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University of Nizwa
Department of Chemical and Petrochemical Engineering
Fluid Mechanics Laboratory (CHPE 307)
Laboratory Manual
i
Course Name: Fluid Mechanics Laboratory
Course Code: CHPE307
Credit: 1
Pre-requisite: CHPE207
SYNOPSIS: This course is a "hands-on" learning experience of the basic principles of chemical
engineering fluid mechanics relating to open channel and pipe flow such as
verification of Bernoulli's Theorem for steady flow of water, flow meter demonstration
(venturi meter, orifice meter and variable-area meter reading), flow over weir, fluid
friction measurement, center of pressure, metacentric height, Archimedes Principle
and basic properties of fluids in static condition.
The course consists of 2 hours laboratory work a week
A total of 10 experiments are assigned for the semester.
The students work in assigned groups.
Students are required to submit four (4) short individual lab reports and four (4)
long group reports. Individual report must be submitted one week after the
conduct of the experiment while the long report must be submitted after two
weeks. Laboratory reports must be made in accordance with the content
requirement and official format provided by the instructor.
Regular quizzes will be given before the start of the lab (pre quizzes) and after
lab reports were submitted (post quizzes )
The schedule of experiments for the whole term is announce at the first day of
the class. Group members are expected to familiarize with their experiment
before coming to the class. Lab Engineers assigned will assist the student in the
conduct of the experiment and in the proper operation of the equipment.
Late lab report will receive a reduction of 5% mark every day that is late. No
lab report will be accepted after one week late, thus will receive zero mark for
that report.
Copying and plagiarism of reports as well as falsification of experimental data
will receive strict warning and zero grade for that report.
Laboratory safety regulations will be strictly observed and followed during the
conduct of the experiments.
Weekly attendance is mandatory and included in the class grade
Assessments: Course Work: Lab Reports 40%
Quizzes 10%
In-Sem Exam 20%
Final Examination: 30%
ii
CONTENTS
LABORATORY
EXPERIMENTS
: Introduction (2 hours)
Lecture on the rules and regulations to be followed in the
laboratory. Discussions of the class requirement, report
format and familiarization with the lab equipment.
Distribution of the Lab Manuals.
1. Bernoulli's Theorem Demonstration (2 hours)
Investigation of the validity of Bernoulli equation when
applied to the steady flow of water in a tapered duct.
2. Flow Over Weirs (Rectangular and V-notch weir) (2 hours)
Study the characteristics of open-channel flow over a
rectangular and a V notch by determination of their
discharge coefficient
3. Hydrostatic Properties : Capillary Effect, Principles ( 2 hours )
Course Outcome(s) Program outcome University
Graduates
Attributes
1. Perform experimental verification of the theoretical
principles involve in fluid mechanics.
2. Critically analyze the results of the experiment and
identify possible causes of experimental errors or
deviation from the ideal value.
3. Operate under supervision the various laboratory
equipment and apparatus in fluid mechanics.
4. Develop technical communication skills .
5. Demonstrate team-work skills
iii
of U-tube Manometer and Effect of Flow on Free
Surface
Demonstrate the capillary effect, the principle of U-tube
manometer and the effect of flow on a free surface.
4. Hydrostatic Properties : Archimedes Principle and
Viscosity Measurement Using Ubbelhode Viscometer
( 2 hours )
Demonstrate the Archimedes Principle and determine the
buoyancy force. Determine a fuid’s viscosity using
Ubbelohde Viscometer.
5. Center of Pressure and Measurement of Metacentric
Height
( 2 hours )
To be able to locate experimentally the Center of Pressure in
a full and partially submerge inclide plane. To compute the
metacentric height of a floating body by determining the
center of gravity and center of buoyancy.
6. Flow Meter Demonstration ( 2 hours )
Observation of the operation and performance of different
flow meter devices ( i.e. venturi meter, orifice meter and
variable area meter) by determining the accuracy and energy
losses at different flowrates.
7. Fluid Friction Losses ( 4 hours)
Determination of the head losses in different pipe diameters,
sudden contraction and sudden enlargement of pipes,
different fittings and valves.
Total 18 hours
REFERENCES
Laboratory Manual in Fluid Mechanics
Text Book
iv
WORKING WITH SAFETY AND PRECAUTIONS IN THE
CHEMICAL ENGINEERING LABORATORY
Since you will be working with potentially dangerous chemicals and
apparatuses in the Chemical Engineering Laboratories there are a few
simple, but very important rules that you must follow:
1. READ THE LABORATORY INSTRUCTIONS BEFORE COMING TO
THE LABORATORY.
2. A LABORATORY COAT MUST BE WORN AT ALL TIMES DURING
LABORATORY EXPERIMENTS.
The laboratory coat must be buttoned up. Loose clothing like scarfs must be
tucked inside the laboratory coat and safety shoes must be worn in Unit
Operation Laboratory.
3. EATING, DRINKING ARE NOT ALLOWED IN THE LABORATORY.
Students are not allowed to stay inside the Laboratory if there are no
Laboratory Activities.
4. IN CASE OF ACCIDENT OR FIRE, FOLLOW INSTRUCTIONS FROM
THE LECTURER OR TECHNICIANS.
5. KEEP YOUR WORKING AREA AND GLASSWARES CLEAN AND
DRY BEFORE LEAVING THE LABORATORY.
6. OBSERVE PROPER HYGINE. WASH YOUR HANDS AFTER DOING
THE EXPERIMENT.
NOTE:
Failure to follow these rules may automatically and without warning result
in a deduction of marks. In repeated cases you may be asked to leave the
laboratory.
v
Chemical Engineering Laboratory Policies and Guidelines
Attendance
Attendance is mandatory and will affect your grade.
Lab Preparation:
All students are expected to read the lab manual experiment for that period before coming
to the class
Lab experiments might require advance preparation outside of the designated lecture and
lab periods. Groups that receive instructions or assignments for advance preparation
must complete the assignment prior to beginning the experiment. No group will be
allowed to begin experimentation unless all advance preparations are complete and
verified as such by the instructor.
Safety
No laboratory coat, no experiment
Safety glasses and gloves must be worn at all times when working in the lab.
Proper attire is required to participate in lab. Laboratory gowns should be worn
while performing the experiment.
Absolutely no food or drink is permitted in the lab.
The use of cell phones and portable music and video players during lab is strictly
prohibited.
Cleanliness and Housekeeping
University housekeeping staff are not required to clean and maintain the equipment. The
Fluid Mechanics and Heat Transfer Equipment uses water or air as the working fluid. In
some cases, performing an experiment will inevitably allow water to get on the
equipment and / or the floor. If no one cleaned up their working area after performing
an experiment, the lab would not be a comfortable or safe place to work in. No student
appreciates walking up to and working with a piece of equipment that another student or
group of students has left in a mess.
