Department of Civil Engineering
Polytechnic Institute of New York University
FLUID MECHANICS
LABORATORY MANUAL
(5th Edition, Spring 2011)
This manual is an important reference manual for laboratory
procedures, report preparation, and grading policies for Fluid
Mechanics Laboratory course in the Civil Engineering Department.
Students should retain a copy of this manual and refer to it frequently
for use.
By Sungho Yoon, Ph.D.
TABLE OF CONTENTS
Page
The Importance of Effective Communication.......................................................................... 3
Course Policies............................................................................................................................ 3
Laboratory Attendance Policy................................................................................................... 3
General Laboratory Policies...................................................................................................... 3
General Guidelines for Laboratory Reports ........................................................................... 4
General Rules.................................................................................................................. 4
Format and Organization................................................................................................. 5
Style................................................................................................................................. 5
Technical Content............................................................................................................ 5
Common Errors and Omissions ...................................................................................... 5
Grading of Laboratory Reports & Required Format ............................................................. 7
Description of Report Sections................................................................................................... 8
Exercise on the Plotting of Graphs…………………………………………………………… 11
Laboratory #1 Fluid Properties…………………………………………………………… 12
Laboratory #2 Manometers………………………………………………………………. 13
Laboratory #3 Hydrostatic Force…………………………………………………………. 15
Laboratory #4 Venturi Meter …………………………………………………………….. 18
Laboratory #5 Impact of Jet ………………………………………………………………
20
Laboratory #6 Flow in Pipe Networks ……………………………………………………
22
Laboratory # Extra Open Channel Flow ……………………………………….…………. 24
THE IMPORTANCE OF EFFECTIVE COMMUNICATION
Today’s employers expect their engineers to be able to communicate efficiently and effectively.
Reports you prepare for a future employer that are poorly organized and difficult for the employe
r to follow are not likely to promote your advancement in that organization. By developing an apt
itude for clear and efficient technical writing and reporting, you will be more valuable to your em
ployer and to society than if you know only the technical side of engineering. This guide should h
elp you toward that goal, both in school and after graduation. While different organizations and i
ndividuals may have slightly different standards or practices, you will find that those presented h
ere are highly desirable. The practices outlined here are also consistent with accepted standards f
or the publication of technical papers.
The chief criterion of a good report is that it shall convey what the investigator has accomplished
and the conclusions he or she has drawn in a way that is clear, concise, neat, and easily understan
dable by the reader. Your report must show a good understanding of the principles upon which th
e experiment was based. A report that is poorly organized and difficult for the instructor to follo
w is not likely to inspire a high grade.
COURSE POLICIES
The following policies apply to Fluid Mechanics Laboratory Course you will take in Civil Engine
ering. You will need to keep this manual and refer to it.
LABORATORY ATTENDANCE POLICY
No absences will be permitted without medical excuse or other bona fide causes. Students may b
e required to complete any work missed due to absence.
GENERAL LABORATORY POLICIES
1. At the beginning of any lab course, the instructor will discuss the specific safety guidelines for
that particular lab. This may include a written handout, safety video, training by the safety depart
ment, etc. This training may be followed by a quiz to ensure complete transfer of this essential in
formation.
2. No alterations of equipment will be made without the consent of the instructor or TA. Suggesti
ons for improving the operation of equipment are always welcome.
3. Any necessary equipment (glassware, thermometers, etc.) and tools, if not already available, m
ust be obtained from an instructor, teaching assistant or laboratory technician.
4. At the end of each laboratory period, groups are responsible for ascertaining that water, air, ele
ctricity, equipment items, etc., are turned off.
5. All glassware, tools, stopwatches, etc., must be returned to the proper cabinets and locked at th
e end of each laboratory period. Such items have a remarkably high vapor pressure and will
evaporate completely if left standing in the open. Each group member is responsible for all equip
ment assigned to the group. Failure to return equipment will result in financial assessment.
6. Do not "borrow" any tools or equipment from other laboratories. If anyone outside of your gro
up "borrows" tools or equipment belonging to the Lab, report it to an instructor.
7. Students are expected to become familiar with the operation of all experimental equipment. Be
sure you understand the operation of all equipment before beginning an experiment. If you have
any questions, ask the instructor or TA.
