tor fluid hydraulics
DESCRIPTION
Fluid Hydraulics Practical ManualTRANSCRIPT
EXPERIMENTAL METHODS
IN
FLUID MECHANICS
AND HYDRAULIC
Engr. Zukbee N. ATor Festus L.
JOMAT Production
Copyright © 2013 Zukbee N. A. & Tor Festus L.
Revised edition
Published byHARRISCO PRESSPort Harcourt Nigeria
ISBN: 989 40986 8 13
ALL RIGHT RESERVED This manuscript may not be reproduced in part or in full or stored in a retrieval system or transmitted in any form or in any means, electronic, mechanical, photocopying, recording or otherwise except for brief quotation in critical articles or review-without the prior written consent of the copyright owner and the publisher. This book is sold subject to the condition that it should not by way of trade or otherwise be lent, hired out or otherwise circulated without the copyright owner consent, in any form of binding or cover that in which it is published and this condition being imposed on the subsequent purchaser.
Designed and Printed: JOMAT Services,
No. 28 Poly R2oad, Bori 08035997597
Email: [email protected]
ii
To
Our wives
Mrs. Sira Zukbee&
Mrs. Kornebari Evelyn Tor
iii
PREFACE
The book Experimental Method in Fluid Mechanics and Hydraulics has been carefully arranged to cover the NBTE practical requirement for students offering Fluid Mechanics and some related hydraulic course in engineering departments, especially Mechanical and Civil Engineering. It also covers the University scheme for practical on the basic fluid mechanics.
There is also an experiment on turbine and pumps to help the student understand the principles behind the operation of pumps and turbines when they are expose to in the industries.
Students who successfully carried out most of the experiment in this book will find Fluid Mechanics very interesting.
iv
Acknowledgement
The Authors wish to acknowledge their friends and colleagues in the Polytechnic for the kind assistance and contribution especially the Head of Department, Engr J. N. Beredam for allowing them use the school facilities to perform most of the practical outline in this book.
Zukbee N. A. & Tor Festus L.
v
CONTENTS
PREFACE ivACKNOWLEDGEMENT VCHAPTER ONE 1
BASIC HYDRAULIC BENCH 1EXPERIMENT 1.1 5THE STABILITY OF A FLOATING BODY 5
CHAPTER TWO 8EXPERIMENT 2.1 8THE POSITION OF HYDROSTATIC PRESSURE 8
CHAPTER THREE 12EXPERIMENT 3.1 12DISCHARGE THROUGH AN ORIFICE 12EXPERIMENT 3.2 15TO DETERMINE THE COEFFICIENT OF DISCHARGE 15
CHAPTER FOUR 17EXPERIMENT 4.1 17BERNOULLI’S THEOREM DEMONSTRATION EXPERIMENT 17
CHAPTER FIVE 20EXPERIMENT 5.1 20DISCHARGE OVER WEIR (Rectangular Notch) 20EXPERIMENT 5.2 23DISCHARGE OVER WEIR (V- Notch) 23
CHAPTER SIX 26EXPERIMENT 6.1 26FRICTION LOSS ALONG A PIPE 26
CHAPTER SEVEN 30EXPERIMENT 7.1 30FLOW CONDITION 30EXPERIMENT 7.2 33OSBORNE REYNOLD’S EXPERIMENT 33
CHAPTER EIGHT 35EXPERIMENT 8.1 35OPEN CHANNEL FLOW VISUALIZATION 35EXPERIMENT 8.2 38VISUALIZATION OF FLOW OVER OR AROUND IMMERSED OBJECT 38
CHAPTER NINE 41EXPERIMENT 9.1 41IMPACT OF JETS 41
CHAPTER TEN 45EXPERIMENT 10.1 45PRESSURE GAUGE CALIBRATION 45
CHAPTER ELEVEN 48EXPERIMENT 11.1 48LOSSES IN PIPE BENDS 48
CHAPTER TWELVE 52EXPERIMENT 12.1 52STEADY UNIFORM FLOW 52
CHAPTER THIRTEEN 54
vi
EXPERIMENT 13.1 54THE CHANGE IN DEPTH AT A HYDRAULIC JUMP 54EXPERIMENT 13.2 56FLOW UNDER A SLUICE GATE WITH A HYDRAULIC JUMP 56
