting m = dAds, W = gdAds and

 Noting that udu = 1/2 d(u2) and dividing
sin  = dz/ds, equation 4.2 becomes by  gives,

(4.3) (4.5)

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Derivation of Bernoulli Equation Derivation of Bernoulli Equation

 Integrating,
Steady:  Bernoulli equation, Eq. 4.6 state that:
Sum of the kinetic (V2/2), potential (gz),
and flow energies (P/) of a fluid particle
Steady, incompressible flow: is constant along a streamline during
steady flow when the compressibility and
(4.6)
frictional effects are negligible.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Derivation of Bernoulli Equation Derivation of Bernoulli Equation

 It can also be expressed between any
two points on a streamline as Where
 P = Static pressure, actual pressure of the fluid.
 u2/2 = Dynamic pressure, pressure rise when
the fluid in motion is brought to a stop.
 Multiplying the Bernoulli equation by
 gz = Hydrostatic pressure, effects of fluid
density gives weight on pressure.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Derivation of Bernoulli Equation Derivation of Bernoulli Equation

 Sum of the static, dynamic, and hydrostatic  Stagnation pressure is expressed by
pressures is called the total pressure.
 Bernoulli equation states that the total pressure
along a streamline is constant.
 Sum of the static and dynamic pressures is called
the stagnation pressure, which represents the  Then the fluid velocity can be calculated
pressure at a point where the fluid is brought to a from
complete stop in a frictionless manner.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Derivation of Bernoulli Equation Derivation of Bernoulli Equation

 Bernoulli equation can also be represented in
terms of "heads" by dividing each term by g,

u  It can also be expressed between any two

points on a streamline as

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Derivation of Bernoulli Equation Derivation of Bernoulli Equation

Where
 Line that represents sum of the static
 P/g = pressure head, height of a fluid column pressure and the elevation heads, P/g +
that produces the static pressure P.
z, is called hydraulic grade line (HGL).
 u2/2g = velocity head, elevation needed for a fluid
to reach the velocity u during frictionless free fall.  The line that represents the total head of
 z = elevation head, potential energy of the fluid. fluid P/g + u2/2g + z, is called energy
Also, H is the total head for the flow. grade line (EGL).

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

HGL and EGL Bernoulli Equation

Where:
P = pressure, kPa
 = density, kg/m3
g = acceleration of gravity, m/s2
z = height, m
u = velocity, m/s
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Bernoulli Equation Flow Measurement – Pitot Tube

 Limitations on the use of the Bernoulli Equation  A device to measure the local
velocity along a streamline. 1 2
– Steady flow: d/dt = 0
– Frictionless flow
– No shaft work: Wpump=Wturbine=0
– Incompressible flow:  = constant u2 = 0 (stagnation point)
– No heat transfer: Qnet,in=0 z1=z2= 0
– Applied along a streamline

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Flow Measurement – Pitot Tube Flow Measurement – Pitot Tube

1 2

man = f

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology

Flow Measurement – Pitot Tube

1 2

man  f

h

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Check your understanding Flow Measurement – Orifice

 Flow through a small orifice
Carbon tetrachloride (S.G = 1.6) flows through a
pipe. The differential gauge attached to the pitot
tube shows a 76 mm deflection of mercury (S.G = 1
A actual
13.6). Find the velocity.
h

Vena contracta

Orifice

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Flow Measurement – Orifice Flow Measurement – Orifice

At the surface:
u1 = 0 (negligible); P1 = 0 (P atm)
At the orifice:
P2 = 0 (P atm)
Take z2 as the datum  z1= h, z2= 0 u theoretical
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Flow Measurement – Orifice Flow Measurement – Orifice

 Discharge through the orifice is given by:
u actual = Cv u theoretical Q = Au
Q actual= A actual u actual
where Cv = coefficient of velocity = Cc A orifice Cv u theoretical
(0.97 - 0.99) = Cc Cv A orifice u theoretical
= Cd A orifice u theoretical
A actual = Cc A orifice Q actual = Cd A orifice 2gh
where Cc = coefficient of contraction where
Cd = Cc Cv (coefficient of discharge)
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Check your understanding Flow Measurement – Venturi

The actual velocity in the contracted section of a  A device for measuring discharge in a pipe.
jet of liquid flowing from a 50 mm diameter orifice
is 8.53 ms-1 under a head of 4.57 m. If the  Consists of a rapidly converging section which
discharge is 0.0114 m3s-1,what is the value of the increases the velocity of flow and hence
coefficient of discharge (Cd)? reduces the pressure.
 Then returns to the original dimensions of the
pipe by a gently diverging 'diffuser' section.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Flow Measurement – Venturi Flow Measurement – Venturi

By using the continuity equation,

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Flow Measurement – Venturi Flow Measurement – Venturi

Rearranging the Bernoulli equation,

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Flow Measurement – Venturi Flow Measurement – Venturi