8. All data are to be recorded in laboratory notebooks. You may be required to produce this
notebook at any time. It must be kept well organized and neat. Pages must be dated and signed. T
his is particularly important for invention disclosures. The use of paper towels or other slips of pa
per for recording data will not be tolerated. Some general guidelines for recording data in the lab
oratory are itemized below:
a. Make a sketch of the experimental set-up and write a brief description.
b. Record initial experimental conditions, such as ambient or sample temperature, base pressure i
n vacuum system, materials used, time of day etc.
c. Record actual measurements, not calculated analyses. This is very important when you have to
analyze anything that went wrong in the experiment. If the data is processed rather than raw, it be
comes more difficult to deconvolute the data and pinpoint the problem.
d. Record anything of significance that happens during the experiment. The more remarks you ha
ve in your notebook, the better you will be able to recall the experiment when you have to write t
he lab report.
9. Please notify the TA or instructor when the supply of an expendable material runs low or when
something is broken. Irresponsible usage of equipment or supplies (film, etc.) may result in finan
cial assessment to the group.
10. All reports assigned must be submitted to complete the requirements of the course. An incom
plete report will not be averaged with other reports to give a passing grade.
GENERAL GUIDELINES FOR LABORATORY REPORTS
Some guidelines for the contents and organization of a good lab report are presented below.
See page 4 for the required format and pages 4 - 7 for a detailed description of each section.
General Rules:
1. A technical report will be submitted for each project by each student unless otherwise instructe
d.
2. Proofreading of laboratory reports is considered to be mandatory, not optional. Spellchecking
alone (by means of a word processor) is strongly recommended, but it does not constitute sufficie
nt proofreading.
3. Reports are due one week after the completion of the experiment. Late reports will be docked a
t the rate of 10% for each laboratory day past the due date. No reports more than three weeks late
will be accepted.
4. All laboratory reports become the property of the Department and must be returned to the
laboratory instructor before a final grade for the course will be issued.
5. Each student is responsible for the originality of his/her technical report and the data utilized.
Copying from unidentified sources such as prior reports is cheating, and it may result in automati
c failure of the course by those involved. Review the University policy on plagiarism.
6. A complete outline of the report format and description of each section is given on pages 4 - 7.
Check with your instructor to determine if changes in format are necessary.
Format & Organization
Organize your report into logical sections with titles for each section. Number all pages except th
e title/cover page. The results you collect should be presented by means of appropriately numbere
d Figures and Tables. These results should be integrated into the Results & Discussion section an
d the Conclusion section of your report and should NOT be reported as a separate section. Numb
er ALL pages except the title page. Each figure must be numbered sequentially and have a captio
n. Each figure must be mentioned or discussed in the text. Similarly, ALL tables must be number
ed sequentially and must be mentioned or discussed in the text. With few exceptions you are exp
ected to consult other reference materials, e.g., textbooks, handbooks, journal articles, or other cl
ass materials, and these should be referenced in the proper manner. A nomenclature section defin
ing all symbols used in the report (e.g. α, ω, E) should be included. If only a few symbols are use
d, they may be defined in the text rather than in a separate section. See the Description of Report
Sections for more specific instructions for each of these sections.
Style
Check for correct spelling, grammar, punctuation, etc. Watch for improper paragraphing. One se
ntence is rarely sufficient to constitute a paragraph. Your sentences and thoughts should be
clearly stated without confusion on the part of the reader.
Technical Content
Technical content deals primarily with the Experimental Procedure, Results, and Discussion secti
ons of your report. You must adequately describe how you obtained the data that you are reportin
g. With few exceptions, it is expected that you will consult other reference materials, e.g., textbo
oks, handbooks, etc., and this reference material will be discussed in your report. You must give
sufficient information to ensure that someone could repeat your experiment and obtain similar res
ults. ALL of your collected data should be presented in your report, ensuring that anyone could
check your calculations. The data you report will frequently include data collected by your cl
assmates in addition to data collected by you. Discuss your results and address any of the "Stu
dy Questions" or "Supplementary Questions" given with the laboratory handout. With few except
ions, your answers to the study or supplementary questions should be included in the Discussion
section and/or in the Conclusion section and should not be attached as an Appendix. You should
also provide pertinent information on difficulties you encountered, if any, and suggestions for av
oiding possible problems.
Common Errors and Omissions
1. Some of the most common errors that students commit in lab reports involve Tables or Figures
. Be aware that ALL figures and tables must be numbered. All figures should have figure caption
s. All tables should have titles. All figures and all tables should be specifically referred to in at le
ast one location in the text.
2. Another common mistake is to neglect page numbering. ALL pages of the report, except for th
e Title page should be numbered, but count the title page as page 1.
