CHEG232 – Fluid Mechanics Lab
Department of Chemical Engineering
A. Syed Ali
CHEG232: Fluid Mechanics Lab - Fall 2022
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CHEG232: Fluid Mechanics Lab - Fall 2022
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Contents
1.
2
3
Flowmeter Calibration ............................................................................................................. 6
1.1
Introduction and Theory .................................................................................................. 6
1.2
Objectives ......................................................................................................................... 6
1.3
Principles and theory ....................................................................................................... 7
1.4
Working Equations ........................................................................................................... 8
1.5
Data Analysis .................................................................................................................... 8
1.6
Apparatus specifications .................................................................................................. 9
1.7
Tabulation ........................................................................................................................ 9
Pump Characterization .......................................................................................................... 10
2.1
Introduction.................................................................................................................... 10
2.2
Objectives ....................................................................................................................... 11
2.3
Principle and working equations .................................................................................... 11
2.3.1
Centrifugal Pumps ................................................................................................... 12
2.3.2
Turbine Pumps ........................................................................................................ 13
2.3.3
Axial Flow Pump ...................................................................................................... 14
2.3.4
Gear Pumps ............................................................................................................. 16
2.3.5
Measurement of Power Input to the Pump ........................................................... 17
2.4
Procedure ....................................................................................................................... 18
2.5
Data analysis................................................................................................................... 18
2.6
Speed and flow corrections............................................................................................ 19
2.6.1
Pump speed ratios .................................................................................................. 19
2.6.2
Flow Measurement using Weir ............................................................................... 19
2.7
Apparatus specifications ................................................................................................ 20
2.8
Tabulation ...................................................................................................................... 21
Fluidization ............................................................................................................................ 23
3.1
Introduction.................................................................................................................... 23
3.2
Objectives ....................................................................................................................... 23
3.3
Principle and working equation ..................................................................................... 23
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3.3.1
Pressure losses in fluidized bed .............................................................................. 25
3.3.2
Loosening speed ..................................................................................................... 26
3.4
4
5
Procedure ....................................................................................................................... 27
3.4.1
Using air as working fluid ........................................................................................ 27
3.4.2
Using water as working fluid................................................................................... 27
3.5
Data analysis................................................................................................................... 28
3.6
Data Analysis .................................................................................................................. 29
3.7
Apparatus Specification ................................................................................................. 29
Fluid friction and drag coefficient for pipes and valves ........................................................ 30
4.1
Introduction.................................................................................................................... 30
4.2
Objective ........................................................................................................................ 31
4.3
Principle and working equation ..................................................................................... 31
4.4
Data Analysis .................................................................................................................. 33
4.5
Tabulation ...................................................................................................................... 34
Compressible Flow................................................................................................................. 35
5.1
Introduction.................................................................................................................... 35
5.2
Objectives ....................................................................................................................... 36
5.3
Principle and working equations .................................................................................... 37
5.4
Data Analysis .................................................................................................................. 38
5.4.1
5.5
6
7
Calculations ............................................................................................................. 38
Tabulation ...................................................................................................................... 39
Fluid friction and Drag coefficient ......................................................................................... 40
6.1
Introduction.................................................................................................................... 40
6.2
Objectives ....................................................................................................................... 41
6.3
Principles and working equations .................................................................................. 41
6.4
Data analysis................................................................................................................... 42
6.5
Tabulation ...................................................................................................................... 43
Pipe Friction ........................................................................................................................... 44
7.1
Introduction.................................................................................................................... 44
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7.2
Objective ........................................................................................................................ 44
7.3
Principle and working equation ..................................................................................... 44
7.3.1
Pipe friction duct: .................................................................................................... 45
7.3.2
Flow measurement: ................................................................................................ 46
7.4
Procedure: ...................................................................................................................... 47
7.5
Data Analysis .................................................................................................................. 48
7.6
Tabulation ...................................................................................................................... 48
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1. Flowmeter Calibration
1.1 Introduction and Theory
Measurement and monitoring of the flow rates of the fluids (gases and liquids) are very
important for chemical process industry. Millions of dollars in annual revenue can be lost by
small error in measurement of fluid flow rates in pipelines carrying liquid hydrocarbons, natural
gas and other condensable and non-condensable fluids. Orifice meter, Venturi meter and Pitot
tube are three most commonly used flow measuring device.
The purpose of this laboratory exercise is to get familiarize with the principles and working
operation of these flow meters. The working fluid for this experiment is water. A schematic
diagram of the experimental setup is shown in the Error! Reference source not found..
Water is circulated from a pump tank through the test pipe and back to calibration tank. The
flow rate of the water is controlled by combination of a gate and globe valve (or control valve in
case of Lotus Scientific fluid friction apparatus). The flow meters in this test rig use the
measurement of a differential pressure as an indirect measure of flow rate.
Orifice meter
Venturi meter
Pitot tube
Water out
Water
Tank
Water in
Figure 1-1 Schematic diagram for flowmeter calibration system
1.2 Objectives
Following are the main objectives of this laboratory;
1. To obtain the calibration curves for Orifice meter, Venturi meter and Pitot tube.
2. To calculate the discharge coefficient (Cv) for orifice and venturi meter and compare it
with published values.
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1.3 Principles and theory
Orifice meter, Venturi meter and Pitot tube are examples of “head-loss” meters. When a
constriction is placed in a closed channel carrying a stream of fluid there will be an increase in
velocity at the point of the constriction. By principles of conservation of energy, the increase in
velocity must be accompanied by a decrease in pressure. The rate of flow (volumetric, mass,
etc.) can be calculated from the knowledge of the pressure reduction, the area available for
flow at the constriction, and the density of the fluid. Details of orifice meters and venturi
meters are given in fluid mechanics text book.
Theses flow meters consist of a restriction in the pipe; either a gradual taper for the venturi
meter or a plate with a hole drilled in the center for the orifice meter. A pressure difference is
measured between the throat of the meter and an upstream pressure tap. After calibration,
this pressure difference can then be used to determine the flowrate of fluid. Because the
principles of operation are identical for both devices, same equation can be used to relate
velocity to pressure drop