CHAPTER FOURTEEN 58EXPERIMENT 14.1 58FLOW OVER A BROAD - CRESTED WEIR 58
CHAPTER FIFTEEN 60EXPERIMENT 15.1 60FLOW THROUGH A VENTURE FLUME 60
CHAPTER SIXTEEN 63EXPERIMENT 16.1 63PERFORMANCE CHARACTERISTICS OF A SINGLE PUMP AT A SINGLE SPEED
63EXPERIMENT 16.2 65PERFORMANCE CHARACTERISTICS OF SIMILAR PUMP IN PARALLEL 65EXPERIMENT 16.3 67PERFORMANCE CHARACTERISTICS OF TWO SIMILAR PUMP IN SERIES 67
CHAPTER SEVENTEEN 69EXPERIMENT 17.1 69PERFORMANCE CHARACTERISTICS OF A PUMP 69
CHAPTER EIGHTEEN 72EXPERIMENT 18.1 72PRESSURE HEAD AND FLOW RATE AT VARIOUS SPEED OF A RECIPROCATING PUMP 72EXPERIMENT 18.2 76RELATIONSHIP BETWEEN PRESSURE HEAD, FLOW RATE, TORQUE, AND POWER OF A RECIPROCATING PUMP 76
CHAPTER NINETEEN 79EXPERIMENT 19.1 79PERFORMANCE CHARACTERISTICS OF PELTON IMPULSE TURBINE 79
REFERENCE 83
vii
Hydraulic Bench/ Floating Body Stability
CHAPTER ONE
BASIC HYDRAULIC BENCH
The hydraulic bench as shown in a line diagram of fig. 1.1 and a three dimensional diagram of fig. 1.2, is intended to provide facilities for performing a number of simple experiments in hydraulics. In fig. 1.1 below is the arraignment of a single unit in which a small centrifugal pump P draws water from a sump S resting below the bench, and delivers it to a bench supply valve V. The delivery pressure at this value is recorded on a Bourdon pressure gauge G, which is provided with a connection A for calibrating the gauge with a dead weight tester.
G
V
A
P
O B
S
D W
F
Fig. 1.1 Line diagram of a hydraulic bench.
Below the bench is a weighing tank W into which the discharge from apparatus being tested on the bench may be directed through a short pipe D terminating at flange F just above the bench level.
1
Hydraulic Bench/ Floating Body Stability
1. S igh t tu be sca le2 . F low con tro l va lve3 . M otor s ta rt/s top4 . D u m p v a lv e h an d le5 . D ra in va lve6 . S u m p tan k cap . 16 0 lts .7 . M e asu rin g cy lin der8 . Tran sparen t p ipe9 . P u m p & m otor10 . S ide c han n els11 . Q u ick re lease c on ne cto r (w ith
flex ib le su pp ly p ipe)12 . In le t stillin g ba ffle s lo ts
13 . O pen ch ann el14 . W eir carr ier15 . Ta n k s tillin g ba ffle16 . Vo l. M ea su rin g tank17 . D u m p v a lv e18 . O ver f low8
7
Fig. 1.2 A Three dimensional diagram of a Hydraulic Bench
The weighting tank W is supported at one end of a weigh beam, the other end of which carries a weight hanger sufficient to balance approximately the dry weight of the tank. The outlet valve B in the base of the tank may be operated through a
2
Hydraulic Bench/ Floating Body Stability
mechanism by an external handle. An over flow pipe O is also provided.Apparatus under test is placed on the bench and connected by flexible pipe to a bench supply valve which normally serves to regulate the rate of flow through the apparatus. Another flexible pipe is lead from the exit of the apparatus to the flange above a weighing tank: so that the discharge from the exit of the apparatus is returned through the open valve at the base of the tank to the sump. The Hydraulic Bench comprises the following;
1. Volumetric measuring tank2. Sump tank, 3. Centrifugal pump, 4. control valve, 5. stilling baffle, 6. slight tube with level scale and 7. a dump valve.
It is also incorporated with it an earth leakage circuit breaker.
