Fluid
Mechanics
Laboratory
GROUP MEMBERS OF BATCH
2012
SOBAN ADIL
MUHAMMAD UMAIR
FAIZAN HUSSAIN
IRFAN HAIDER
RAMEEL KHAN
Fluid Mechanics Laboratory
List of Experiments
1. To calibrate a pressure gauge using a dead weight pressure gauge calibrator.
2. Experimental Study of Reynolds number and observing laminar, transitional and
turbulent flow.
3. Determination of discharge (water flow measurement) through hydraulic bench.
4. To study the characteristics of centrifugal pump in series and parallel.
5. To study loss of energy in bends.
6. To determine the exact sections of venturi tube at various probing stations using
Bernoulli theorem.
7. To obtain the characteristics curves of a centrifugal pump at various impeller
speeds. (Newly Designed)
a. Flow rate vs Brake Horsepower [Nh(Q)]
b. Flow rate vs Efficiency [η(Q)]
c. Flow rate vs Head [H(Q)]
List of Equipment
S. No
Name of Equipment
No. of Units
Vendor
Working
Status
1
Pressure Sensors
Calibration System
1
Edibon
In Use
2
Dead Weight Calibrator
1
Edibon
In Use
3
Manometer
1
-----
In Use
4
Energy Losses In Bends
1
Edibon
In use
5
Osborne-Reynolds
1
Edibon
Maintenance
Required
6
Centrifugal Pump
Characteristics +
Accessories
1
Edibon
In Use
7
Bernoulli’s Theorem
1
Edibon
In Use
8
Hydraulics Bench
1
Edibon
List of Desired Equipment
In Use
1
Francis Turbine Unit
1
Edibon
Desired
2
Kaplan turbine Unit
1
Edibon
Desired
Pressure Sensors
Calibration System
This procedure is under the jurisdiction of the Geotechnical Services
Branch, code D-3760, Research and Laboratory Services
Division, Denver Office, Denver, Colorado. The procedure is issued under
the fixed designation USBR 1050. The number immediately
following the designation indicates the year of acceptance or the year of last
revision.
1. Scope
This designation outlines the procedure for
calibrating pressure transducers.
This calibration procedure is used to determine tile
accuracy of pressure transducers over the full pressure range
as set forth in the manufacturer's specifications.
2. Auxiliary Tests
The pressure gauge used in this procedure must
be calibrated in accordance with USBR 1040 prior to
performing this calibration procedure.
3. Applicable Documents
USBR Procedures:
USBR 1040 Calibrating Pressure Gauges
USBR 3900 Standard Definitions of Terms and Symbols
Relating to Soil Mechanics
4. Summary of Method
A pressure transducer and a standard pressure
gauge are connected to a pressure source. Pressure is applied
in predetermined increments over the full range of the
pressure transducer. The pressure transducer voltage output
is compared at each increment to a pressure gauge reading.
The percent error of the pressure transducer when
compared to the pressure gauge reading is calculated for
each pressure increment over the full range calibrated. From
these percent error values, a determination is made to accept
or reject the pressure transducer for laboratory use.
5. Significance and Use
A calibrated pressure transducer must be used in
the laboratory to ensure reliable test results.
This calibration procedure is to be performed upon
receipt of the pressure transducer and annually thereafter.
Dead Weight
Calibrator
Deadweight testers can be calibrated using either the
“Fundamental” or “Calibrated” methods to measure the pressure
and effective area. A fundamental calibration involves having the
effective area of the gauge determined using only measurements of
the SI base units (e.g. mass, length) plus a suitable model. A
calibrated calibration has the effective area determined via
calibration against a gauge for which the effective area or generated
pressure is already known.
Methods of Calibration
Fundamental Characterization of Deadweight Testers
The dimensional characterization of both the piston and cylinder are
usually performed under conditions of atmospheric pressure and
room temperature. Depending upon the shape of both the piston
and the cylinder and the support structure for the mass loading
mechanism, the detailed dimensional characterization is usually
confined to that part of the piston that is inside the cylinder during
normal operation. Pistons of unusual shape are not normally
characterized using this technique.