Consequently, students are required to clean up their area at the conclusion of the
performance. Cleanup will include removal of spilled water ( or any liquid), and wiping
the table top on which the equipment is mounted ( if appropriate). The lab should
always be as clean or cleaner than it was when you entered. Cleaning the lab is the
vi
students responsibility as the user of the equipment. This is an act of courtesy that
students who follow you will appreciate.
Lab Reports
Follow only the format provided by the Instructor. See the Department
Guidelines for Writing Lab Report provided by the Instructor for format and
content requirements. A report that is not according to the format will reduced
its mark
Individual mini lab reports are due exactly one week following completion of
experiments for each equipment.
Full reports are due exactly two week following completion of experiments
for each equipment
Policies on Late Reports
Late lab report will have 5 marks deducted on the total marks of every member
for everyday late.
No late report will be received after a week that is late
Academic Dishonesty
The group should ONLY work together on collection of the data. data analysis,
computation, discussion and conclusions are expected to be done individually.
Copies of analysis, computation, discussion and conclusions will received no
credit for individual report.
The information and data may be shared by all members in their individual
report
Falsification of experimental data or plagiarism will absolutely result in a grade of
zero for the lab
.
Lab Teams
The instructor shall group the students into 5 members each. All members of each group
are to participate fully in carrying out each experiment assigned to the team.
vii
Format and Mark Distribution for a Full Lab Report
Full Lab Report
Title Page
Summary
1. Introduction
2. Apparatus
3. Procedure
Figures and Tables
4. Data/
Results
5. Discussion
Objectives and background of
the experiment
6. Conclusion
7. Reference
viii
Use the following design when writing the formal lab reports. You are expected to know the
details of this design and to understand the logical sequence of ideas within it. It has a
corresponding marks that based from what is expected on each part.
Part of Report Content Maximum
Marks
Title Page Shows the title of the Experiment and some
important facts (name, dates,). Please use the
template provided for you.
5%
Summary One paragraph summary of the lab report, on its own
page, stating the purpose of the experiment or the
problem, major equipment used and the last sentence
should be the major conclusion (note the Verb
Tenses )
10%
1. Introduction A restatement of the objectives of the experiment
and background of the experiment. One to two
sentences only
5%
2. Apparatus - Equipment, instrumentation and materials used
during the experiment
5%
3. Procedure
This section briefly reports the steps that you
followed in carrying out the experiment. Do not
repeat word for word what is in the lab notes but
concisely summarise in your own words the key or
major steps which were taken in the experiment
10%
4. Data/Results Evidence collected during the experiment; numbers read
directly from laboratory instruments (clocks, rulers,
balances, etc., but not calculators). Data should be well
organized and tabulated when possible Use illustrations
(sample problems) to show how you converted DATA
into RESULTS. Use computers programs or
spreadsheets used in the analysis. Use care in scale
reading and use significant figures when taking
measurements. Develop a sense of how much data is
desirable. Understand the need for carrying out multiple
experiments and strive to get reproducible data when
practical. Do not hide or eliminate suspected faulty data
but present it. Later, in your CONCLUSIONS, you may
explain why you have decided not to use suspected errors
in your analysis.
Other forms of evidence, qualitative in nature, that may
be useful in the interpretation of QUANTITATIVE
DATA; for example, something unexpected that
happened during the carrying out of the PROCEDURE
that may affect your CONCLUSIONS. These
15%
ix
observations may be the only form of evidence collected.
Then a RESULTS section may be unnecessary, and
CONCLUSIONS will be based upon the
QUALITATIVE DATA.
Computation Show a sample computation 5%
5. Discussion The most important part of your report. In
discussion section you discuss the results by
commenting on the results obtained and interpreting
what the result mean. And explaining any results
which are unexpected. You need to:
identify any discrepancies and to state the
percentage error and analyze them
identify any sources of error in your
measurements
and if possible, suggest how your experiment
could have been performed more accurately
In some experiment, some questions are provided.
Please use this to guide you in discussion
35%
6. Conclusion This section states whether the aims of the
experiment were achieved or not, and briefly
summarizes the key findings. That is, concisely
discuss those things you know with confidence as a
result of lab experiment.
You can also comment on how closely your
measurements and calculations agree and summarize
the main reasons for any discrepancies. You can
also use this section to briefly describe suggestion
for future work including ideas for improving the
design of the experiment.
10%
7. References List down all reference materials that you use in
writing this lab reports (books, handbooks, websites,
etc )
100%
x
xi
Fluid Mechanics Laboratory (CHPE 307)
List of Experiments
1. Viscosity Measurement using Ubbelohde Viscometer .............. 1
2. Principle of U-Tube Manometer ................................................ 7
3. Flow Meter Demonstration ...................................................... 11
4. Centrifugal Pump ..................................................................... 19
5. Bernoulli’s Theorem Demonstration ....................................... 27
6. Fluid Friction in Pipes and Fittings .......................................... 35
7. Archimedes’ Principle Demonstration ..................................... 49
xii
1
1. Viscosity Measurement using Ubbelohde Viscometer
Objective
To determine the kiematic viscosity of given fluid using Ubbelohde Viscometer.
Theory
Viscosity is a fundamental characteristic property of all fluids. When a liquid flows, it has
an internal resistance to flow. Viscosity is a measure of this resistance to flow. Viscosity
can also be termed as a drag force and is a measure of the frictional properties of the
fluid. Viscosity is a function of temperature and pressure. Viscosity is expressed in two
distinct forms:
a. Absolute or dynamic viscosity ()
b. Kinematic viscosity ()
Dynamic viscosity involves a tangential force per unit area while the kinematic viscosity
does not involve force. The ratio between the dynamic viscosity and density is defined as
kinematic viscosity of fluid and is denoted by
;
density mass
viscositydynamic viscosityKinematic
Typical SI units of kinematic viscosity ( ) are m2/s or cm
2/s, the latter being referred to
as stoke (St). Standard SI units of dynamic viscosity () is N.s/m2 or kg/(m.s) or Pa.s.
Ubbelohde Viscometer
Ubbelohde viscometer is useful for the determination of the kinematic viscosity of
transparent Newtonian liquids in the range of 0.3 to 100,000 cSt. A Ubbelohde
viscometer has the same viscometer constant at all temperatures. This property is
advantageous when measurements are to be made at a number of different temperatures.
The liquid is induced to flow only down the walls of the bulb below the capillary, thus
forming a suspended level, ensuring that the lower liquid level is automatically fixed and
coincides with the lower end of the capillary
2
Using Ubbelohde Viscometer, the kinematic viscosity is calculated using the following
formula:
= K (t-y)
where = kinematic viscosity (mm2/s)
K = constant for respective viscometer
t = measured time
y = Hagenbach correction factor (refer to table 1)
Details of Ubbelhode Viscometer Ubbelohde Viscometers ref no.: 501 11
Viscometer capillary number: la
Capillary I.D: 0.95mm
Constant K approx.: 0.0507
Measuring range approx: 5 to 50 mm2/s
Equipment and Accessories
Ubbelohde Viscometer, Stop watch, water, hydraulic oil, dish washer solution
Set- up
Ubbelohde Viscometer Apparatus
Note: If air bubble forms in the capillary during the test, it is advisable to repeat the
measurement.