Experiments are not carried out on the hydraulic bench alone but it is used in conjunction with the following apparatus:-1. A Dead Weight Pressure gauge calibrators.2. Metacentric Height Apparatus 3. Bernoulli’s Theorem Demonstration Apparatus 4. Basic Weirs5. Orifice and Jet Apparatus 6. Impact of Jet Apparatus7. Osborne Reynolds’s Apparatus8. Pipe Friction Apparatus9. Flow visualisation channel 10. Losses in Bends Apparatus11. Flow Demonstration Apparatus12. Hydrostatic Pressure Apparatus
3
Hydraulic Bench/ Floating Body Stability
A measuring cylinder 7 is provided with the hydraulics bench for
measurement of very small flow rates.
Attention is drawn to the following points which should be
observed for safe and satisfactory operation of the bench.
1. Before starting the pump ensure that the sump is full and
that the bench supply valves are turned off.
2. If a leak develops so that water drips on to the electric
motor or starter, stop the pump immediately and isolate it
from the electrical supply by withdrawing the plug which
supplies it. The connection should not be made until the
leak has been sealed. A small amount of water leaking on to
the bench top, however, is of small concern, as it drains
back into the sump.
3. When making connections by flexible hose it is usually
sufficient to rely on friction between the metal pipe and
the hose to maintain the water tightness of the
connection. Where however the connection is subjected to
the full pressure delivered to the bench supply valve, or if
the hose is a loose fit on the metal pipe, it is advisable to
secure the connection with a hose clip tightened by a
screw driver or a key made for the purpose.
4. At all times other than when a discharge measurement is
being made, the dump valve in the base of the measuring
tanks should be kept open. Although each tank has an
overflow pipe. But this is inadequate to deal with the
maximum discharge.
4
Hydraulic Bench/ Floating Body Stability
EXPERIMENT 1.1
THE STABILITY OF A FLOATING BODY
AIMTo demonstrate the stability of a body floating in a fluid.
APPARATUS 1. Hydraulics Bench 2. Metre Rule 3. Weighing Machine4. Metacentric Height Apparatus
T H E O R Y:M
Fig. 1.3 Metacentric height Apparatus
5
Hydraulic Bench/ Floating Body Stability
THEORY
If a jockey weight m is moved a horizontal distance x from its position and if the total weight of the floating assembly is W; then the corresponding movement of the centre of gravity G of the whole assembly in the direction parallel to the base of the
floating body is . If this movement produces a new
equilibrium position at angle , then the metacentric height is
given by GM = , where M is the metacentric.
If B is the centre of buoyancy, the distance BM may also be
calculated from . Where I = 2nd moment of area about an
axis through the centriod of the area of the body at the plane of the water surface, the axis being perpendicular to the plane in which angular displacement take place.
V = volume of liquid displaced.
For a rectangular pontoon B lies at a depth below the water surface
equal to the total depth of immersion, and .
GM = BM – BG
PROCEDURE
First weigh the various components of the floating assembly and
measure the length and width of the pontoon. Determine the
centre of gravity of the pontoon by turning it on its side and
supporting it at the stem on the edge of a steel rule to obtain the
point at which it balances. To obtain a convenient point of
balance, it may be necessary to move the adjustable weight along
the stem to a suitable position. Mark the point of balance –
Centre of Gravity. Float the pontoon in the volumetric tank
water. Record angles for various positions of the jockey weight
6
Hydraulic Bench/ Floating Body Stability
on both sides of the centre O with an increment of 10mm. Set
the adjustable weight at another different height for a new
position of centre of gravity and repeat the procedure.
PRESENTATION OF RESULTS AND CALCULATIONS
Dimensions of Pontoon Length = …………., Width = …………., Jockey weight = …… Weight of assembled pontoon = ……….Position centre of gravity CG from base of pontoon.Y = …………., Depth of immersion, d = ………….
Position of centre of Buoyancy CB = ………….
x Right x Left
Plot GM against and read GM when = 0
x is distance of moveable mass is angle of heel GM is metacentric height
Check by calculation BM =
GM = BM – BG =
QUESTIONS 1. Does the position of the metacentric depend on the position of
the centre of gravity?
2. Does the metacentric height vary with angle of heel?
7
Hydrostatic Pressure
CHAPTER TWO
EXPERIMENT 2.1
THE POSITION OF HYDROSTATIC PRESSURE
AIMTo determine the position of the centre of pressure of an immersed plane surface and to compare it with the theoretical position.