2 P  P /  
2

V  Cv  1
1
 1  A2 / A2 
2 1 


1/ 2

Eq: 1-1
Pitot tube is an instrument for measuring a ‘point’ velocity. A Pitot tube has two pressure taps,
one connected to stagnation point at the tip of the tube and a second connected to the static
pressure tap. The analysis of a Pitot tube is done by applying the Bernoulli equation to the
streamline leading to stagnation point, which leads to an equation of the following form
V 
2
2( P  P )
2
3

Eq: 1-2
The discharge coefficient is essentially a correction factor to account for frictional heating in the
meter, and for any non-uniformity in flow. The discharge coefficient can be estimated if the
Reynolds number for the fluid is known.
For pitot tube the differential head measured between the total and static tapings is equivalent
to the velocity head of the fluid
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𝑢2
= (ℎ1 − ℎ2 )
2𝑔
Eq: 1-3
where u is the mean velocity of water through the pipe in m/s,
(ℎ1 − ℎ2 ) is the differential head in meters of water
g is the acceleration due to gravity m/s2
1.4 Working Equations
The flow rate can be calculated by
𝑄=
𝐶𝑑 𝐴0
√1−𝛽 4
√2𝑔Δℎ = {
𝐶𝑑 𝐴0
√1−𝛽 4
√2𝑔} √Δℎ
Eq: 1-4
Where Cd – Coefficient of discharge
 = A0 / A1
Eq: 1-5
Pitot tube velocity is √2𝑔ℎ
Eq: 1-6
1.5 Data Analysis
1. Plot differential pressure head for venturi meter, orifice meter and Pitot tube against
measured flowrate.
2. Calculate new coefficient of discharge (Eq: 1-4) for orifice and venture by taking the
average.
3. With the new Cd( Eq: 1-4) calculate the corrected flowrates
4. Plot corrected flowrates (Eq: 1-4)Vs actual ( orifice and venturi)
5. Plot calculated flowrate Vs actual for pitot tube
6. Find the percentage of error and explain graphically.
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1.6 Apparatus specifications
Pipe diameter is 24mm – d1
Orifice diameter is 20 mm – d0
Venturi diameter is 14 mm – d0
Coefficient of discharge for Orifice plate is 0.98
Coefficient of discharge for venturimeter is 0.62
1.7 Tabulation
No.
Measured
Flowrate
Calculated
Head
Orifice
Venuri
Flowrate
Pitot
Orifice
Venturi
Pitot
Coefficient of
Flowrate with new
Velocity
discharge
Cd
Orifice
Venturi
Orifice
Venturi
Cd
Cd
Cd
Cd=
=_________
________
Flowrate
Pitot
Error
Orifice
Units
1
2
3
4
5
6
7
8
9
10
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Venturi
Pitot
2 Pump Characterization
2.1 Introduction
Transportation of fluids is normally carried out by the use of a pump (for liquids), or a blower
or compressor (for gasses). For gasses, blowers are used when the pressure rise of the fluid is
required to be minimal, while compressors are used if an appreciable increase in fluid pressure
is desired. The selection of the correct pumps and blowers for a particular application is
essential for efficient and satisfactory operation.
Figure 2-1 Pump Characteristics apparatus from Armfield
This lab is designed to investigate the relationship between pressure head, power
consumption, efficiency and flow rate for turbine, centrifugal, axial flow and gear pumps using
water as the fluid. Characteristic curve, which is a graphical depiction of these relationships,
will be constructed for all pumps and blower. Basic information on different types of pumps
and blower is given in appendix. Armfield Multi-Pump test rig will be used. A schematic
diagram of the experimental setup is shown in the Figure 2-1.
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2.2 Objectives
Following are the main objectives of this laboratory;
1. To construct characteristic curves for turbine pump, centrifugal pump, axial flow pump
and gear pump.
2. To investigate the differences between head/flow relationships as indicated from the
characteristic curves.
2.3 Principle and working equations
Characteristic curves for a pump present information on head vs. flow, power vs. flow, and
efficiency vs. flow. This information is useful in finding the design point for a given pump, e.g.
the point where the efficiency is the greatest. If possible, it is desirable to operate the pump or
blower at this point. Efficiency is defined as power to the fluid divided by power to the pump:

Pf
Eq: 2-1
Pp
Pf (Watts) = Power to the fluid = gQH
Pp = Power to the pump =
2N
60
Eq: 2-2
Eq: 2-3
Note that the pump head in equation is the difference between the discharge pressure and the
suction pressure at the given flow rate.
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2.3.1 Centrifugal Pumps
The pedestal type, centrifugal pumps consist of a shrouded impeller running on a central
spindle, supported on double ball bearing. The blades of the impeller are generally curved as
shown in the Figure below. Fluid from the suction of the pump enters the volute casing at the
“eye” and spirals outwards around the impeller circumference until exiting the casing at the
discharge. As the fluid passes through the impeller, energy is imparted to it by the curved blade
of the impeller resulting in fluid leaving the impeller with an increase of both pressure and
velocity. This type of pump is not self-priming but operates with a flooded suction. Centrifugal
pumps are used when high volumetric flow rates are required with low discharge head; water
pumps in automobile engines are good examples of a centrifugal pump. Centrifugal pumps can
be operated with the discharge valve closed since they do not develop high pressures. Care
must be exercised however to be certain that the suction to the pump is flooded so that air
cannot enter the pump. The presence of air causes a condition known as “cavitation” that can
damage or even destroy the pump impeller. The limitation of delivery pressure and inability to
self-priming themselves are two main disadvantages of centrifugal pumps. The former can be
overcome by using twin or multi-stages usually on the same spindle axis. The fitting of a selfprimer will eliminate the latter disadvantage.
A typical centrifugal curve and set of characteristic curves are represented in the Figure A1. In
the Figure, discharge flow is either in volumetric (e.g. m3/s) or mass (e.g. kg/s) units. The
characteristic curve shows the relationship between discharge rate and head, discharge rate
and power, and discharge rate with efficiency.
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Figure 2-2 Centrifugal pump with characteristic curve
2.3.2 Turbine Pumps
A turbine pump is also called a regenerative pump or re-generative or peripheral pump. These
devices are for applications where high head and low flow are required; most automotive fuel
pumps are turbine pumps. In a turbine pump, the impeller is a flat wheel with tooth-like blades
(see Figure below). Intake and discharge passages are separated by a seal. As the rotor
revolves, it drags along fluid which is in contact with its surface. The velocity of the fluid in
contact with the housing is zero, and the fluid in contact with the rotor moves at the velocity of
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the rotor; fluid motion is by transfer of momentum from the fluid in contact with the rotor to
the bulk fluid. For this reason, turbine pumps are sometimes referred to as “viscosity pumps”,
meaning that if the fluid has a very low viscosity the pump will not work.
Figure 2-3 Turbine pump with characteristic curve
2.3.3 Axial Flow Pump
Axial flow pump consist of propeller running in a casing with fine clearances between propeller
and casing. In passing through the propeller, the blades impart a whirl component into the fluid
which the outlet guide vanes remove prior to the fluid entering the discharge pipe. The
propeller is mounted on an extended shaft running on a plain bearing. (See diagram)The
volumetric tank is utilized to provide an increased suction head to the axial flow pump and a
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plug is provided to seal the inlet in the base of the tank when the axial flow pump is not in use.
Delivery is controlled via a gate valve mounted on the working surface top and feeding the
channel direct.
The axial flow pump is best suited to conditions where a large discharge flow is to be delivered
against a low head. Land drainage, irrigation and sewage pumping are some typical
applications. The pump efficiency is comparable with that of the Centrifugal type. However, its
higher relative speed permits smaller and cheaper pumping and driving units to be provided.
Figure 2-4 Axial flow pump with characteristic curve
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2.3.4 Gear Pumps
A positive displacement gear pump consist of a case casing and two gear-shaped impellers,
rotating with close clearance, enmeshing such that water entering the suction port is trapped in
the spaces between adjacent teeth and carried round to be squeezed out and discharged
through the outlet port.
High pressures are achieved with gear pumps and a pressure relief valve is incorporated set to
75 m head, to protect the pump and system. The suction port is connected directly to the sump
tank and its delivery port is connected to the selection manifold and measuring system via a
globe valve. An important advantage of this type of pump is that no valves are required in the
suction or delivery: it is capable of pumping air, gas, or liquid without any detrimental effect
and does not require priming. High pressures are possible, although the flow rates are limited.
The main disadvantage of this type of pump is that very close clearances are required between
the ends of the rotors and the casing. Any wear or corrosion in this region by the materials
being pumped will reduce the efficiency of the pump.
Figure 2-5 Gear pump head
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Figure 2-6 Gear pump with characteristic curve
2.3.5 Measurement of Power Input to the Pump
To compute the efficiency of the pump, the power input to the pump must be determined. This
can be easily calculated if the torque from the electric motor and the speed of the pump are
both known:
Pp = power to the pump =
2N
60
Eq: 2-4
Where
N = pump rotational speed (rev/min)
τ = torque on pump electric driver motor (N-m)
Rotational speed for the pump is obtained from the rotational speed of the electric motor
(digital tachometer or stethoscope) and the appropriate gear ratio. For the multi-pump test rig,
torque on the electric motor (in Nm) can be determined directly by means of a calibrated lever
attached to the electric motor. If the balance arm weight does not have the extra weight
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attached, torque is read from the top scale. With the extra weight attached, torque is read from
the bottom scale.
2.4 Procedure

Make sure the reservoir is filled with clear water above minimum level, if the
water level is low add more water.

Connect the test rig to power supply and switch ON the main power supply.

Select the respective pump and close other discharge valves.

Switch on the power to pump module and increase the speed to 100% gradually.

Close the discharge valve gradually and note down/measure flow rate, inlet
pressure, outlet pressure, motor torque.