3
Ubbelohde Viscometer Diagram
Procedure
1. Place the Ubbelohde Viscometer on a level table carefully.
2. Prepare a solution of dish wash liquid with water. Take 40 ml of water in a beaker,
and slowly add 10 ml of dish wash liquid. Mix the solution (avoid bubble formation).
3. Transfer 15 ml of test sample to the Viscometer through filling tube (3) into reservoir
(4).
4. Connect a syringe to the capillary tube (1). Close the venting tube (2) by a finger or
rubber stopper. Steadily apply vacuum to capillary tube by pulling the syringe piston.
This will cause successive filling of the reference level vessel (5), the capillary tube
(1), the measuring sphere (8), and the pre-run sphere (9).
5. Discontinue the syringe suction. Open the venting tube.
6. Liquid column will separate at the lower end of the capillary (7) and form suspended
level at the dome-shaped top part (6).
7. Remove the syringe from tubing. Fluid begins to flow down through capillary.
8. Measure the time interval it takes the leading edge of the meniscus of sample to
descend from the upper edge of upper timing mark M1 to the upper edge of lower
timing mark M2.
9. Repeat step 4 to 8 for 2 times to get an averaged time interval.
10. Refer to the attached table (Column Ia) for Hagenbach correction factor (y).
4
Experimental Data and Results
Observations
Data Calculations & Results Time taken
Trial-1, t1
(s)
Trial-2, t2
(s)
Average, t =
(t1+t2)/2 (s) Constant, K
Correction
Factor, y Viscosity, = K(t-y),
mm2/s
0.0507
Calculations
Kinematic viscosity, = K (t-y) mm2/s
Where = kinematic viscosity (mm2/s)
K = constant for respective viscometer = 0.0507
t = measured time (s)
y = Hagenbach correction factor (refer to the table at the end of this experiment
under the column Ia)
Discussion Compare the kinematic viscosity determined in this experiment with that of pure water.
List at least two substances with viscosity higher than water.
Conclusion Using Ubbelhode viscometer, the kinematic viscosity of the given fluid was found to be:
-------------------mm2/s.
5
------------End of Experiment---------
6
7
2. Principle of U-Tube Manometer
Objectives
To demonstrate the working principle of U-tube manometer
To determine the pressure inside a vessel using U- tube water and mercury
manometers
Theory
Pressure measurement is one of the most common of all the measurements made on
systems. Pressure measurement is concerned with the determination of force per unit
area exerted by a fluid at a point.
Manometers
Manometer is a device used to measure the unknown pressure by balancing a column of
liquid against the pressure to be measured. Refer to Figure 1 for a standard U-tube
manometer. One leg of manometer is connected to the unknown process pressure, and the
other leg is open to atmosphere. The difference between the two column heights indicates
the pressure difference between the unknown process pressure, and the known
atmospheric pressure. If the density of manometer fluid is known, the unknown process
pressure can be calculated by doing a pressure balance between the two legs of the
manometer.
The unknown gauge pressure can be calculated using the following equation:
P = gh, where h = |h2-h1|
If the unknown pressure measured is vacuum pressure, the gauge pressure is P = -gh,
and h = |h2-h1|
In both the above cases, absolute pressure can be obtained by the following equation:
Absolute Pressure = Gauge Pressure + Atmospheric pressure
Note that Gauge pressure will be –ve in case of vacuum pressure.
8
Figure 1. U – Tube manometer measuring positive pressure
Equipment and Accessories U-tube water, and mercury manometers, and hand pump
Figure 2. Water and Mercury Manometers
9
Procedure
1. Fill the U-tube manometer with coloured water and mercury. Ensure the water level is
half of its full level.
2. Connect both of the U-tube manometers to the pressure vessel.
3. Open both the hand valves.
4. Connect the digital manometer’s high (+) port to the top part of the pressure vessel.
5. Connect the tube from the bottom of the pressure vessel to the hand pump. Lock the
tube to the hand pump.
6. Slowly apply pressure to the pressure vessel. Keep an eye on the water manometer.
Ensure the water is in safe zone. (Caution: Apply the pressure SLOWLY).
7. Close the hand valve which is located at the bottom of the pressure vessel to hold the
pressure.
8. Record the water height difference, and mercury height difference in the Table.
Data and Results
Observations Calculations
Manometer h1
(mm)
h2
(mm)
Differential
Height, h
(m)
Gauge
Pressure
in the
vessel, P
= gh
(kPa)
Absolute
Pressure
(kPa)
mercury
water
h
h
measured theoretical
Water
Manometer
13.5 Mercury
Manometer
Digital Manometer Readings
Digital manometer reading (kPa)
Digital manometer reading (cm Hg)
Digital manometer reading (m H2O)
10
Calculations
Differential Height, 1000
21 hhh
(m)
Gauge pressure inside the vessel, 1000
hgP
(kPa)
Where, = density of manometer fluid (kg/m3)
water = 1000 kg/m3; mercury = 13500 kg/m
3
g = gravitational acceleration (9.81 m/s2)
h = Differential height between manometer legs (m)
Absolute pressure = gauge pressure + atmospheric pressure
Atmospheric pressure = 100 kPa
Absolute pressure = gauge pressure (kPa) + 100 (kPa)
From the manometer readings calculate the ratio of differential heights = mercury
water
h
h
Also the theoretical ratio of differential heights can be calculated by the following
equation:
5.13100
13500
ρ
ρ
Δh
Δh
water
mercury
mercury
water
Discussion 1. Compare and discuss the pressures obtained using both the manometers and the
digital manometer.
2. Discuss the differences in h measured in both the manometers considering the
density differences between water and mercury.
3. Between the water and mercury manometers, which will be suitable for measuring
low pressures, and which will be suitable for measuring high pressures? Why?
Conclusion
The pressure inside a pressurized gas vessel was determined using both water and
mercury manometers, and the results were compared, and analyzed.
---- End of Experiment ----
11
3. Flow Meter Demonstration
Objectives To investigate the operation and characteristics of three different basic types of flow
meter - venturi meter, orifice plate, and variable area meter using Bernoulli's
equation.
To compare the theoretical volume flow rates with the directly measured flow rate.
To determine the head loss across each of the flow meter devices.
Theory Application of the Bernoulli’s equation yields the following result which applies for both
the venturi meter and the orifice plate.