APPARATUS1. Hydrostatic pressure apparatus 2. Hydraulic bench
THEORY The force (F) acting on a submerged surface is F = P.A - g XA.This is the algebraic sum of all the small forces acting on their respective position and it act through a point called centre of pressure. Taking moment about O, and note that force on trip = xgAMoment of force on strip = x2gABut x2A =Io (2nd moment of area about “O”)
And moment = FZ FZ = gIo
Since F = A for resultant force
Then
From parallel axis theorem
8
Hydrostatic Pressure
Fig. 2.1 Hydrostatic Pressure Apparatus
9
Hydrostatic Pressure
This equation is applied also for partially submerged plated except that the Area of plate varies
Z =
That is, centre of pressure is down the section of plate that is
submerged.
PROCEDURE
From the end of the balance arm hang the balance pan and
position the balance arm on the knife edge pivot. From the drain
cock, connect a hose sump and also connect hose from the bench
feed to the triangular aperture on the top of the Perspex tank.
With the help of the adjustable feet and spirit level, level the
tank. Move the connecter balance mass until the balance arm is
horizontal with the drain cock close, admit water to the
apparatus until the level reaches the bottom edge of the
quadrant. Place a mass on the balance pan: slowly add water
into the tank until the balance arm is horizontal. Record the
water level on the plate and the mass on the balance pan.
Repeat the above procedure for each increment of mass until the
water level reaches the maximum reading on the scale. Remove
also each increment of mass noting masses and water level until
all the masses have been removed.
10
Hydrostatic Pressure
PRESENTATION OF RESULT AND CALCULATION
No. Mass m(g) mm xCA xCT (mm)12345
A = actual
T = TheoreticalmgP = FxCA
Plot xc actual against xc theoretical for the partially and fully
submerged cases.
CONCLUSION
1. Why is the centre of pressure always below the centriod?
2. Explain the reason for any discrepancies between the actual and
the theoretical results.
11
Discharge Through an Orifice
CHAPTER THREE
12
Discharge Through an Orifice
EXPERIMENT 3.1
DISCHARGE THROUGH AN ORIFICE
AIMTo determine the coefficient of velocity for a small orifice
APPARATUS 1. Hydraulic Bench
2. Orifice and Jet Apparatus
3. Stop Watch.
THEORY
Note: The plan of vena contractor is taken as the datum for measuring X.
PROCEDURE Adjust the feet to level the apparatus and ensure that the part of
the Jet coincides with the row of measuring needles.
Connect the apparatus to the bench delivering valve and the
overflow pipe hose to the sump tank. After placing a sheet of
paper on the backboard raise the needles to clear the path of the
water jet and also raise the overflow pipe.
13
Discharge Through an Orifice
Open the flow control valve, to admit water into the head tank.
Adjust the valve until the water is just spilling into the overflow.
Record the head h on the scale. Assess the position of the vena
Fig
. 3.1
Ori
fice
an
d je
t app
arat
us
14
Discharge Through an Orifice
contractor visually and note the distance from the orifice. Adjust
each of the needles in turn to determine the jet path, making the
position of the top of the needles on the sheet of paper using the
other orifice plate.
Repeat for various values of h by moving the overflow. Repeat
using another orifice plate.
PRESENTATION OF RESULT AND CALCULATION
Orifice A Orifice BHead
h(mm)
Height
Y(mm)
Distance
X(mm)
X2(mm2) Head
h(mm
)
Height
Y(mm)
Distance
X(mm)
X2(mm2)
Plot against y.
Find CV from the slope of the graph.
15
Discharge Through an Orifice
EXPERIMENT 3.2
TO DETERMINE THE COEFFICIENT OF DISCHARGE
AIMTo find experimentally the coefficient of discharge for a small
orifice for flows under constant and varying head.