3. You will be told in advance which format to use for individual experiments. If you are not told
, please ask.
4. Never have any writing that presents itself upside down when the report is held in the normal
reading position, or when it is held with the left or bound edge at the top.
5. Avoid using color in your graphs or figures. Even if you print your report using a color printer
your report may be copied in black and white and colors do not reproduce well. If you do use col
or check to see how it reproduces.
GRADING OF LABORATORY REPORTS & REQUIRED FORMAT
The final laboratory grade will be determined by averaging the grades received on individual labo
ratory reports. Each laboratory report will be graded on the basis given below. Please see the foll
owing section for detailed descriptions of each section. The Appendices contain additional
information. Slight variations in the format may be permitted at the discretion of the instru
ctor.
Required Report Format:
Order of Presentation in the Rreport
Title Page
Abstract
Table of Contents
Introduction
Theory
Experimental Apparatus & Procedure
Result & Discussion
Results
Discussion
Summary & Conclusions
References
Assigned %
5
10
10
Suggested order of Writting
1st
3rd
2nd
4th
6th
5th
20
25
15
5
7th
8th
9th
10th
10
DESCRIPTION OF REPORT SECTIONS
Title
Page
–
The title page should include a title for the experiment being reported, the author(s), and the na
mes of the group leader and group members if appropriate. The title page should also indicate the
date on which the report is due, the date it is actually submitted, the name of the instructor, and t
he name of the TA who supervised the experiment.
Abstract
–
A good abstract is brief, about 200 to 300 words. The goal is to provide the reader with some id
ea of the objectives of the report and a summary of the most important results and conclusions.
Table
of
Contents
–
The Table of Contents lists the divisions and subdivisions of the report and the page numbers o
n which they appear.
Introduction
–
The introduction should state the subject, purpose and scope of the work. It should provide the r
eader with enough background information to explain the motive for the work, including conditio
ns and limitations under which the experiments were performed. If necessary, include literature r
eferences on the subject. A mere restatement of the objective on the lab handout is not sufficient.
Theory
–
Any theory or equations needed in analyzing or computing report data should be included. This
section may be combined with the introduction if brief, or presented in a separate section, if lengt
hy. State only the principles upon which the equations are based and provide references.
Experimental
Apparatus
–
The testing equipment and materials used in the project should be described in this section in su
fficient detail so that the reader would know what specific equipment or instrument was used. Inc
lude line drawings, circuit diagrams, flow sheets, etc., if appropriate for special apparatus or arra
ngements. Drawings are not necessary for common items (balances, graduated cylinders, etc.) wh
ich can be simply identified by size or type. Photographs are acceptable, but only if they print wel
l.
Experimental
Procedure
–
Procedures used should be described in sufficient detail and clarity that someone else could repe
at the experiment and obtain similar results. Include for example, time required to reach steady st
ate, time between measurements, length of an individual experiment or measurement, number of
measurements taken, sampling techniques, etc. Measurements of pressures, flow rates, temperatu
res should be described here as well. This section is often combined with the previous section.
Results
–
All of the data you collect must be presented as either Tables or Figures as appropriate, in this s
ection. Figures include photographs, photomicrographs, graphs, charts, drawings, etc. Tables mus
t be sequentially numbered using Roman numbers. Figures must be sequentially numbered using
Arabic numbers. If the results are presented in a separate section from the discussion, then this se
ction would be simply a presentation of the data or results, without any interpretation of it. Unles
s otherwise instructed you should present your results together and integrated with a discussion a
s described below. ALL of your Tables and Figures should be specifically referred to by number
in the text of your discussion. You should not have any Tables or Figures that are not mentioned i
n the text of your report. Tables and Figures should appear after their first mention in the text. If s
mall they may be inserted between or within a paragraph. Larger Tables or Figures may be placed
on a separate page, and that page should be numbered in sequence with other pages. In addition
to a number each table or figure should have an informative title or caption, or legend, so that eac
h
figure
or
table
is
selfexplanatory. There should be no need for the reader to refer back to the text for necessary inform
ation. This is very important. Never have any writing that presents itself upside down when the re
port is held in the normal reading position, or when it is held with the left or bound edge at the to
p.
Tables
–
If tables are less than a page long, they may be run in the text, in other words, it is not necessary
to place a ¼ page table on a page by itself. When possible, avoid continuing tables from one pag
e to the next. If you must continue a table on the next page you must repeat the column headings.