For each set of input parameters allow sufficient time for stabilization and note
down the measured parameters.
2.5 Data analysis
1. Construct the characteristic curves for the following devices:
a. Centrifugal pump
b. Turbine pump
c. Gear pump
d. Axial flow pump
2. Give a brief comparison of “design point” for each of these devices.
3. Referring to the power / flow graph, should the pump under test be started with its flow
valve open or closed? Explain why.
4. State three suitable industrial applications for the type of pump under test. Correlate
the industrial application with the test data obtained.
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2.6 Speed and flow corrections
2.6.1 Pump speed ratios
The tachometer on the instrument panel indicates the speed in revs./min. of the dynamometer motor.
In order to calculate the actual pump speed, please refer to the Pump/Motor teeth ratios in the table
below:
Pump Speed = Motor Speed x (Teeth on Motor Pulley / Teeth on Pump Pulley )
e.g. When testing the centrifugal pump the tachometer reads 960 revs./min.
Pump Speed = 960 x 2317 = 1299 rev/min.
Pump
Centrifugal
Axial
Gear
Turbine
Pump / motor teeth Max pump speed
ratio
Motor at 1450 RPM
Motor : Pump
23:17
1960
27:14
2800
23:32
1040
27:14
2800
Bourden pressure
m.H2O
0 to 10
0 to 2
0 to 75
0 to 40
2.6.2 Flow Measurement using Weir
The flowrate from certain pumps can change dramatically if the suction head changes. This is
especially a problem with the centrifugal pump. Accordingly, the volumetric tank on the
Armfield Multi-Pump Test Rig should not be used to make the flowrate measurement for the
centrifugal pump as this requires diverting the discharge water to the volumetric tank, thus
decreasing the suction head on the pump. An alternate method of flowrate measurement must
be used for the centrifugal pump. Fortunately, the apparatus incorporates a weir device that
can be used for this purpose. Weirs are important flow measuring devices where open channel
applications are found (for example, in civil engineering).
For the rectangular notch weir, the following relationship should be used:
Q  Cd
2
B 2g H 3/ 2
3
Eq: 2-5
Where,
Q= flow rate in m3/s
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Cd= coefficient of discharge = 0.6
g= acceleration of gravity (9.81 m/s2)
B= width of notch (m) = 5 cm
H= height of water above zero reference point (from vernier) in meters
The vernier should be zeroed at the bottom of the notch. To measure the height of the water,
move the vernier until the point is just touching the surface of the water. The height of water
above the zero reference point is then read directly from the vernier scale (in mm).
2.7 Apparatus specifications
Pf
= Power to the fluid (Watts)
ρ
= Fluid density (Kg/m3)
g
= Acceleration of gravity (9.81 m/sec2)
Q
= Volumetric flow rate (m3/s)
H
= Pump head (m)
Pp
= Power to the pump
N
= Rotational speed of the pump (rev/min)
τ
= Torque on pump electric driver motor (N-m)
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2.8 Tabulation
Centrifugal
No
Flowrate
Speed
Measured
Torque Inlet
head
Outlet
head
Calculated
Head Input Outlet Efficiency
power power
Speed
Measured
Torque Inlet
head
Outlet
head
Calculated
Head Input Outlet Efficiency
power power
Unit
1
2
3
4
5
6
Turbine
No
Flowrate
Unit
1
2
3
4
5
6
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Gear
No
Flowrate
Speed
Measured
Torque Inlet
head
Outlet
head
Calculated
Head Input Outlet Efficiency
power power
Unit
1
2
3
4
5
6
Axial
No
Height
Measured
Speed Torque Inlet
head
Outlet
head
Calculated
Actual
Head Input Outlet Efficiency
flowrate
power power
Unit
1
2
3
4
5
6
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3 Fluidization
3.1 Introduction
Fluidization is an important unit operation that is widely used in chemical engineering process
where good mixing and contact between a gas and a solid is required. Industrial example of
applications of fluidization technology includes;
1)
Drying of solids
2)
Coating
3)
Chemical reactors
4)
Gas absorption and ion exchange
Fluidized bed systems have extremely good heat and mass transfer characteristics, hence fluid
beds are widely used for chemical reactors where the solid phase is a catalyst.
3.2 Objectives
Following are the main objectives of this laboratory:
1. To investigate the relationship between velocity and pressure drop for both fixed and
fluidized bed with air as the working fluid.
2. To investigate the relationship between velocity and pressure drop for both fixed and
fluidized bed with water as the working fluid.
3. To predict the minimum velocity or loosening speed 𝑊𝑙𝑜 for both systems and compare it
with experimental value.
3.3 Principle and working equation
When a fluid passes in upflow through a bed of finely-divided solids, the buoyancy force and
drag force of the fluid works against the gravitational on the particles. If we monitor the
pressure drop as a function of the flow rate, an idealized representation of the relationship is
shown below in Figure 1.
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Figure 3-1 Pressure Drop vs. Superficial Velocity
In the first section, the gravitational force on particle is greater than the sum of the buoyancy
and drag forces and particle remains stationary (fixed bed). The bed is seen to expand as bulk
density is reduced resulting in surface rise of the bed. At some point, the gravitational and
buoyant + drag forces are roughly in balance, and the particles will begin to move out randomly
(fluid bed). When the bed is fluidized, all gas in excess of that required for minimum fluidization
passes through the bed in the form of bubbles. Depending on the nature of the solid and fluid
phases, the fluidization may be either particulate or aggregative. Particulate or smooth
fluidization is characterized by the absence of large scale fluid voids; gross instabilities in the
bed are not observed (Figure 3-1 Pressure Drop vs. Superficial Velocity). Aggregative fluidization
is characterized by violent agitation of the bed .
If the velocity is increased, ultimately the upward forces will greatly exceed the gravity, and the
particle will be pneumatically conveyed out of the bed (entrained flow).
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Figure 3-2 Modes of Fluidization
3.3.1 Pressure losses in fluidized bed
From the equilibrium of drag, weight and lift the pressure ∆𝑝 of a fluid flowing through the