Volume flow rateρ
Δp
A
A
ACQ d 2
1
2
1
2
2
Where 2
2p
g h
and h - head difference from manometer connected to the flow meter (m)
g - the acceleration due to gravity, 9.81 m/s2
Cd - the discharge coefficient for the meter, Cd for Venturi meter = 0.98
Cd for Orifice plate = 0.63
A1 - area of the test pipe upstream of the meter, in m2
A2 - throat area of the meter, in m2
Cd is necessary because of the simplifying assumptions made when applying the
Bernoulli equations. Values of this coefficient are experimentally determined.
The energy loss that occurs in a pipe fitting (so-called secondary loss) is commonly
expressed in terms of a head loss (h, metres), and can be determined from the manometer
readings.
In the experimental set-up, the venturi meter, variable area meter and the orifice plate are
installed in a series configuration to permit direct comparison. Flow through the test
section is regulated using a flow control valve. This together with the bench control
valve permits variation of the system static pressure. Pressure tappings in the circuit are
connected to eight-blank manometers which are arranged to give a set of readings around
the flow meters in the system.
Equipment Required: Hydraulic bench, flow meter apparatus, stop watch
12
Set-up:
Figure 1. Flow meter Demonstration Apparatus with the Hydraulic Bench
Figure 2. Schematic of the Flow meter apparatus
13
Technical Data
The following dimensions are used in the appropriate calculations:
For the Venturi Meter
Upstream Pipe Diameter = 0.03175 m
Hence
Cross sectional area of upstream pipe, A1 = 7.92 x 10-4
m2
Throat diameter = 0.015 m
Hence
Cross sectional area of throat, A2 = 1.77x 10-4
m2
Upstream Taper = 21 degrees
Downstream Taper = 14 degrees
For the Orifice Plate
Upstream Pipe Diameter = 0.03175 m
Hence
Cross sectional area of upstream pipe, A1 = 7.92x10-4
m2
Throat diameter = 0.020 m
Hence
Cross sectional area of throat, A2 = 3.14 x 10-4
m2
The manometers are connected so that the following pressure differences can be obtained
h1 - h2 Venturi meter reading
h1 - h3 Venturi loss
h4 - h5 Variable area meter loss
h6 - h7 Orifice plate reading
h6 - h8 Orifice plate loss
14
Procedure for Setting-up
1. Place the flow meter test rig on the bench and ensure that it is level (necessary for
accurate readings from the manometers)
2. Connect the inlet pipe to the bench supply and the outlet pipe into the volumetric tank
3. Start the pump and open the bench valve and the test rig flow control valve, to flush
the system.
4. Bleed air from the pressure tapping points and manometers.
5. Check that all manometer levels are on scale at the maximum flow rate (full-scale
reading on the variable area meter)
6. These levels can be adjusted further by using the air bleed screw or the hand pump
supplied.
7. Fix the flow rate and take the necessary readings
Procedure Taking Set of Results
1. Start at the maximum flow rate, fix the flow rate and record all manometer heights
and the variable area meter reading.
2. Carry out a timed volume collection using the bench tank by closing the ball valve
and measuring (with a stopwatch) the time taken to accumulate a known volume of
fluid in the tank as measured from the sight-glass.
3. Repeat these measurements at various flow rates so that 5 sets of data are collected.
Note: Ensure that you understand the operating principle of each of the three flow meters
15
Experimental Data
Trial
No.
Flow Measurement Variable Area
Meter Reading
(l/min)
h1 (mm)
h2 (mm)
h3 (mm)
h4 (mm)
h5 (mm)
h6 (mm)
h7 (mm)
h8 (mm) Volume, V
(litre)
Time
taken, t
(sec)
1
2
3
4
5
Calculations & Results
Trial
No.
Measured
Flow Rate
Qact
(m3/sec)
Calculated Flow Rate
(m3/sec)
Flow Rate Error (%) Head Loss (m)
Variable
Area
Meter, a
Orifice ,
o
Venturi,
v
Variable
Area
Meter
Ha=(h4-h5)/
Orifice Ho=h6-h8
(m)
Venturi Hv=h1-h3
(m)
Variable
Area
Meter
Qa
Orifice
Qo
Venturi
Qv
1
2
3
4
5
16
Calculations
Measured flow rate, t
VQact
1000 (m
3/s)
Variable Area Meter
Flow rate shown by variable area flow meter,
601000
Re
adingMeterAreaVariableQa (m
3/s)
Flow Rate Error for orifice plate, 100Q
)Q(Qε
a
aacta
(%)
Head loss across variable area flow meter, ha = h4-h5 (m)
Orifice Plate
Flow rate calculated from Orifice readings,
O
d
o hg
A
A
ACQ
2
1
2
1
2
2 (m3/s)
For orifice plate, Cd = 0.63 (-)
ho = (h6-h7)/1000 (m)
Flow Rate Error for orifice plate, 100Q
)Q(Qε
o
oacto
(%)
Head loss across orifice plate, ho = h6-h8 (m)
Venturi Meter
Flow rate calculated from venture readings,
V
d
v hg
A
A
ACQ
2
1
2
1
2
2 (m3/s)
For venturi, Cd = 0.98 (-)
ho = (h1-h2)/1000 (m)
Flow Rate Error for venture meter, 100Q
)Q(Qε
v
vact
v (%)
Head loss across venture meter, hv = h1-h3 (m)
17
Graphs and Charts Plot the head loss across variable area meter (ha), orifice plate (ho), and venturi meter (hv)
against actual flow rate in the following way:
ha, ho, and hv (y-axis) vs Qact (x-axis)
Discussion 1. Comment on the differences in accuracy of the flow meters. Could these differences
be due to experimental error?
2. In your data, which is the most accurate meter? Compare with the literature.
3. Why does the variable area meter show less variation in head loss with flow rate than
the other two meters?
4. Which meter incurs the smallest pressure loss?
Conclusion The flow was measured using variable area meter, venturi meter, and orifice plate, and
they were compared with respect to accuracy of flow rate, and the pressure loss across
each meter.
The ------------------------ meter gave least % error between measured flow rate and
calculated flow rate.
The ------------------------------ meter gave least head loss
---- End of Experiment ----
18
19
4. Centrifugal Pump
Objectives
To conduct the operation of centrifugal pump at different operating conditions
To develop the characteristic curves for the centrifugal pump, and determine the
operating parameters at the Best Efficiency Point (BEP).
Theory
The centrifugal pump is a radial flow rotodynamic machine, wherein fluid enters the rotor
or impeller at one radius and leaves at a larger radius. The fluid is drawn into the centre
of a rotating impeller and is thrown outwards by centrifugal action as shown. As a result
changes in kinetic, potential and pressure energy occur. Thus any understanding of the
pump behavior and performance assessment requires measurement or calculation of these
quantities.