APPARATUS 1. Hydraulics Bench
2. Orifice and Jet Apparatus
3. Stop Watch.
See Fig. 3.1above
THEORY
PROCEDURE Measure the orifice diameter, removing the orifice plate if necessary, measure the internal dimensions of the header tank. Connect the apparatus to the bench, levelling by adjusting feet, ensuring the overflow pipe runs into the sump tank. Raise overflow pipe to a suitable level, release water into the tank. Control the flow until the water is just spilling into overflow. Record the head h on the scale, measure the flow rate using the volumetric tank, or by intercepting the jet with a measuring cylinder. Repeat for different water levels. For flow under varying head, the overflow pipe is raised to obtain maximum head, the header tank filled to overflow level and the inlet water feed closed. Start a stop watch when the level reaches the first convenient scale mark (noted as h). Take a reading of the head (h2) at 20 second intervals.
16
Discharge Through an Orifice
The above should be repeated using the other orifice.
PRESENTATION OF RESULTS AND CALCULATIONS:
Constant Head Variable HeadHead h(mm) Volume
water(l)
TimeT
(sec)
Q Q2 Head h(mm)
Height(mm)
TimeT
(sec)
(a) Plot Q2 against h and obtain Cd from the slope of the graph
for constant head.
(b) Plot T against and obtain Cd from the slope of the graph
for variable.
Determine RO Reynolds number at each head and plot Cd versus
RO.
17
Discharge over Weirs
CHAPTER FOUR
EXPERIMENT 4.1
BERNOULLI’S THEOREM DEMONSTRATION
EXPERIMENT
AIM To investigate the validity of Bernoulli’s theorem as applied to
the flow of water in a tapering duct.
APPARATUS 1. Bernoulli’s theorem demonstration apparatus (Venturi
meter) 2. Hydraulic bench3. Stop watch
Fig. 4.1 Bernoulli’s theorem apparatus THEORY
18
Discharge over Weirs
If an incompressible fluid is to flow through a venture meter and if the cross-sectional area at any section (1) upstream is denoted as a1, and at the throat section (2) as a2 and at any other section n as qn1, then piezometer tubes at these sections will register ht, h2 and hi. Assuming that there is no loss of energy, Bernoulli’s theorem
states that
From the continuity equation Q = a1 V1 = a2 V2 = an, Vn
Substituting this in Bernoulli equation for V1 will give
In practice there is some loss of energy between section (1) and (2) and it is customary to allow for such discrepancy by writing.
Where Cd is known as the coefficient of the meter.
PROCEDURE First open the control valve downstream of the meter and the bench supply valve so as to allow water to run for a few seconds to clear air pockets from the supply system. Then gradually close the control valve. When the water levels have risen to a convenient height, gradually close the bench valve, so that, as both valves are finally shut off the meter is left containing static water under moderate pressure. Set the adjusting screws at the base, so that the piezometers each read the same value. Take the
19
Discharge over Weirs
reading of the maximum available (h1 – h2) i.e. with h1 close to the top of the scale and h2 close to the bottom.(This condition is achieved by gradually opening both the bench valve and the control valve. Successive openings of either valve will increase the flow and the difference between h1 and h2. If difficulty is experienced in reaching the desired condition air may be released from or admitted to the manifold through the small air valve at its end).Measure the quantity of water flowing by collecting it in the weighing tank, record the time taken to collect this amount and while this is in progress read values of h1 and h2 from the scale. At reducing values of (h1 – h2), take a series of readings
PRESENTATION OF RESULTS AND CALCULATION
Tube No.
Dia. of cross section (mm)
Area of cross section (mm2)
Mamometer levels (h)mm
Flow Rate Q
Probe Distance (mm)
Probe Manometer level (mm)
Fluid Velocity (m/s)
1.2.3.4.5.6.
Choose any two value of h and plot a graph of Q vs (h1 – h2)1/2
Calculate the coefficient of the meter.
20
Discharge Over Weirs
CHAPTER FIVE
EXPERIMENT 5.1
DISCHARGE OVER WEIR (Rectangular Notch)
AIM To study the characteristics of flow over a rectangular notch.
APPARATUS1. Hydraulic bench
2. Rectangular notch
3. Hook and pointer gauge
4. Stop watch
THEORY The total flow rate Q through a rectangular weir is given by:
Where b = width of rectangular weir
H = head on weir
Taking into account losses and contraction of the jet, Q for a
rectangular notch can be given as
Where Cd is the coefficient of discharge.
Also it can be said that
Q = KHn or Log Q = Log K + nLog H
21
Discharge Over Weirs
If experimental results are plotted having Log H as abscissa and
Log Q as ordinate, then the slope of the straight line = n, and the
intercept on the axis of Log Q = Log K.