turbulent mass of particles is given by
∆𝑝 = 𝑔 (1 −
𝜌𝑓
𝜌𝑝
).h. 𝜌𝑝𝑠
Eq: 3-1
𝜌𝑓 Density of the fluid
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𝜌𝑝 Density of the particle
𝜌𝑝𝑠 Density of the particle mass
h Height of the mass
3.3.2 Loosening speed
This is the fluid speed at which the mass of solid matter passes the transition to a fluidized bed.
The speed of the fluid in the space between the particles can be calculated form Reynolds
number, the diameter of the particles and the kinematic viscosity of the fluid.
𝑊𝑙𝑜 =
𝑅𝑒𝑙𝑜
.𝑣
𝑑𝑝 𝑓
Eq: 3-2
𝑊𝑙𝑜 speed of the fluid between the spherical particles
𝑅𝑒𝑙𝑜 Reynolds number of the fluid
𝑑𝑝 Diameter of the particle
𝑣𝑓 kinematic viscosity
Form factor is applied when the particles shape is irregular,
𝑊 = 𝑊𝑙𝑜 𝜑
Eq: 3-3
𝜑 Form factor
W corrected speed of the fluid
The voids fraction defines the size of the fractions of hollow space in the mass. It is calculated
from the density of the particle material and the mean density of the mass.
𝜀 =1−
𝜌𝑓
𝜌𝑝
Eq: 3-4
𝜀 void fraction
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The equilibrium of pressure loss and particle drag yields a relationship between the
dimensionless number Re ad Ar
𝑅𝑒𝑙𝑜 = 42.86(1 − 𝜀) (√1 + 3.11. 10−4 . 𝐴𝑟.
𝜀4
− 1)
(1 − 𝜀)2
Eq: 3-5
Ar is the Archimedes Number
𝐴𝑟 =
𝑔. 𝑑𝑝3 𝜌𝑝 − 𝜌𝑓
.
𝑣2
𝜌𝑓
Eq: 3-6
𝑄
Fluid speed 𝑊𝑓 = 6𝐴 in m/s
𝑍
Eq: 3-7
3.4 Procedure
3.4.1 Using air as working fluid
1) Switch on the air compressor.
2) Adjust the air flow rate in small increments covering the entire range of flow span.
3) At each setting allow the conditions to stabilize then record the height of the bed, the
differential reading on the manometer and state of bed.
4) In order to observe the hysteresis characteristics of the bed, adjust the air flow in
increment of 1 l/min from maximum flowrate to the minimum flow rate and record the
corresponding height of the bed, differential pressure and state of bed.
3.4.2 Using water as working fluid
1) Switch on the water pump.
2) Adjust the water flow rate in small increments covering the entire range.
3) At each setting allow the conditions to stabilize then record the height of the bed, the
differential reading on the manometer and state of bed.
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4) In order to observe the hysteresis characteristics of the bed, adjust the water flow in
increment of 1 l/min from maximum flowrate to the minimum flow rate and record the
corresponding height of the bed, differential pressure and state of bed.
3.5 Data analysis
1. Plot Fluid speed against p for both air and water, graphically find loosening speed and
compare with the theoretical value Eq: 3-2
2. Plot the fluid speed Eq: 3-7 against pressure explain the hysteresis effect.
DATA RECORDING
S.
No.
O
C
Ambient pressure:
mm Hg
Working Fluid
Air
Flowrate
(l/min)
1.
Ambient temperature:
Pressure (mm H2O)
H1
H2
Water
Bed Height
(mm)
0
State of
Bed
Flowrate
(l/min)
Pressure (mm H2O)
H1
H2
Bed Height
(mm)
State of
Bed
0
2
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
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18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
0
0
3.6 Data Analysis
1. Plot a graph of pressure vs. superficial velocity for both air and water as working fluid
and comment on the hysteresis behavior of the beds.
2. Determine experimentally the minimum fluidization velocity for both air and water
systems.
3.7 Apparatus Specification
Az cross sectional area of cylinder is 15.21 cm2
𝑑𝑝 Diameter of the particle: 0.240 mm (air); and for water it is 0.505mm
𝑣𝑓 Kinematic viscosity: 16 x 10-6 m2/s (air); and for water it is 1 x 10-6 m2/s
𝜌𝑓 Density of the fluid 1.25 kg/m3
𝜌𝑝 Density of the particle 2500 kg/m3
𝜌𝑝𝑠 Density of the particle mass 1500 Kg/m3
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4 Fluid friction and drag coefficient for pipes and valves
4.1 Introduction
Flow of fluids through fittings and valves in closed conduits is always accompanied by
significant loss in energy of the fluid by virtue of friction. Frictional head loss can be divided
into two types:
Skin friction, associated with the friction between the fluid and the wall of the conduit.
Form friction, associated with frictional head loss from changes in velocity and direction as the
fluid passes through globe and gate valves.
The lab is designed to investigate the frictional losses due to skin friction and form friction. The
experimental setup is shown in Figure 4-1 Experimental setup for fluid friction factor
experiment. Water will be used as a working fluid for measuring the frictional pressure drop. In
the first part of the experiment, the relationship between fluid flowrate and the head loss due
to fluid friction (frictional pressure drop) in smooth pipes will be studied. Second part of the
experiment deals with the frictional losses associated with flow through a variety of valves &
fittings including sudden expansions & contractions, and change of direction of flow.
CHEG232: Fluid Mechanics Lab - Fall 2022
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Figure 4-1 Experimental setup for fluid friction factor experiment
4.2 Objective
Following are the main objectives of this experiment;
1. To investigate the relationship between the frictional head losses (friction factor) and
fluid flow rate (Reynolds number) for pipes of varying diameter and compare with
accepted correlations.
2. To determine the experimental value of the loss coefficient (K) for a gate and globe
valves at a particular valve position. Also to study the effect of Reynolds’s number and
valve position (% opening) on loss coefficient for these valves.
4.3 Principle and working equation
Frictional pressure drop for fluids flowing in closed conduits is generally divided into two
types;
1) Skin friction associated with the interaction of the fluid and the wall of the conduit.
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31
2) Form friction associated with changes in velocity caused by disruptions in the flow
pattern such as fittings, valves, changes in direction, sudden expansions and sudden
contractions.
A convenient method for modeling frictional losses involving skin and form frictional head loss
terms along with the pressure, velocity, and elevation head loss terms is the Bernoulli equation
(assuming incompressible flow):
Pb
Vb2
Pa
Va2
 gZ a 