Figure 1. Liquid Flow Path inside a Centrifugal Pump
The general relationship between the various forms of energy based on the First Law of
Thermodynamics applied to a unit mass of fluid flowing through the pump is expressed
as
FdpvoldzgvdWS ..)2/( 2
Where: sW is the mechanical shaft work performed on the fluid
)2/( 2vd is the changed in kinetic energy of the fluid
20
dzg. is changed in potential energy of the fluid
F the frictional energy loss as heat to the surroundings or in heating the fluid
itself as it travels from inlet to outlet
dpvol. changed in pressure energy equal to /)( 12 pp . Where is
constant density of the incompressible fluid and 2p refers to the pump
discharged outlet and 1p to the pump inlet
The three terms of the right hand side represent the useful work or what we called the
total dynamic head H of the pump by converting the units from work per unit mass to
“head” expressed as a length.
)./)(()()2/)(( 1212
2
1
2
2 gppzzgvvH
The term "head" refers to the elevation of a free surface of water above or below a
reference datum.
On this apparatus the pipe diameters are similar, and so we can simplify the equation
where gph / . The gauges measure the inlet and outlet pressures in terms of a head
h.
)()( 1212 hhzzH
The relative vertical positions of the inlet and the outlet are represented by the )( 12 zz
which is also called the head difference, dH
Therefore, the head generated across the pump can be written as
)( 12 hhHH d
The datum head correction factor for each measurement position will be adopted and
given in this experiment.
Centrifugal Pump Characteristics
The best way to describe the characteristics of a centrifugal pump is through the use of
the Head/Flow characteristics. The pump can be operated at reduced speed to show the
effect on the performance. However, the performance of a centrifugal pump reduces
dramatically with speed and changes in readings will be extremely small when operating
below approximately 30 Hz
21
Figure 2. Centrifugal Pump Characteristic Curves
Equipment and Accessories Hydraulic bench, Centrifugal pump unit, stopwatch
kW
Input
22
Set-up for Single Pump
Figure 3. Centrifugal Pump with Hydraulic Bench
Figure 4. Schematic of a Centrifugal Pump Operation
The inlet of the centrifugal
pump should be connected
to the sump drain of bench
Sump drain should
be fully open
The outlet on the top of the
pump should be connected to
the discharge manifold.
Outlet gauge
Inlet gauge
Centrifugal pump
Hydraulic Bench
Discharge control valve
23
Procedure 1. Ensure that the Centrifugal pump has been connected to the Hydraulic bench as
shown in the diagram for single pump operation.
2. Open the hydraulic bench sump valve and close the control valve on the hydraulic
bench.
3. Switch ON the power to the centrifugal pump inverter
4. Press the ‘RUN’ key on the motor speed controller then increase the speed of the
pump motor to the maximum (50 Hz) using the Up (▲) key.
5. Fully open the discharge control valve.
6. Record the inlet head (hi), outlet head (ho)
7. Record the power input (Wi) in kW from the panel on the pump.
8. Record using a stop watch, the time (t) taken to collect known volume (V) of water
(example: 10 litres).
9. Slightly reduce the discharge control valve, and record the readings mentioned in
above steps 6, 7, 8.
10. Continue the steps 6-9 and record at least 5 sets of readings including now flow
(discharge control valve fully closed).
11. Repeat the above procedure at pump speed of 40 Hz
12. When finished, press the “STOP” button to stop the pump
13. Disconnect the electrical supply to the equipment
Calculations Complete the calculations using the formula given on the table, and show the details of
calculations for at least one volume flow rate.
24
Table 1. Data and Results Observations Calculations/Results
Motor
Speed
(Hz)
Trial
No.
Flow Measurement Inlet Head
ih
(m of
water)
Outlet
Head
oh
(m of
water)
Pump Power
Input, iW
(kW )
Flow Rate Q
= V/(1000×t)
(m3/s)
Head
developed,
H = ho-hi
(m of water)
Pump Power
Output
Wo =
HQg/1000
(kW)
Efficiency
=
(Wo/Wi)×100
(%)
Volume
of
Water, V
(litre)
Time to
Collect, t
(s)
50
1
2
3
4
5 0 0 -1 0 0 0
40
1
2
3
4
5 0 0 -1 0 0 0
25
Graphs
Graph-1: For 50Hz operation, on a single graph plot H, Wi, and (y-axis)
vs Q (x-axis)
Graph-2: For 40Hz operation, on a single graph plot H, Wi, and (y-axis)
vs Q (x-axis)
Note: Refer to the graph shown in Figure 2 of theory part for model graph.
Discussion
1. Write your interpretation by analyzing the Graph-1, and Graph-2
2. What is the best efficiency point (BEP) in the experiment, what is the significance of
knowing the BEP in engineering design and operation? Provide the details from the
graph in the Table 2.
Table 2. Details of best operating conditions based on Best Efficiency Point (BEP)
Motor
Speed
Operating parameters at BEP from the graph
Efficiency,
(%)
Discharge Rate, Q
(m3/s)
Head developed, H
(m)
Power Input,
Wi
(kW)
50 Hz
40 Hz
Conclusion
The centrifugal pump was operated at two different speeds such as 50 Hz, and 40 Hz.
The pump characteristic curves were obtained from the experimental data. From the
characteristic curves, the BEP (Best Efficiency Point), and the corresponding conditions
were found.
The operating conditions at the BEP are as follows:
Pump Speed BEP Flow Rate Head Developed (H)
(Hz) (%) (m3/s) (m)
40
50
----End of Experiment---
26
27
5. Bernoulli’s Theorem Demonstration
Objectives
To investigate the validity of the Bernoulli’s equation using a venturi meter
To calculate the volume flow rate through venturi, and compare it with the measured
flow rate
Theory
A venturi meter is a tube with a constricted throat that increases velocity and decreases
pressure. It is used for measuring the flow rate of compressible and incompressible fluids
in pipeline.
The Bernoulli’s equation represents the conservation of mechanical energy for a steady
incompressible, frictionless flow.
2 2
1 1 2 21 2
2 2L
p v p vz z H
g g g g
Where:
LH = Head loss
p = static pressure detected at a side hole
v = fluid velocity, and
z = vertical elevation of the fluid, hence
1z = 2z for a horizontal tube
This equation states that at two sections of a flow field, the total energy remains the same
provided that there is no loss or gain of energy between the two sections.
With the Armfield apparatus, the static pressure head p, is measured using a manometer
directly from a side hole pressure tapping
The manometer actually measures the static pressure head, h, in meters which is related
to p using the relationship :
ph
g
This allows the Bernoulli equation to be written in a revised from, ie:
2 2
1 21 2
2 2
v vh h
g g
28
The velocity related portion of the total pressure head is called the dynamic pressure
head.