Abbreviations may be used in the column and row headings, but the nature of the quantities bein
g listed must be clear. For tables the number and caption appears above the table not below. Be s
ure to include the units of any tabulated values. Tables are numbered strictly with Roman number
s.
Figures
–
Avoid using color in your graphs or figures. Even if you use a color printer your report may be c
opied in black and white and colors do not reproduce well. Unlike tables, figure numbers and cap
tions must appear underneath the figure. In most engineering reports graphical presentation of the
results is overwhelmingly employed because of the ease of showing trends, scatter of the points
and as an aid in correlating the data. Consequently, well prepared graphs (figures) are essential fo
r writing an intelligent discussion. It is preferable to use appropriate graphing software or a sprea
dsheet with graphing capabilities such as Microsoft Excel. Each graph should be considered an in
dependent unit and should be
understood with little or no reference to the rest of the report. It should not be necessary to refer t
o another page or a nomenclature table to learn what the symbols or the plotted lines represent, it
should be clearly indicated on the graph. Additional requirements for acceptable graphs are given
in Appendix A (pages A-12 and A-13).
Discussion
–
This is perhaps the most important part of the report, for it represents your interpretation of the r
esults of the experiment. The results should be presented in graphical form wherever possible, bu
t tables are also effective. If there are any calculations, they should be presented here. For instanc
e, in the example shown above, the film resistivity can be calculated from the sheet resistance by
a simple formula that should be shown. The resistivity can be plotted against the process pressure
, thus showing the effect of pressure on resistivity. Frequent references should be made to figures
, tables and equations, and an analysis of the data should be included. Sample calculations are us
ually better presented in an appendix. Compare your results with theory or previous work and dis
cuss points of similarity or divergence. Evaluate trends in the results and any conclusions that can
be drawn. Development of conclusions must begin in this section where they can be supported b
y logical argument, even though they will be dealt with exclusively in another section. In the eve
nt of poor results, explain how the experiment could be modified to obtain satisfactory ones. Be s
ure to present a logical and practical approach for these improvements. This important section d
emonstrates your thinking and understanding of what you intended to do.
Summary
&
Conclusions
–
This section is a recapitulation of the most important points made in the discussion and is intend
ed to leave the reader with a strong impact and provide a ready reference. It is not a copy of the
abstract. Be brief but complete. Some prefer to present these points as a numbered or bulleted lis
t (use complete sentences). Incorporate a discussion of study questions if any were included on th
e lab handout, especially if these help you to formulate the conclusions that you have drawn. For
maximum credit, you should attempt to show that you have understood the objectives and the pri
nciples involved. How does the material you learned in another class, found in another textbook,
or read in the library relate to this experiment? In other words show some original thinking and a
nalysis. Treat the abstract and conclusions with respect. Scientists and engineers often read these
first to see if the rest of the report is worth reading.
References – References must be provided for the work done.
Exercise on the Plotting of Graphs
Example - Raw sampling data of load (P) and elongation (L):
P (Kips/in2)
40
20
5
15
35
a)
b)
c)
L (in)
0.00134
0.00067
0.00018
0.00051
0.00115
P (Kips/in2)
3
30
10
42
25
L (in)
0.00011
0.00099
0.00033
0.00142
0.00083
Plot elongation as a function of load (P is independent variable).
Determine the empirical equation describing this relationship using graphical
methods.
Determine the equation using least square methods.
Homework - Raw sampling data of flow-rate (Q) and stream depth (H):
Q (gpm)
1
3
4
6
9
12
a)
b)
c)
d)
Notes:
1.
2.
3.
4.
5.
6.
H (ft)
38.8
50.6
71.6
87.7
107.5
123.7
Q (gpm)
16
20
25
30
40
50
H (ft)
142.9
159.7
178.9
195.8
225.8
252.2
Q(gpm)
75
100
200
300
400
500
H (ft)
309.8
357.9
506.3
620.1
716.0
800.5
Plot flow-rate as a function of stream depth using values of Q and H given.
Plot log(Q) vs. log(H) on rectangular paper.
i)
Using the graph determine empirical relation between Q and H:
solve log(Q) = a + b*log(H)
ii)
Solve log(Q) = a + b*log(H) using least squares.
Plot Q vs. H on log-log paper.
i)
Using the graph determine K and m in Q = K*Hm.
What is the relationship between a and K, and why?
Independent variable on horizontal axis, dependent on vertical.
All graphs must have title and both axes must be labeled (including units).
Straight edge or french curve must be used.
Use least squares to determine slope and intercept, unless stated otherwise.