 gZ b 
 h fs  h ff

2

2
4-1
Where, hfs and hff are skin friction and form friction loss.
For steady flow of an incompressible fluid in a circular conduit, it can be shown that;
h fs 
P

 4f
L V2
D 2g
4-2
So when the head loss increase the velocity increase as well. The head loss results in various
conditions due to the flow restrictions and surface. For steady flow of an incompressible fluid
in a circular conduit, it can be shown that:
h ff 
P

K
V2
2
4-3
Information concerning accepted values for the loss coefficient for valves and fittings can be
found in reference texts.
Several well-established correlations exist for the fanning friction factor. These include:
1) Moody Diagram (Figure 6.10 in Fluid Mechanics for Chemical Engineers by de Nevers). The
Moody Diagram shows how Fanning friction factor changes as a function of the Reynolds
CHEG232: Fluid Mechanics Lab - Fall 2022
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number for fluid flowrates ranging from laminar (Re <2000) to highly turbulent. The effect
of pipe roughness is also incorporated in this diagram.
2) Laminar flow correlation: f 
16
Re
3) Turbulent flow correlations;
1/ 3 

 10 6  
 
f  0.0013751  20,000 


D Re 

 

a. f = 0.046 Re-0.2
4-4
(for hydraulically smooth pipes and tubes only)
b. The von Karman equation: f  0.0014 
0.125
Re 0.32
4) Other relevant equations are:
a. Reynolds number: Re 
D V  

4.4 Data Analysis
1. For each pipe plot head loss vs. velocity and identify laminar, transition and turbulent
flow regions.
2. Determine the Fanning friction factor for a wide range of flowrate from laminar to highly
turbulent and determine the relationship between Reynolds number and the friction
factor.
3. Compare your experimental results to the results from the Moody diagram and relevant
empirical correlations.
4. Determine the loss coefficients (K) for gate and globe valves by using head loss vs. flow
rate data at a given valve position (% opening).
5. Determine effect of Reynolds number and valve position (% opening) on loss coefficient
(K) for gate and globe valves.
6. Determine loss coefficient (K) for the various fittings investigated/studied.
7. Determine the effect of Reynolds number on the loss coefficients for above fittings.
8. Compare the experimental results with theoretical results.
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4.5 Tabulation
Pipe Diameter:
No
Measured
Flowrate Head
Calculated
Reynolds
Velocity K
Number
Valves:
No
Measured
Flowrate Head
Percentage of Opening
Calculated
Reynolds
Velocity K
Number
Uni
t
CHEG232: Fluid Mechanics Lab - Fall 2022
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5 Compressible Flow
5.1 Introduction
The velocity of a fluid flowing in a closed conduit will increase as applied pressure gradient
increases. For incompressible fluids, the relationship between flowrate and pressure drop is
given by the Bernoulli’s equations. For compressible fluid however, the observed behavior is
somewhat different as shown in the
Figure 5-1 Mass flowrate variation with pressure drop for incompressible and compressible
flow
As shown, compressible fluid (e.g. gases and vapors) there is a limiting value for the fluid
flowrate beyond which the fluid flow rate will not increase no matter how high the pressure
gradient. This phenomenon is called choking.
For compressible fluids, the choking point is reached when the velocity of the fluid reached
‘Mach number = 1; that is the velocity of the fluid is equal to the speed of the sound (sonic
CHEG232: Fluid Mechanics Lab - Fall 2022
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velocity). At this point, the downstream process information can no longer be transmitted
upstream by the pressure (sound) wave, and so the fluid doesn’t know what the implied
pressure gradient actually is.
Choking can be achieved in laboratory with a convergent-divergent nozzle such as that shown
in Figure 2. The flow will be choked when the velocity of the fluid is equal to the speed of the
sound (‘Mach number = 1) in throat of the nozzle.
The purpose of this lab is to examine the phenomenon of choking with air as working fluid.
Figure 5-2 Convergent Divergent Nozzle
5.2 Objectives
Following are the main objectives of this laboratory:
1. To investigate the relationship between velocity and pressure drop in a convergingdiverging nozzle with air as working fluid.
2. To calculate an empirical value for the speed of sound and critical pressure ratio.
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5.3 Principle and working equations
A fluid is considered to be compressible if the density of the fluid changes more than 10 %.
Assuming an ideal gas, the density can be calculated from the following expression;

P MW
RT
5-1
The viscosity of the air can be calculated from the following expression;
 393   T  273 


 T  393   273 
  1.71  10 5 
3/ 2
5-2
For an ideal gas, the speed of sound (c) can be calculated as follows;
c
P
RT


MW
5-3
Where,

CP
(For air,  =1.4)
CV
1
Mass flowrate 𝑚̇ = 𝜌1 𝑎1 𝑉1 = 𝑟 𝛾 𝜌0 𝑎1 𝑉1
As can be seen, for an ideal gas the sonic velocity is a function of temperature only.
Flowrate through a closed conduit can be given by;