Using the hydrostatic equation applied to the air-over-liquid manometer of the figure, the
pressure drop and the head loss are related by
hg
pp
21
By combining the continuity equation with the Bernoulli equation
2211 VAVAQ
It can be shown after simplification that the volume flow rate through the venturi meter
4
1
4
2
2
1
2
D
D
hgAQth
Equipment and Accessories
Hydraulic bench, Bernoulli’s Apparatus Test Equipment, Stopwatch
Set-up
Bernoulli's Theorem Apparatus with the Hydraulic Bench
29
Parts of the Bernoulli's Theorem Apparatus
Procedure - Set-up
1. Level the apparatus on the hydraulic bench so that its base is horizontal
2. Connect the water inlet and outlet
3. Ensure that the rig outflow tube is positioned above the volumetric tank, in order to
facilitate timed volume collections.
30
4. Connect the rig inlet to the bench flow supply
5. Close the bench valve and the apparatus flow control valve
6. Start the bench pump
7. Gradually open the bench valve to fill the test rig with water
8. If there are air trapped in the tubes, bleed the manometers
9. In order to bleed air from pressure tapping points and manometers, close both the
bench valve and the rig flow control valve.
10. Open the air bleed screw and remove the cap from the adjacent air valve.
11. Connect a length of small bore tubing from the air valve to the volumetric tank.
12. Open the bench valve and allow flow through the manometers to purge all air from
them
13. Tighten the air bleed screw and partly open the bench valve and test rig flow control
valve
14. Open the air bleed screw slightly to allow air to enter the top of the manometers (you
may need to adjust both valves in order to achieve this)
15. Re-tighten the screw when the manometer levels reach a convenient height
Note: the maximum volume flow rate will be determined by the need to have the
maximum (h1) and minimum (h5) manometer readings both on scale.
Procedure – Taking a Set of Results
1. Set the initial flow rate by leveling the h1 in the maximum and the h5 manometers on
the minimum scale. This is the maximum volume flow rate
2. Take the readings of the static heads h1 , h2, h3, h4, h5 and h6 manometers when the
levels have steadied at the this maximum flow rate.
3. Performed a timed volume collection to determine the volume flow rate by closing
the ball valve and use a stopwatch to determine the time taken to accumulate a
known volume of the fluid in the sight glass of the tank
4. Reduce the volume flow rate to give the h1 – h5 head difference of about 50 mm.
31
5. Repeat the whole process 2-3
6. Repeat the whole process when h1 – h5 difference approximately 25mm
7. When finish close the bench flow control valve then switch off the bench pump.
The Venturi Meter Diagram
32
Table: Data and Results Observations Calculations/Results
Flow measurement Distance
into Duct
(m)
Area of Duct
A
(m2)
Static
Head, h
(mm)
Velocity
v = Q/A
(m/s)
Actual
Flow
Rate,
Qact
(m3/s)
Dynamic
Head
v2/2g
(m)
Total
Head h0
(m)
Qth
(m3/s)
Q Error
(%)
Total Head
loss
h1 – h6
(m)
Volume
V
(litre)
Time, t
(s)
10
h1 0.00 490.9 x 10-6
h2 0.0603 151.7 x 10-6
h3 0.0687 109.4 x 10-6
h4 0.0732 89.9 x 10-6
h5 0.0811 78.5 x 10-6
h6 0.1415 490.9 x 10-6
10
h1 0.00 490.9 x 10-6
h2 0.0603 151.7 x 10-6
h3 0.0687 109.4 x 10-6
h4 0.0732 89.9 x 10-6
h5 0.0811 78.5 x 10-6
h6 0.1415 490.9 x 10-6
10
h1 0.00 490.9 x 10-6
h2 0.0603 151.7 x 10-6
h3 0.0687 109.4 x 10-6
h4 0.0732 89.9 x 10-6
h5 0.0811 78.5 x 10-6
h6 0.1415 490.9 x 10-6
33
Figures to be prepared
1. Plot the flow rate Qact and Qth as a function of Head loss h (m) with head loss in the
x-axis.
2. Plot the dynamic head, and static head vs. Qact (x-axis).
Calculations
1. Actual flow rate, t
litreincollectedvolumeVQact
1000
)( w (m
3/s)
2. Total head
Total Head = Static Head + Dynamic Head
3. Theoretical flow rate, Qth
4
1
4
5
5
1
2
D
D
hgAQth
Where A5 = 78.5×10-6
m2, D1 = 25 mm, D5 = 10 mm, and h = h1 – h5
3. % Q error = 100
th
thact
Q
4. Show the complete calculations
Discussions
1. Comment on the possible causes of Q error.
2. What is the relationship between flowrate and the pressure drop?
3. Comment on the graph of Total Head vs velocity
4. Based on the results, how are the pressure head, velocity head , cross-sectional area
and head loss related. Does it verify the Bernoulli's Equation. ?
Conclusion
Bernouli’s theorem was demonstrated using Bernoulli’s equation across a
venturi.
--- End of Experiment ---
34
35
6. Fluid Friction in Pipes and Fittings
Objectives To determine the pressure or head loss in different pipe diameters, sudden contraction
and sudden enlargement, different fittings and different valves
To determine the flow condition in the pipe either is laminar or turbulent flow.
Theory - Pressure Loss (∆Pf) or Head Loss (∆hf) in Pipes due to Friction
Based on Bernoulli’s theorem, the total head of a fluid flowing in a pipeline can be
expressed as follows:
zg
u
g
Ph
2
2
Where g
P
is pressure head (m)
g
u
2
2
is dynamic or velocity head (m)
z is potential or elevation head (m)
When a real fluid flows through pipes, energy is lost inevitably due to frictions which
occur as a result of viscous drag. Fluid friction produces eddies and turbulence, and these
form of kinetic energy are eventually converted into thermal energy. Losses in energy can
be expressed in term of pressure or head loss.
There are different forms of equations to calculate the losses due to friction in pipes, and
fitting, which are presented under the heading calculations
Energy Losses across Sudden Enlargement & Sudden Contraction Figure 1 shows the changes in flow pattern, velocity and pressure due to sudden
decrease/increase in flow area.
Figure 1. Fluid Flow Pattern in Sudden Contraction (decrease in flow area) & Sudden
Enlargement (increase in flow area)
Energy Losses in Fittings
36
A piping system is normally made up of several connective components. All these
components are generally referred to as fittings. Fittings are being used for a number of
purposes such as to change the direction of flow of a fluid (bends) as well as to regulate
the flow rate (valves) and etc. However, all these fittings inevitably impose resistance on
the flowing fluid, resulting in losses of energy. All these losses have to be taken into
account in order to develop an effective piping system.
a) Losses in Bends, Elbows and Junctions
Energy is lost whenever direction of flow in a pipe is altered. Referring to a 90o bend as
shown in Figure. When fluid flows in a curved path, there is a radial force acting
inwards on the fluid to provide inward acceleration. This is accompanied by an increase
in pressure near the outer wall of the bend, staring from point A and rising to a maximum
at B. Furthermore, there is a reduction in pressure near the inner wall giving a minimum
pressure at C and a subsequent rise from C to D. Between A and B and between C and D,
the pressure increases in the direction of flow (adverse pressure gradient). A large radius
of curvature of the bend will cause separation of the flow from the boundary and
therefore energy losses in turbulence. The magnitude of these losses is thus mainly
dependent on the radius of curvature of the bend. Energy losses also arise from secondary
flow where it is set up at right angles to the pipe cross section which increases the
velocity gradient and hence the shear stress of the wall.