Once a set of dimensional measurements has been performed on
both the piston and cylinder, there are several ways in which the
area of both the piston and cylinder can be specified. Depending
upon the severity of the departure of the piston surface from true
cylindricity, an average radius of the piston and cylinder may be
calculated, or more sophisticated approaches including distortion of
the piston by the applied pressure and thermal expansion of the
piston can be applied. The overall area of the piston and cylinder
assembly is then computed using an appropriate mathematical
model.
This technique is used primarily by national standards laboratories,
such as the National Institute of Standards and Technology that are
responsible for establishing reference measurements for a larger
group such as the United States.
Calibrated Characterization of Deadweight Tester
The calibrated characterization of deadweight testers involves the
transfer of effective areas of one piston and cylinder to another
utilizing pressure based cross-float techniques. To use this
technique, identical piston and cylinders are placed in identical
mountings with the output pressures connected. Means, such as a
differential pressure meter are included to identify the time when a
pressure balance between the two pressure generating components
has been achieved at the reference levels of both the test and
reference units. During the test the weights are exchanged on the
columns and the piston and cylinders are exchanged in the
mountings to reduce the uncertainty of measurement. This
technique is used primarily by industry and calibration laboratories.
The reference or master pressure generating units (Piston-Cylinder
& Weights) are usually tested at a standards laboratory
(AMETEK masters are tested at NIST).
Manometer
Manometers
A somewhat more complicated device for measuring fluid pressure
consists of a bent tube containing one or more liquid of different
specific gravities. Such a device is known as manometer.
In using a manometer, generally a known pressure (which may be
atmospheric) is applied to one end of the manometer tube and the
unknown pressure to be determined is applied to the other end.
In some cases, however, the difference between pressure at ends of
the manometer tube is desired rather than the actual pressure at the
either end. A manometer to determine this differential pressure is
known as differential pressure manometer
Two Essential Rules
Manometers are devices that allow us to measure pressure
differences. To relate the measured height differences on the
manometer to pressures, we apply two rules.
1. The first rule is that within a body of fluid, all points at the same
level are at the same pressure.
2. The second rule is that the pressure at the bottom of a column of
fluid is equal to the pressure at the top plus the density times the
acceleration due to gravity (g) times the height of the column.
Manometers - Various forms
1.
2.
3.
4.
5.
Simple U - tube Manometer
Inverted U - tube Manometer
U - tube with one leg enlarged
Two fluid U - tube Manometer
Inclined U - tube Manometer
Energy Losses In
Bends
Principle
Change in flow velocity due to change in the geometry of a pipe
system (i.e., change in
cross-section, bends, and other pipe fittings) sets up eddies in the
flow resulting in
energy losses.
Introduction
In hydraulic engineering practice, it is frequently necessary to
estimate the head loss
incurred by a fluid as it flows along a pipeline. For example, it may
be desired to
predict the rate of flow along a proposed pipe connecting two
reservoirs at different
levels. Or it may be necessary to calculate what additional head
would be required to
double the rate of flow along an existing pipeline.
Loss of head is incurred by fluid mixing which occurs at fittings such
as bends or
valves, and by frictional resistance at the pipe wall. Where there are
numerous fittings
and the pipe is short, the major part of the head loss will be due to
the local mixing
near the fittings. For a long pipeline, on the other hand, skin friction
at the pipe wall
will predominate. In the experiment described below, we investigate
the frictional
resistance to flow along a long straight pipe with smooth walls.
Osborne-Reynolds
Centrifugal Pump
Characteristics +
Accessories
INTRODUCTION
Pumps have come to occupy an important place in a large
number of industries which have different requirements.
Attempt to meet the needs of industries has resulted in the
design and development of various types of pumps. To match a
pump for a particular application and to use a pump effectively,
it is necessary to know the pump characteristics. In this
experiment, students are exposed to the method of
determination of pump characteristics, which is similar for all
types of pumps. The experiment is conducted using a parallelseries centrifugal pump test rig.
Purpose
a) To determine the pump characteristics H versus Q, P, versus Q,
and  versus Q at
a given speed.
b)
To verify speed laws Q N and H  N2 for the same pump.
Scope
This experiment demonstrates the method used for the
determination of the characteristics of a pump and the way the
graphs are plotted to illustrate the pump characteristics. The
speed laws show how the pump characteristics are predicted
at different speeds of operation, knowing the characteristics at
one particular speed. The use of the test-rig, helps the student
to familiarize himself with the operation of pumps.