2 P
m  Oa1.   1 . OO
 1
 2

r  r  




5-4
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Experimental mass flowrate can be calculated by
𝑚̇ = 𝑎1 √2𝜌0 (𝑃0 − 𝑃1 )
5-5
As shown in 5-4, the mass flow rate becomes constant at the point where the down stream
pressure divide by upstream pressure equals to 0.5283. This is known as critical pressure ratio.
This value can be calculated by the following expression;
P  2 

rC  2  
P1    1 
5.4
1 / 11 /  
5-6
Data Analysis
1. Plot a graph of pressure drop (PO-P3) vs. mass flowrate (m) and comment about the
characteristic features.
2. Plot (PO-P2) vs. (PO-P1) and (PO-P2) vs. (PO-P3) and comment on the shapes of the graphs.
3. Determine an empirical value of the speed of the sound, and compare your
experimental results for the sonic velocity to the value predicted from equation3
4. Determine experimentally the “critical pressure ratio” and compare it to the theoretical
value.
5.4.1 Calculations
1. The chocking point should be found by plotting pressure ratio (down stream to
upstream) verses mass flowrate.
2. The theoretical and experimental values of critical pressure and speed of sound.
CHEG232: Fluid Mechanics Lab - Fall 2022
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5.5 Tabulation
Measured
No
Velocity
PO-P1
PO-P2
PO-P3
Calculated
P2/P1
Mass
flowrate
unit
CHEG232: Fluid Mechanics Lab - Fall 2022
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6 Fluid friction and Drag coefficient
6.1 Introduction
Flow of fluids through fittings and valves in closed conduits is always accompanied by
significant loss in energy of the fluid by virtue of friction. Frictional head loss can be divided
into two types:
Form friction, associated with frictional head loss from changes in velocity and direction
as the fluid passes through fittings, valves, and around bends in the piping system.
The lab is designed to investigate the frictional losses due to skin friction and form friction. The
experimental setup is shown in Figure 1. Water will be used as a working fluid for measuring
the frictional pressure drop. In the first part of the experiment, the relationship between fluid
flowrate and the head loss due to fluid friction (frictional pressure drop) in smooth pipes will
be studied. Second part of the experiment deals with the frictional losses associated with flow
through a variety of valves & fittings including sudden expansions & contractions, and change
of direction of flow.
Figure 6-1 Experimental setup for fluid friction factor experiment
CHEG232: Fluid Mechanics Lab - Fall 2022
40
6.2 Objectives
Following are the main objectives of this experiment;
To determine the experimental value of the loss coefficient (K) for the following valves
and fittings and to compare these values with accepted values from the literature.
 90° elbow
 90° Elbow fitting
 Sudden contraction
 Sudden expansion
 45 ° bend
6.3 Principles and working equations
Frictional pressure drop for fluids flowing in closed conduits is generally divided into two
types;
1. Skin friction associated with the interaction of the fluid and the wall of the conduit.
2. Form friction associated with changes in velocity caused by disruptions in the flow
pattern such as fittings, valves, changes in direction, sudden expansions and sudden
contractions.
A convenient method for modeling frictional losses involving skin and form frictional head loss
terms along with the pressure, velocity, and elevation head loss terms is the Bernoulli equation
(assuming incompressible flow):
Pb
Vb2
Pa
Va2
 gZ a 

 gZ b 
 h fs  h ff

2

2
6-1
Where, hfs and hff are skin friction and form friction loss.
CHEG232: Fluid Mechanics Lab - Fall 2022
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For steady flow of an incompressible fluid in a circular conduit, it can be shown that;
h fs 
P

 4f
L V2
D 2g
6-2
For steady flow of an incompressible fluid in a circular conduit, it can be shown that:
h ff 
P

K
V2
2
6-3
Information concerning accepted values for the loss coefficient for valves and fittings can be
found in reference texts.
Other relevant equations are:
Reynolds number: Re 
D V  

6.4 Data analysis







For each fitting head loss vs. velocity and identify laminar, transition and turbulent flow
regions.
Determine the Fanning friction factor for a wide range of flowrate from laminar to
highly turbulent and determine the relationship between Reynolds number and the
friction factor.
Investigate the effect of roughness on the friction factor.
Compare your experimental results to the results from the Moody diagram and relevant
empirical correlations.
Determine loss coefficient (K) for the various fittings investigated/studied.
Determine the effect of Reynolds number on the loss coefficients for above fittings.
Compare the experimental results with theoretical results.
CHEG232: Fluid Mechanics Lab - Fall 2022
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6.5 Tabulation
No
Measured
Flowrate Head
Calculated
Reynolds
Velocity K
Number
CHEG232: Fluid Mechanics Lab - Fall 2022
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7 Pipe Friction
7.1 Introduction
This experiment is designed to investigate the friction coefficient of pipes while air is used as
the working fluid. The relationship between fluid flowrate and the head loss due to fluid friction
(frictional pressure drop) in smooth pipes with different diameter will be studied.
7.2 Objective
To investigate the relation between friction loss and velocity for incompressible flow and to find
an approximate value for the friction coefficient f.
To investigate the relation between the friction coefficient and the Reynolds number for a
given pipe.
7.3 Principle and working equation
The compressible flow bench comprises a multi stage motor driven air compressor unit
supplied with seven interchangeable test sections and al the instrumentation necessary for
carrying out experiments. The air compressor is a four stage centrifugal machine incorporating
aluminum impellers.
CHEG232: Fluid Mechanics Lab - Fall 2022
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7.3.1 Pipe friction duct:
There are three sets of pipes available for testing with different diameter
CHEG232: Fluid Mechanics Lab - Fall 2022
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Bore
Development Length
Test portion length
13 mm
400 mm
600 m
19 mm
600 mm
600 mm
24 mm
900 mm
900 mm
Basic Equations:
The following assumptions are made throughout the subsequent theoretical development,
● Flow variables are uniform over across section perpendicular to the flow direction,
the duct can be considered to be a single stream tube with one dimensional flow.
● Flow is steady.
● Potential energy changes are negligible.
7.3.2 Flow measurement:
The experimental ducts are fitted with intake sections profiled from a plane upstream face into
a parallel throat, the flow rate is determined from the pressure drop P0 – P1between still
atmospheric conditions and the throat.
To a first order of approximation assuming no losses, work, heat transfer or density changes
between inlet and throat and assuming uniform velocity distribution in the throat
A convenient method for modeling frictional losses involving skin and form frictional head loss
terms along with the pressure, velocity, and elevation head loss terms is the Bernoulli equation
(assuming incompressible flow):
CHEG232: Fluid Mechanics Lab - Fall 2022
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Pb
Vb2
Pa
Va2
 gZ a 