A pipe bend, elbow or junction therefore causes an additional head loss. This extra loss is
conveniently expressed in term of number of velocity heads loss, given as follow:
Where k is the coefficient of friction
37
The value of k depends on the total angel of bend as well as the relative radius of
curvature R/d (where R is the radius of curvature of pipe centre and d is the pipe
diameter). k also increases with surface roughness but varies slightly with Re-.
b) Miter Bend
A Mitre or 90o elbow bend (shown in Figure 5) is used where there is insufficient space
for large radius. This bend would result in a greater head loss as the direction of flow is
changed abruptly. R/d for it is 0 while k is approximately 1.1.
c) In-line Strainer
In-line strainer is a type of fitting used to mechanically remove unwanted solids from
flowing fluids by means of a perforated or wire mesh straining element. It is installed in
pipelines to protect pumps, meters, control valves, steam traps, regulators and other
process equipment. The pressure drop or head loss across it is also given by equation (8).
38
Approximate loss coefficients (k) for some commercial pipe fittings are being given as
follows:
Losses in Valves
Various types of valve are being installed in a piping system to regulate or control fluid
flow. Common ones are gate, globe and ball valves. Each has their own characteristics
and applications. However, all of them have the common problem, which is causing
additional losses of head. Generally, the more intricate the passage through which fluid
has to pass, the greater the head loss. For turbulent flow, the head loss can be represented
by the same equation (8): ∆hf = k (u² / 2g) . Here, u represents the mean velocity in the
pipe. The k factor values depend critically on the exact shape of the flow passages.
Figures below show the structure of some of the commonly found valves:
Equipment
Fluid Friction Apparatus
39
Set-up
Fluid Friction Apparatus
40
Procedure for Set-up
1. Place the apparatus on a level table.
2. Plug the 3 pin plug of the apparatus to the laboratory 240 VAC power supply. Switch
ON the power supply.
3. Fill the water tank of the apparatus until 3/4 of its full capacity.
4. Switch ON the trainer main power supply. Ensure the water pump is running.
5. Allow the water to flow into all the pipes of the trainer.
6. Connect the digital manometer to any two of the pressure points. Ensure the digital
manometer is working properly.
7. Disconnect the digital manometer.
8. Switch OFF the trainer main power supply.
9. The apparatus is ready to use.
Procedure – Measurement of head loss across pipes and fittings
1. Place the apparatus on a level floor and near to the water supply.
2. Plug the 3 pin plug of the apparatus to the laboratory 240 VAC power supply. Switch
ON the power supply.
3. Fill the water tank of the apparatus until 3/4 of its full capacity.
4. Open all the valves of the trainer.
5. Switch on the pump, and wait for 2 minutes for the flow to stabilize
General Procedure for all measurements
6. Based on the pipe or fitting for which the head loss is to be measured, make sure that
water flows through only that particular pipe/fitting by closing all the other valves.
7. Adjust the flow rate to 2 GPM using variable area flow meter.
8. Switch on the differential pressure meter, and make the reading Zero, by pressing the
“Zero” button.
9. Connect the differential pressure meter to the ports between the pipe section or pipe
fitting for which the pressure drop is to be measured, and record the pressure drop in
the unit of kPa.
41
Table 1. Friction loss in different Diameter Pipes
Observations Calculations
Flow Pact
(kPa)
Flow rate, Q
(m3/s)
Velocity, V
(m/s)
Re
(-)
Friction Factor, f
(-) Pth
(kPa)
% Error in P
Pipe: 1/8” (ID 10.3 mm); Flow Area, A = 8.3323×10-5
m2
2 GPM
4 GPM
6 GPM
Pipe: 1” (ID 18 mm); Flow Area, A = 2.5447×10-4
m2
2 GPM
4 GPM
6 GPM
Table 2. Friction loss across sudden contraction and sudden enlargement Observations Calculations
Flow Pact
(kPa)
Flow rate, Q
(m3/s)
Velocity, V (m/s) Friction Factor, Kc Pth
(kPa)
% Error in P
Sudden Contraction (1/2"-1/8"); d1 = 17 mm; d2 =10.3 mm
2 GPM
4 GPM
6 GPM
Sudden Enlargement (1/2"-1/8"); d1 = 10.3 mm; d2 =17 mm
2 GPM
4 GPM
6 GPM
42
Table 3. Friction loss across elbows and bends
Observations Calculations
Flow Pact
(kPa)
Flow rate, Q
(m3/s)
Velocity, V
(m/s)
Friction factor, K Pth
(kPa)
% Error in P
90 Elbow
2 GPM
4 GPM
6 GPM
45 Elbow
2 GPM
4 GPM
6 GPM
Long Radius Bend
2 GPM
4 GPM
6 GPM
Mitre Bend
2 GPM
4 GPM
6 GPM
43
Table 4. Friction loss across valves
Observations Calculations
Flow Pact
(kPa)
Flow rate, Q
(m3/s)
Velocity, V
(m/s)
Friction Factor, K Pth
(kPa)
% Error in P
Gate Valve
2 GPM
4 GPM
6 GPM
Ball Valve
2 GPM
4 GPM
6 GPM
44
Calculations Common data for all calculations:
Density, = 1000 kg/m3; dynamic viscosity (water), = 9×10
-4 Ns/m
2;
Unit Conversion: 1 GPM = 6.31×10-5
m3/s
Friction Losses for flow through pipes Convert the flow rate (Q) from GPM to m
3/s using the conversion factor.
Flow area, 4
2DA
(m
2)
Reynolds Number,
DVRe
V velocity of water (m/s)
density of water (1000 kg/m3)
dynamic viscosity of water ( 0.0009 Ns/m2)
D = inner diameter of pipe (m)
Identify the flow regime based on the value of Reynold’s number using the following
classification:
Laminar flow: Re < 2000; Transition region: 2000 > Re < 4000
Turbulent flow: Re > 4000
Head loss for turbulent flow (Re>4,000) by using Darcy’s Equation
Friction factor for smooth pipes (Blausius equation), 25.0Re
3164.0f (-)
Head loss,
g
V
d
lfh f
2
2
(m)
l – length of the pipe (m); assume length = 1 m
V – velocity of fluid (m/s)
d – diameter of the pipe (m)
g – acceleration due to gravity (m/s2)
Theoretical pressure drop due to friction, 1000
f
th
hgP
(kPa)
Calculate the % error between theoretical pressure drop and measured pressure drop as
%100||
th
thact
P
PPError
Show the complete calculation for at least one flow rate, one pipe size
Graphs On a single graph, plot theoretical pressure drop (y-axis) vs Flow rate in GPM (x-axis)
for both the pipes, and mark the diameter on the respective lines.