When using log paper use appropriate number of cycles.
If graphs are computer produced, insure that they are consistent with the previous notes—
Delete any irrelevant information that the computer generates.
Lab 1 — Properties of Fluids
Purpose:
To determine the viscosity of an oil using a fall sphere viscometer.
Apparatus:
a)
b)
c)
d)
Long, clear tube
Spheres of known diameter
Oil sample
Thermometer
Procedure:
1. Place oil in long tube.
2. Mark a distance on the tube, making sure that the top mark is not too close to the oil surface.
3. Drop sphere of known diameter into oil, and measure time needed to cover distance marked.
4. Measure temperature and specific gravity of the oil.
Equations:
If the sphere is traveling at its terminal velocity over the entire marked distance, and if the
Reynolds number (Re) of the sphere is small enough to ensure that laminar flow dominates, then
Stokes law may be utilized to determine the viscosity.
 s   D 2

18 U
where:
is the dynamic viscosity in poises,
s is the specific weight of the sphere,
D is the diameter of the sphere, and
U is the velocity of the sphere.
(note: This equation was developed assuming (1) coefficient of drag (CD
1)
Re and (2) Re <
Calculations:
1.
Determine the following for each size sphere (S.G.glass = 2.5):
a)
S.G., U (in m/sec), and s (in N/m3) of sphere,
b)
the dynamic viscosity of the oil ( oil) in Poises,
c)
the kinematic viscosity of the oil ( oil) in Stokes,
d)
the Reynolds number (Re = oilUD/ oil).
Discussion:
1. Compare the results of (b) to the viscosity figures in Appendix A of text and comment.
2. How could this experiment be modified for more accurate viscosity measurement?
3. Why is not the top mark too close to the oil surface?
LAB 2 - Principles of Manometers
Purpose:
Utilize manometers to determine specific weight (), density (), and specific
gravity (S.G.) of unknown fluids and to verify hydrostatic principles.
Procedure:
1.
a)
b)
c)
Add water to the manometer and record initial positions.
Add unknown fluid #1 to right leg and record positions.
Add unknown fluid #2 to left leg and record positions.
a)
b)
c)
Add unknown fluid #3 to the manometer and record initial positions.
Add water to right leg and record positions.
Add approximately ___ inches of water to left leg and record positions.
2.
Calculations:
1.
2.
3.
Compute  (in lb/ft3),  (in slug/ft3), and S.G. of all three unknown fluids.
Compare calculated results from (1) with published values (use text or other reference)
and guess what unknowns could be.
Using the data from procedure (1a) and (1b), predict the position of the (water) free
surface in the right leg when ___ inches of water is added to the left leg. Compare the
prediction with your data from (1c).
LAB 2 - Principles of Manometers (cont.)
Water with Fluid
(1a)
(1b)
(1c)
Lab 3. HYDROSTATIC PRESSURE APPARATUS
F1-12
1. Objective
To determine the hydrostatic thrust acting on a plane surface immersed in water when the
surface is partially submerged or fully submerged.
To determine the position of the line of action of the thrust and to compare the position
determined by experiment with the theoretical position.
2. Method
By achieving an equilibrium condition between the moments acting on the balance arm of
the test apparatus. The forces acting are the weight applied to the balance and the hydrostatic
pressure on the end face of the quadrant.
3. Equipment Required
In order to complete the demonstration we need a number of pieces of equipment.
 The F1-12 Hydrostatic Pressure Apparatus (including set of weights)
 Source of clean water (typically F1-10 Hydraulics Bench)
 A jug (not supplied)
 Calipers or ruler, for measuring the actual dimensions of the quadrant, if desired (not sup
plied
For siphoning water:
 A beaker, measuring cylinder, or similar container of water of similar height to the flotati
on tank
 A length of small bore flexible tubing
4. Equipment Set Up
For improved accuracy of results, measure the dimensions B, D of the quadrant end-face
and the distance H and L and record the values for future reference. Position the empty F1-12
flotation tank on the F1-10 Hydraulics Bench or other suitable level surface, then adjust the
screwed feet until the built-in circular spirit level indicates that the tank is level in both planes.
Position the balance arm on the knife edges and check that the arm is free to swing. Locate the
empty weight hanger in the groove at the end of the balance arm. Move the counter-balance
weight until the balance arm is horizontal, indicated by the central index mark on the beam level
indicator.
5. Procedure
Add a small mass (typically 50g) to the weight hanger.