DESCRIPTION OF EQUIPMENT
The test-rig, which is shown schematically in Figure 1 consists
of a centrifugal pump driven by a variable D.C. motor in which
a tension gauge is used for measuring the input torque. The
closed loop piping for testing of the centrifugal pump is done
by either closing or opening appropriate valves in the test rig.
In the pipe circuit the flow measuring devices is the digital flow
meter. The head across the pump is measured using the
pressure gauges at suction and discharge pipe section. The
input power to the electric motor is measured by balancing the
torque arm attached to the stator which develops an equal and
opposite torque to that of the rotor. The electric motor has
operating speed range of 0 to 2880 rpm.
BASIC THEORY OF PUMP
It is well known that the following variables significantly affect
the performance of constant-shape pumps.
D
 impeller diameter
Q
 volume flow rate

 density of fluid
N
 rotational speed
or
g
 gravitational acceleration
H
 head across the pump

 dynamic viscosity of fluid
f (D, Q, , N, g, H, ) = 0
From the above variables, it can be shown by dimensional
CH=
CQ=
analysis using Buckingham π Theorem that:
Neglecting the Reynolds number (Re) effect, one parameter
law for a geometrically similar pump is obtained. For such
pumps:
For the same pump:
PROCEDURE
Experiment
The experiments are to be conducted at two rpms. Ensure that
the correct water circuit has been identified for the
experiment. Set the motor speed to the higher value and the
valve fully open, using the speed controller button on the
control panel to adjust the speed. Determine: (i) the mass
required to balance the torque arm, (ii) head using the
pressure gauges and (iii)flow over flow meter Repeat the
experiment with the regulating valve at five other valve
settings for the same speed. The final reading is taken with
the valve fully closed. These valve settings are approximately
set with the help of the digital flow meter. Plot the head versus
flow curve as the experiment is conducted. Make sure all
experimental points lie on a smooth curve and they are evenly
spaced between fully opened and closed valve settings.
Repeat the above procedure for the second speed. During the
experiment, other measuring devices may be used for counter
checking the experimental points. If any experimental point is
dubious, repeat that point and check the validity of that
particular point.
Bernoulli’s Theorem
Objective of the Experiment
1. To demonstrate the variation of the pressure along a convergingdiverging pipe
section.
2. The objective is to validate Bernoulli’s assumptions and theorem
by
experimentally proving that the sum of the terms in the Bernoulli
equation along a
streamline always remains a constant.
Apparatus Required:
Apparatus for the verification of Bernoulli’s theorem and
measuring tank with stop watch setup for measuring the actual flow
rate.
Theory:
The Bernoulli theorem is an approximate relation between pressure,
velocity, and elevation, and
is valid in regions of steady, incompressible flow where net
frictional forces are negligible. The
equation is obtained when the Euler’s equation is integrated along
the streamline for a constant
density (incompressible) fluid. The constant of integration (called
the Bernoulli’s constant) varies
from one streamline to another but remains constant along a
streamline in steady, frictionless,
incompressible flow. Despite its simplicity, it has been proven to be
a very powerful tool for fluid
mechanics.
Bernoulli’s equation states that the “sum of the kinetic energy
(velocity head), the pressure
energy (static head) and Potential energy (elevation head) per unit
weight of the fluid at any
point remains constant” provided the flow is steady, irrotational,
and frictionless and the fluid
used is incompressible. This is however, on the assumption that
energy is neither added to nor
taken away by some external agency. The key approximation in the
derivation of Bernoulli’s
equation is that viscous effects are negligibly small compared to
inertial, gravitational, and
pressure effects. We can write the theorem as
Pressure head ()+ Velocity head ()+ Elevation (Z) = a constant
Where, P = the pressure.(N/m2)
r = density of the fluid, kg/m3
V = velocity of flow, (m/s)
g = acceleration due to gravity, m/s2
Z = elevation from datum line, (m)
Pressure head increases with decrease in velocity head.
P1/w+V1
2/2g+Z1= P2/w+V2
2/2g+Z2= constant
Where P/w is the pressure head
V/2g is the velocity head
Z is the potential head.