 Expressed in terms of the manometer
readings.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Flow Measurement – Venturi Check your understanding

A Venturi meter is being used to measure flow in a
 Discharge can be expressed in terms of the pipeline of diameter 250 mm which carries water.
manometer reading , giving: When the pressure difference between the throat and
the entrance of the Venturi meter is 300 mm on a
mercury manometer, determine the flow in the pipeline.
The Venturi meter has a throat diameter of 80 mm and
a coefficient of discharge of 0.97. The relative density
of mercury is 13.6.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Flow Measurement – Notch & Weir Flow Measurement – Notch & Weir
 A weir is a notch on a larger scale - usually
 A notch is an opening in the side of a tank
found in rivers.
or reservoir which extends above the
surface of the liquid.  Device to raise water levels.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Flow Measurement – Notch & Weir Flow Measurement – Notch & Weir

Assumption:
 Velocity approaching the weir is small,
 KE can be neglected.
 Velocity through strip depends only on the depth
below the free surface
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Flow Measurement – Notch & Weir Flow Measurement – Notch & Weir
Width = b B

Depth = h Rectangular weir

u = 2gh b = B = constant H

Q = Au = bh 2gh h=H

 Substitute into general weir equation
Integrate from free surface, h = 0 to weir crest, h = H

* will be different for different shape of weir or notch

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Flow Measurement – Notch & Weir Darcy Weisbach Equation

 Proposed by Julius Weisbach, a German
 Coefficient of discharge, Cd which accounts for professor who in 1850 published the first
losses at the edges of the weir and contractions modern textbook on hydrodynamics.
in the area of flow is introduced  An important and widely used equation in
hydraulics.
 It enables calculation of the head loss due to
friction within a given run of pipe.
 Valid for duct flows of any cross section and for
laminar and turbulent flow.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Darcy Weisbach Equation Darcy Weisbach Equation

Pressure drop Head loss
 The loss of pressure in a flow system measured
using a length parameter (i.e., inches, meter etc.).
 Pressure loss in terms of head loss, hL
Where:
f = friction factor
L = pipe length, m
d = pipe diameter, m
u = average flow velocity, m/s
g = acceleration of gravity, m/s2
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Roughness Roughness
 Relative pipe roughness is the ratio of the
pipe surface roughness () to its diameter
(D).
 Relative pipe roughness = /D

Types of Roughness
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Friction factor Friction factor

Friction Loss  Friction coefficient (f), depends on the
 flow (laminar/transient/turbulent)
 The loss of pressure or head due to the
resistance to flow in the pipe and  roughness of the tube or duct.
fittings.
 For fully developed laminar flow the roughness of
 influenced by pipe size and fluid the duct or pipe can be neglected.
velocity.
 usually expressed in feet of head.
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Friction factor Moody Diagram

 For hydraulically SMOOTH pipes (= 0) in
turbulent flow:

 For ROUGH pipe in turbulent flow, use the

Moody Diagram to obtain f.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Colebrook equation Check your understanding

 Colebrook equation is a curve-fit of the data Water at 40 F ( = 62.42 lbm/ft3 and  = 1.038 x
which is convenient for computations (e.g., 10-3 lbm/ft.s) is flowing through 0.12 in diameter 30
using EES) ft long horizontal pipe steadily at average velocity
of 3.0 ft/s. Determine (a) the head loss and (b) the
pressure drop.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Hagen-Poiseuille Law Hagen-Poiseuille Law

For laminar flow,

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Hagen-Poiseuille Law Check your understanding

 Discharge in the pipe for laminar flow: Oil at 22 C ( = 888 kg/m3 and  = 0.8 kg/m.s) is
flowing steadily through 5 cm diameter 40 m long
pipe. The pressure at the inlet and outlet are
measured to be 745 and 97 kPa, respectively.
Determine the flowrate of oil through the pipe if
the flow is laminar.

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
 •16/03/2024

• Universiti Kuala Lumpur • Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology • Malaysian Institute of Chemical and Bioengineering technology

Major Losses Minor Losses

 Piping systems include fittings, valves, bends,
 Head loss due to the friction of fluid flowing elbows, tees, inlets, exits, enlargements, and
through a length of pipe. contractions.
 These components interrupt the smooth flow of fluid
and cause additional losses because of flow
 For Laminar Flow separation and mixing
 Minor losses

u
 For Turbulent Flow
Where, KL = loss coefficient.
CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits

• Universiti Kuala Lumpur

• Malaysian Institute of Chemical and Bioengineering technology

Minor Losses
 Total head loss in a system is comprised of major
losses (in the pipe sections) and the minor losses (in
the components)

ui uj
hL,total

i pipe sections j components

u
hL,total

 If the piping system has constant diameter

CLB 11003 Chapter 4: Fluid Flow in Pipes and Conduits
•16/03/2024