Close the drain valve at the end of the tank then slowly add water to the tank. This can be
done in one of two ways:
Water can be poured into the tank from a suitable receptacle such as a jug or water may
be pumped into the flotation tank from the F1-10 Hydraulics Bench using a flexible tube attached
to the quick release outlet fitting in the bed of the channel.
Fill the flotation tank with water initially until the balance arm rises. Avoid wetting the
balance arm or the quadrant above the water level in the tank.
After initially filling the tank, small adjustments of water level are best performed using a
jug, allowing time for the water to settle before taking readings.
Alternatively, set a beaker, measuring cylinder or similar container full of water beside
the tank. Fill the flexible tube with water, and hold the ends sealed (a thumb over each end is
suitable). Place one end below the water surface in the cylinder and the other end into the tank
via the triangular cut-out at the pivot end. This will set up a siphon system. Water can be added
to the tank by pouring it into the vessel using the jug, then allowing time for the water levels to
balance. Siphoning allows greater control over the water entering the tank, and produces less
disturbance of the water within the tank.
Add water until the hydrostatic thrust on the end-face of the quadrant causes the balance
arm to rise. Ensure that there is no water spilled on the upper surfaces of the quadrant or the
sides, above the water level. Continue to add water until the balance arm is horizontal, checking
this by aligning the flat of the balance arm with the central mark on the level indicator. You may
find it easier to slightly over-fill the tank, and obtain the equilibrium position by opening the
drain cock to allow a small outflow.
When the arm is horizontal read the depth of immersion from the scale on the face of the
quadrant. Care should be taken to ignore the meniscus by moving the head up and down until the
eye is sighing along the true surface of the water.
Repeat the above procedure for different load increments by adding further weights to the
weight hanger. The weights supplied allow increments of ten, twenty, and fifty grams to be used,
depending on the number of samples required. Fifty-gram intervals are suggested for an initial set
of results, which will give a total of nineteen samples.
Continue until the water level reaches the top of the upper scale on the quadrant face.
Repeat the procedure in reverse, by progressively removing the weights.
Note any factors that you think are likely to affect the accuracy of your results.
6. Results
All readings should be recorded as follows:
Constants
Height of End Face:
Width of End Face:
Length of Arm:
Height to Pivot:
Variables
Mass
Added
M
(kg)
Measured
Turning
Moment
(Nm)
D
B
L
H
(m)
(m)
(m)
(m)
Depth
Hydrostatic
Thrust
d
(m)
F
(N)
Distance
To Centre
Of
Pressure
h
(m)
Turning
Moment
(Nm)
7. Conclusions
Comment on the variation of thrust with depth. Comment on the relationship between the
depth of the centre of pressure and the depth of immersion. For both of the above, comment on
what happens when the plane has become fully submerged. Comment on and explain the
discrepancies between the experimental and theoretical results for the depth of centre of pressure.
Lab 4 - Flow through a Venturi Meter
Purpose:
To investigate the pressure distribution and determine the flow coefficient of
aventuri meter.
Procedure:
1.
2.
3.
4.
Start water flow and adjust (add/release) air to the manifold to keep the manometers on
scale.
Manipulate the openings of the supply and control valves to obtain the maximum
difference between manometers A (entrance) and D (throat).
Record all manometer readings for two trials only—Record manometers A and D for
remaining trials. Also record the mass of water collected and the time required to
collect the water.
Reduce flowrate by adjusting control valve, obtaining a smaller manometer drop, and
repeat step (3).
Calculations:
1.
2.
3.
4.
5.
Calculate the ideal and actual differential pressures (in millimeters of water column, mm–
w.c.) along the venturi meter, i.e., at points A through D—Set manometer D to 0 mm–
w.c. and reference all differential pressures from manometer D.
For run 1, plot both the ideal and actual differential pressures against the distance from A
through L on the same rectangular graph and comment. Repeat this step for run 2.
For each run compute the following:
a)
Actual flow rate (Q) in m3/s,
b)
Velocity at A (VA) in m/s,
c)
The drop in pressure head between inlet and throat sections in meters (
=hA –
hD),
1/2
d)
in m1/2, and
e)
Flow coefficient of the venturi (CV).
1/2
Plot Q against
on a rectangular graph. Find the empirical equation, and use this
equation to find the average value of CV.
Plot CV against VA on a rectangular graph and comment.
Notes:
1.
Use SI units (e.g., m/s, m3/s).
2.
For repetitive calculations show one set of calculations.
3.
Tabulate results.