The Bernoulli’s equation forms the basis for solving a wide variety
of fluid flow problems such
as jets issuing from an orifice, jet trajectory, flow under a gate and
over a weir, flow metering by
obstruction meters, flow around submerged objects, flows
associated with pumps and turbines
etc.
The equipment is designed as a self-sufficient unit it has a sump
tank, measuring tank and a
pump for water circulation as shown in figure1. The apparatus
consists of a supply tank, which is
connected to flow channel. The channel gradually contracts for a
length and then gradually
enlarges for the remaining length.
In this equipment the Z is constant and is not taken for calculation.
Procedure:
1. Keep the bypass valve open and start the pump and slowly start
closing valve.
2. The water shall start flowing through the flow channel. The level
in the Piezometer tubes
shall start rising.
3. Open the valve on the delivery tank side and adjust the head in
the Piezometer tubes to
steady position.
4. Measure the heads at all the points and also discharge with help of
diversion pan in the
measuring tank.
6. Varying the discharge and repeat the procedure.
Hydraulics Bench
Introduction
In most of the experiments in this laboratory you will use a
hydraulic bench to determine the flowrate
of water through various sets of apparatus. The purpose of the
present experiment is to gain
some familiarity with the used of the hydraulic bench.
The hydraulic bench
The operating principles of a hydraulic bench are surprising simple.
It consists of the following
• A tank that contains a reservoir of water.
• A pump to remove water from the tank and direct it to a piece of
fluid apparatus.
• An on-off switch to start-stop the pump.
• A valve to control the rate at which water is pumped from the tank.
• An inlet in the top of the apparatus to collect water after it has
been used.
• A water-container immediately below the inlet in the top of the
hydraulic bench. The water
container also has a valve in its base that can be opened or closed by
a handle set into the
hydraulic bench.
• A lever arm connected to water-container. The lever arm has a
base upon which a set of
weights can be placed. The lever arms have a 3:1 mechanical
advantage, i.e. a 1.5 kg mass
of water is required to lift a 4.5 kg mass placed on the balance
Note, the weights that come with the weighing tanks give the
masses of the water in the containers.
• There are some sensors connected to an LED to detect the motion
of the lever arm past a
reference point.
Front view of one of the hydraulic
benches. The sets of weights are placed
on the base connected to the lever arm in
the centre of the photograph.
The on-off switch is located to the top
right of the bench with the control valve
located immediately to its left.
The weighing container is the white plastic
container in the centre of the tank.
Side-view of the hydraulic bench.
The lever arm is the metal bar sitting at
an angle. The lever to open/close the
base of the weighing tank is in middle of
the tank towards the top of the weighing
container.
• The operation of the hydraulic bench is relatively simple.
• The pump is started with the valve in the base of the weighing tank
open.
• Once you have got organized, close the valve in the base of the
weighing tank.
• The lever arm will rise and hit the sensor on the top rim of the
bench. You should start the
stop-watch the instant the arm hits the rim.
• You should then place an appropriate mass on the hanger at the
end of the lever arm. The
lever arm will then go down.
• The lever arm will start to rise again when the additional mass of
water in the weighing tank
approaches the mass placed on the hanger.
• Stop the stop-watch when the lever arm triggers the sensor again.
• The flow-rate is just the mass divided by the elapsed time.
Experiment
Set the flow rate using the outlet valve located at the front of the
hydraulic bench. The valve
should be about 55% open.
Measure the actual flow rate using the weigh tank in the hydraulic
bench and a stopwatch. Repeat
this measurement ten times. There should be two independent
measurements of the time taken to
fill the weighing tank. You should record your readings in a table. A
suggested Table design is
shown below
Run number Mass of water
collected (kg)
Collection time (kg) Weighing tank
flow-rate
(litre/sec)
• Determine the mean flow rate of water through the optical bench.
• Determine the standard deviation of the flow rate?
• To what precision do you think it is possible to determine the flow
rate?
• Was there any discernible change in your readings from run
number 1 to number 10.
Now open the valve fully and determine the maximum possible flow
rate of the hydraulic bench.
Bernoulli’s Theorem
Hydraulics Bench
Manometer
Osborne-Reynolds
Centrifugal Pump
Characteristics +
Accessories
Energy Losses In
Bends
Dead Weight
Calibrator
Pressure Sensors
Calibration System