45
Friction Loss across Sudden Contraction & Sudden Expansion
Sudden Contraction For sudden contraction, d1 = 17 mm = 17×10
-3 m, and d2 = 10.3 mm = 10.3×10
-3 m
Convert the flow rate (Q) from GPM to m3/s using the conversion factor.
Flow area, 4
2
22
dA
(m
2)
Velocity, 2
2A
Qu (m/s)
Calculate 2
1
2
2
2
1
2
2
1
2
4
4
d
d
d
d
A
A
(-)
Read the value of Kc from the below table (Table 5) for corresponding A2/A1
Head loss across sudden contraction, g
uKch f
2
2
2 (m)
Theoretical pressure drop due to friction, 1000
f
th
hgP
(kPa)
Calculate the % error between theoretical pressure drop and measured pressure drop as
%100||
th
thact
P
PPError
Show the complete calculation of at least one flow rate.
Table 5
A2/A1 0.0 0.2 0.4 0.6 0.8 1.0
Kc 0.5 0.48 0.42 0.32 0.18 0.00
Sudden Enlargement For sudden expansion, d1 = 10.3 mm = 10.3×10
-3 m, and d2 = 17 mm = 17×10
-3 m
Convert the flow rate (Q) from GPM to m3/s using the conversion factor.
Flow area, 4
2
11
dA
(m
2)
Velocity, 1
1A
Qu (m/s)
2
2
1
2
1 12
A
A
g
uh f (m)
Theoretical pressure drop due to friction, 1000
f
th
hgP
(kPa)
Calculate the % error between theoretical pressure drop and measured pressure drop as
%100||
th
thact
P
PPError
46
Show the complete calculation of at least one flow rate.
Graphs On a single graph, plot theoretical pressure drop (y-axis) vs flow rate in GPM (x-axis) for
sudden contraction and sudden expansion, and label the respective lines.
Friction loss across elbows and valves Use the following procedure to calculate the head loss across all elbows and valves.
For all elbows, inner diameter = 16.14 mm = 0.0164 m
Flow Rate, Q = 2 GPM = 2 × (6.31×10-5
) 1 GPM = 6.31×10-5
m3/s
Flow area, 4
2d
A
(m2)
Velocity, A
Qu (m/s)
g
uKh f
2
2
(m)
Theoretical pressure drop due to friction, 1000
f
th
hgP
(kPa)
Calculate the % error between theoretical pressure drop and measured pressure drop as
%100||
th
thact
P
PPError
Table 6. Friction loss coefficients for elbows
Fitting K, Fiction
Coefficient
Valve Type K, Fiction
Coefficient
Mitre Bend 3.0928 Globe Valve 15.083
90 Elbow 1.9423 Gate Valve 1.5597
45 Elbow 0.8240 Ball Valve (fully
open) 0.7998
Long Radius Bend 0.6110 Needle Valve 324.71
Graphs
1. On a single graph, plot theoretical head loss (y-axis) vs Flow rate in GPM (x-axis)
for all elbows, and label them.
2. On a single graph, plot theoretical head loss (y-axis) vs Flow rate in GPM (x-axis)
for all valves, and label them.
47
Discussion
1. Compare the actual and theoretical pressure drops on each experiment. What are the
common causes of error?
2. Compare the difference in pressure drop for different pipe diameters, and explain the
possible reasons for the difference.
3. Compare the difference in pressure drop across different elbows, and explain the
possible reasons for the difference.
4. Compare the difference in pressure loss across different valves, and explain the
possible reasons for the difference.
Conclusion The frictional loss across pipes with diameters, and pipe fittings such as sudden
contraction, sudden expansion, and different valves were measured, and compared with
the theoretically calculated head loss.
---- End of Experiment ----
48
49
7. Archimedes’ Principle Demonstration
Objectives
To demonstrate the Archimedes Principle
To determine the buoyancy force
Theory
When an object is immersed in water, it feels lighter. In a cylinder filled with water, the
action of inserting a mass in the liquid causes it to displace upward. In 212 B.C., the
Greek scientist Archimedes discovered the following principle: an object that is
immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by
the object. This became known as Archimedes’ principle.
The weight of the displaced fluid can be found as
W = mg (N)
Substituting m = V in the above equation,
W = V g (N)
W – Buoyancy force (N)
m – Mass of fluid displaced by the immersed object (kg)
V – Volume of fluid displaced by the immersed object (m3)
g – Acceleration due to gravity (m/s2)
It is important to note that the buoyancy force does not depend on the weight or shape of
the submerged object, only on the weight of the displaced fluid.
Equipment and Accessories
Lever balance, set of weights, measuring cylinder (100 ml), ruler.
50
Set- Up
Figure: Archimedes Principle - Equipment and Accessories
Procedure
1. Place the lever balance unit on a level table.
2. Hanger both of the weight hangers together with 200 g of weight to the lever balance.
Do measure the bottom area of the weight hanger.
3. Ensure the lever balance is in balance position where the pointer pointing at the red
line. Else, adjust the adjustable nut located at the side of the balance.
4. Place a beaker to one side of the weight hanger. Fill the beaker with water until the
lever balance becomes unbalanced.
5. Apply some small weight to the top pan of the lever balance until it becomes balance.
Note down the amount of weight applied. (Ensure the weight is not fully submerged
into the water, else, reduce the amount of water in the beaker).
6. Measure the height between the bottom surface of the weight hanger and water
surface. Record this water level.
7. Calculate the theoretical upward force and compare this result with weight applied.
Data and Results
51
Observations Calculations/Results
Weight
applied, m
(g)
Height, h (bottom
of weight to water
surface)
(mm)
Diameter of
the weight
hanger, d
(mm)
Weight applied
Wact,
(g)
Volume of
water
displaced, V
(m3)
Theoretical
Buoyancy Force,
Wth
(N)
Calculations
Measured buoyancy force, gm
Wact1000
(N)
Where m – Weight applied (kg)
Theoretical Buoyancy Force
Area of the immersed weight, 2
4dA
(m
2)
where d - diameter of the weight hanger ( m)
Volume of water displaced, V = Ah
where h – height between the bottom of the weight hanger immersed in water and
the surface of the water (m)
Wth = V g (N)
Where - Density of water (1000 kg/m3)
G – Gravitational acceleration (9.81 m/s2)
% Error %100||
th
thact
W
WW
Discussion: Write your comments on the differences in the results, and what are the
possible causes of error?
Conclusion: The Archimedes’ principle was demonstrated, and the buoyancy force was
found to be:
-------------- N (measured)
-------------- N (calculated)
---- End of Experiment---