Lab 4 - Flow through a Venturi Meter (cont.)
Manometer (Typ.)
A
B
C
E
D
K
J
H
G
F
L
Flow Direction
Venturi
Sketch: Venturi Meter with Manometer Tubes
Data:
Manometer Tube
A
B
C
D
E
F
G
H
J
K
L
Diameter, Di (mm)
Area, Ai (mm2)
Distance from A, (mm)
Run #
1
2
3
4
5
6
7
8
9
10
Mwater
t
A
0
B
C
D
E
F
G
H
J
K
L
Lab 5. IMPACT OF A JET
F1-16
1. Objective
To investigate the reaction forces produced by the change in momentum of a fluid flow.
2. Method
By measurement of the forces produced by a jet impinging on solid surfaces which
produce different degrees of flow deflection.
3. Equipment
In order to complete the demonstration we need a number of pieces of equipment.
 The F1-0 Hydraulics Bench which allows us to measure flow by timed volume collection.
 The F16 Impact of Jets Apparatus with 4 flow deflectors, having deflection angle of 30, 9
0, 120 and 180 degrees.
 A stopwatch to allow us to determine the flow rate of water (not supplied)
4. Technical Data
The following dimensions from the equipment are used in the appropriate calculations. If
required these values may be checked as part of the experimental procedure and replaced with
your own measurements
Diameter of nozzle
d = 0.008
m
Hence
Cross sectional area of nozzle
A=5.0265 x 10-5
m2
5. Procedure – Equipment Set Up
Remove the top plate (by releasing knurled nuts) and transparent cylinder from the jet
impact test rig and check and the exit diameter of the nozzle. Replace the cylinder. Screw one of
the four flow deflectors (having identified its deflection angle) onto the end of the shaft. Locate
the accessory in the channel of the hydraulic bench then connect the inlet tube to the bench quick
release connector.
Replace the top plate on the transparent tank but do not fit the three knurled nuts.
Using the spirit level attached to the top, level the transparent tank by adjusting the feet.
Replace the three knurled nuts then tighten in sequence to retain the top plate level –
indicated by the spirit level. Care must be taken not to over tighten the knurled nuts, as this will
damage the top plate- the nuts should only be tightened enough to level the plate. Ensure that the
vertical shaft is free to move and supported by the spring beneath the weight pan.
6. Procedure - Taking a Set of Results
With no weights on the weight pan adjust the height of the level gauge until it aligns with
the datum line on the weight pan. Check that the position is correct by gently oscillating the pan.
(The pan should come to rest with the level gauge aligned with the datum line once more.) Place
a mass of about 0.4kg on the weight pan and open the bench valve to produce a flow. Adjust the
valve position until static equilibrium is achieved with the weight pan datum line aligned with
the level gauge (check again by gently oscillating the pan).
Observe (and note) the flow behavior during the tests.
Now carry out a measurement of volume flow rate using the volumetric tank. This is
achieved 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. You should
collect fluid for at least one minute to minimize timing errors. Repeat this measurement twice to
check for consistency and then average the reading.
Repeat this procedure for a range of masses applied to the weight pan.
Then repeat the whole test for each of the other three flow deflectors.
Note: The 30 degree target demonstrates the reduced forces at small deflection angles. Comparis
on with theory at this reduced deflection angle will be poor at reduced flow rates.
Nozzle
Dfelctor
Diameter Type
Voume
Time
Collected to
Collect
α
V
(degrees) (m3)
t
(sec)
Mass
Flow
Applied Rate
(m)
W
(kg)
Velocity Velocity2 Force
Qt
v
3
(m /sec) (m/sec)
v2
(m/s)2
Fy
(Newtons)
Calculated Slope
Slope
From
From
Theory
Experiment
7. Application of Theory
Plot a graph of velocity2 against applied mass. Compare the slope of this graph with the
slope calculated from theoretical. Comment on the agreement between your theoretical and
experimental results and give reasons for any differences. Comment on the significance of any
experimental error.
Lab 6 - Flow in Pipes and Pipe Fittings
Purpose:
To study the friction losses in pipes.
Procedure:
1.
The pump is turned on and off by pushing the black and red buttons.
2.
When starting the pump, be sure that the discharge valve is closed.
3.
The switch to the left of the digital read-outs is used to turn the meters on and off.
4.
Before you begin, look carefully at the layout of the pipe runs.
5.
9 different pipe runs for this experiment and only one runs is examined at a time.
6.
The pipe runs are containing different fittings and some pertinent information is given in
the proper order.