 gZ b 
 h fs  h ff

2

2
Where, hfs and hff are skin friction and form friction loss.
For steady flow of an incompressible fluid in a circular conduit, it can be shown that;
𝑃2 − 𝑃3 4𝑓𝑙𝑣 2
=
𝜌
2𝑑
Eq: 7-1
𝑣2 =
2𝑘(𝑃0 − 𝑃1 )
𝜌
Eq: 7-2
𝑃2 − 𝑃3 =
4𝑓𝑙
. 𝑘(𝑃0 − 𝑃1 )
𝑑
Eq: 7-3
The Reynolds number 𝑅𝑒 =
𝜌𝑉𝑑
𝜇
𝜇 = 1.71 × 10
−5
393
𝜃 + 273 3/2
(
)(
)
𝑁𝑠/𝑚2
𝜃 + 393
273
Eq: 7-4
Where 𝜃 is the temperature in °C
7.4 Procedure:
1. Switch on the fan and set the desired flow rate via the speed control knob.
2. Record the velocity c at the measuring point and the differential pressure
3. Repeat the measurements for different flowrates.
CHEG232: Fluid Mechanics Lab - Fall 2022
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7.5 Data Analysis
Plot P2-P1 against P0-P1 and from the slope deduce a value of f, comment on whether f is a
constant
Tabulate f, Re, log10f, log10Re,
1
√𝑓
, log10(Re√𝑓). Plot log10f against log10Re, plot
1
√𝑓
against
log10(Re√𝑓).
Does the empirical relationship found by Blasius f=0.3164 𝑅𝑒 −1/4 apply and over what range?
Does the Nikurdase-von karman relationship
1
√𝑓
= 4.0 𝑙𝑜𝑔10 (𝑅𝑒√𝑓) − 0.396 apply and over
what range?
7.6 Tabulation
No
Measured
Flowrate P0-P1
P2-P1
𝑃2 − 𝑃3
f
Re
Calculated
1
log10f log10Re
log10(Re√𝑓)
√𝑓
Unit
1
2
3
4
5
6
CHEG232: Fluid Mechanics Lab - Fall 2022
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APPENDICES
Fluid Mechanics
Appendix A: Nomenclature and Specification of Flowmeter Calibration
Appendix B: Nomenclature and Specification for Pump Characterization
Appendix C: Nomenclature and Specification for Fluid Friction & Drag Coefficient
CHEG232: Fluid Mechanics Lab - Fall 2022
49
Appendix A: Nomenclature and Specification for Flowmeter Calibration
NOMENCLATURE
V1 = Velocity in the throat (m/s)
P1 = Upstream pressure (N/m2)
P2 = Pressure at the throat of the meter (N/m2)
A1 = Cross-sectional area of the upstream pipe (m2)
A2 = Cross-sectional area of the throat (m2)
ρ
= Density of fluid (Kg/m3)
Cv = Discharge coefficient
V2 = Mean velocity of water through the pipe (m/s)
P3 = Pressure measured at the downstream pressure tap (N/m2)
Fall 2018
Appendix B: Nomenclature and Specification for Pump Characterization
NOMENCLATURE
Pf
= Power to the fluid (Watts)
ρ
= Fluid density (Kg/m3)
g
= Acceleration of gravity (9.81 m/sec2)
Q
= Volumetric flow rate (m3/s)
H
= Pump head (m)
Pp
= Power to the pump
N
= Rotational speed of the pump (rev/min)
τ
= Torque on pump electric driver motor (N-m)
CHEG232: Fluid Mechanics Lab – Spring 2019
Appendix C: Nomenclature and Specification of Fluid Friction Experiment
NOMENCLATURE
Pa, Pb = Pressure at points a and b
Va, Vb = Average velocity of fluid at points a and b
Za, Zb = Elevation of conduit relative to some datum plane
hfs = Head loss due to skin friction only
ρ = Fluid density
hfs = Head loss due to friction
f = Fanning friction factor
L = Distance between pressure taps
V = Average velocity
D = Pipe diameter
ε = Surface roughness factor (see Table 6.2 in de Nevers)
CHEG232: Fluid Mechanics Lab – Spring 2019
Table A1: K values for fittings
CHEG232: Fluid Mechanics Lab – Spring 2019
REFERENCES
1. A Syed Ali and A Nafees Unit Operation Lab Manual, 2016 Chemical Engineering.
2. W. L. McCabe, J. C. Smith and P. Harriott “Unit Operations of Chemical Engineering” 6 th
Edition, J. Wiley and Sons (2001).
3. Kunni and Levenspiel “Fluidization Engineering”, 2nd Edition, Butterworth-Heinemann
(1991).
4. Bird, Stewart, and Lightfoot “Transport Phenomena”, J. Wiley and Sons (2002).
CHEG232: Fluid Mechanics Lab – Spring 2019