Pipe run (type of fittings)
Number of fitting
45 degree elbows
Straight
Long returns (180 degree)
Short returns (180 degree)
Open gate valves
Open globe valves
Run tees
90 degree tees
90 degree elbows
12
4
12
5
5
12
16
16
Total length of pipe
(from flange to flange)
15.33 ft
13.625 ft
66.8125 ft
24.208 ft
17.8438 ft
12.875 ft
12.71875 ft
11.3125 ft
17.729 ft
The pipes are drawn copper and have an OD of 0.625 inches and an ID of 0.527 inches.
The venturi meter display is calibrated to read the differential pressure in inches of water.
The display for the pressure drop across the fitting is calibrated to read the differential pressure in
inches of mercury.
Calculations:
1.
Using the data collected
a)
Flow rate
b)
Velocity
c)
Head loss
d)
Friction factor
e)
Reynold's number.
2.
Plot ∆h against V on log-log paper, and determine its empirical equation. What can you
say about the type of flow?
3.
Plot friction factor against Reynold's number on log-log paper, and compare it with the
appropriate curve from the Moody diagram (in text).
4.
Using the data, determine the average loss coefficient for the elbow.
5.
Plot pipe fitting and valve loss coefficients vs. Q on the same rectangular graph. What
do you observe?
Notes:
1.
2.
3.
4.
Use English units (e.g., cfs, ft, and ft/s).
For repetitive calculations show one set of calculations.
Tabulate results.
Use temperature of 70OF if needed.
Extra Lab – Open Channel Flow
Propose
To
evaluate
surface-wave
speed,
friction
change effects in a channel flow of rectangular cross section.
effects
and
area-
Procedure
1. Fill the channel with water up to a certain depth. When the water is still, create a disturbance a
nd measure its propagation velocity. Repeat the same experiment for three different depths
2. Place two different bumps, one at a time, on the channel bottom with either negative or positiv
e slope. Run the channel at two different speeds, for each bump, corresponding to subcritical and
supercritical upstream conditions. Observe the change in the surface level due to the presence of t
he bump
3. Design and execute an experiment where the flow passes smoothly from subcritical to supercri
tical conditions through the critical state. Measure the flow rate and the flow depth at three statio
ns corresponding to the three flow regimes.
4. Design and execute and experiment where the flow passes from supercritical to subcritical conditions through a
hydraulic jump. Measure the flow rate and the flowdepth before and after the jump.
Background
Many flows in nature occur with a free surface, such as in an open channel, where the principal d
riving force is gravity. Surface waves can form in flows with a free surface. The speed of a single
wave, c, is analogous in many respects to the speed of a sound wave in compressible fluid medi
um, a, and is given by, c = (gy)1/2. The propagation of disturbances in openchannel flow depends on the value of the Froude number, Fr, of the flow defined as,
Fr = V/(gy)1/2
where V is the mean velocity of the flow and y is the local depth. Open channel flow may be clas
sified on the basis of Froude number: (1) Fr < 1, the flow is subcritical and disturbances can trav
el upstream so downstream conditions can affect the flow upstream. (2) Fr = 1, the flow is critica
l (3) Fr > 1, the flow is supercritical and no disturbances can travel upstream thus downstream co
nditions cannot be felt upstream. These regimes of flow behavior are qualitatively analogous to t
he subsonic, sonic, and supersonic regimes of gas flow.
The specific energy, E, is defined as,
E = V2/2g + y = Q2/2gA2 + y
where Q=VA is the volume flow rate. At the minimum value of specific energy, Fr=l, correspond
ing to critical flow and in rectangular channel of width b we have,
Yc = (Q2/gb2)1/3 and Emin = 3/2Yc
The effects of channel cross section or area change predominates in a horizontal rectangular chan
nel of constant width, b. Thus, the slope of the free surface, dy/dx, in a flow over a bump, h(x), in
the channel bed is given by,
dy/dx = (dh/dx) / (Fr2- 1)
When the flow at a section is supercritical and downstream conditions require a change to subcrit
ical flow, a gradual change with a smooth transition through the critical point is not possible. The
transition occurs abruptly through a hydraulic jump. The abrupt change in depth involves a signi
ficant loss of mechanical energy. The ratio of downstream to upstream depths across a hydraulic j
ump is given by,
y2/y1 = 0.5{(1+8Fr12)1/2-1}
The ratio is an only a function of the upstream Froude number, and an increase in depth requires
an upstream Froude number greater than one.