(R ectan gu lar)F
ig. 5
.1 R
ecta
ngu
lar
not
ch a
ppar
atu
s
22
Discharge Over Weirs
PROCEDURE First level the apparatus. Admit water from the bench supply to
the apparatus until the level is approximately correct and bale
out or in using a small beaker until the crest of the weir lies just
in the surface. Place a steel rule on the crest. Then set the hook
gauge on the water surface in the still tube and take the zero
reading. From the bench supply valve, regulate the flow. First
start with a maximum discharge and subsequent readings with
roughly equal decrement in head. Measure the discharge and
head on the weir at each stage. About six different discharges for
each notch should be made.
PRESENTATION OF RESULTS AND CALCULATION
Record breadth of notch1. Tabulate volumes, time and heads2. Compute and tabulate Q, , Cd, , Log Q, Log H
Plot against H Log Q ,, Log H
Cd ,, H
Note:
CONCLUSION
1. Is Cd constant?
2. Estimate an average valve of Q for the test
3. Can the empirical formula Q = KHn use in describing the
relationship between Q and H? If yes find the value of K and n.
4. If Cd is not constant suggest a functional relationship
between Cd and .
23
Discharge Over Weirs
EXPERIMENT 5.2
DISCHARGE OVER WEIR (V- Notch)
AIM To study the characteristics of flow over a V-notch.
APPARATUS1. Hydraulic bench
2. V-Shaped notch
3. Hook and pointer gauge
4. Stop watch
THEORY The total flow rate Q through a V-notch of angle 2, is given by
Where H = head on weir
Taking into account losses and contraction of the jet, Q for V
notch can be given as
Where Cd is the coefficient of discharge. Also it can be said that
Q = KHn or Log Q = Log K + nLogH
If experimental results are plotted having Log H as abscissa
and Log Q as ordinate, then the slope of the straight line = n, and
the intercept on the axis of Log Q = Log K.
24
Discharge Over Weirs
PROCEDURE First level the apparatus. Admit water from the bench supply to
the apparatus until the level is approximately correct and bale
out or in using a small beaker until the crest of the weir lies just
in the surface. The reflection of the V in the surface serves to
(V-no tc h )F
ig. 5
.2 V
-not
ch a
ppar
atus
25
Discharge Over Weirs
indicate whether the level is correct or not. Then set the hook
gauge on the water surface in the still tube and take the zero
reading. From the bench supply valve, regulate the flow. First
start with a maximum discharge and subsequent readings with
roughly equal decrement in head. Measure the discharge and
head on the weir at each stage. About six different discharge for
each notch should be made.
PRESENTATION OF RESULTS AND CALCULATION FOR V- NOTCH
1. Record breadth of notch.2. Tabulate volumes, time and heads
3. Compute and tabulate Q and
4. Plot against H and find Cd from the slope of the graph.
QUESTION1. Is Cd constant throughout experiment?2. What are the advantage and disadvantage of plotting
against H instead of Q against .
26
Flow Profile
CHAPTER SIX
EXPERIMENT 6.1
FRICTION LOSS ALONG A PIPE
AIMTo investigate the variation of friction head along a circular pipe
with the mead flow velocity in the pipe.
APPARATUS 1. Hydraulic bench
2. Pipe friction apparatus
3. Measuring cylinder
4. Thermometer
5. Stop watch
THEORY The frictional resistance to which a fluid is subjected as it flows
along a pipe results in a continuous loss of energy or total head
of the fluid. Osborne Reynold recorded a number of experiments
to determine the laws of resistance in pipes. The parameters
which determine whether flow is laminar or turbulent in any
particular case are given by Reynold as
Where Re = Reynold’s number = Density of fluidV = Velocity of flowD = Diameter of pipe = Coefficient of Viscosity of the fluid
27
Flow Profile
Re has a practical maximum value of 2000 laminar flow. For pipe flow calculations, the Darcy-Weisbach equation
is generally adopted, when
Fig
6.1
Pip
e F
rict
ion
app
arat
us
28
Flow Profile
hf = Head loss or drop in hydraulic grade line
L = Length of pipe
f = Friction factor
Loss of head for laminar flow can also be expressed by the
pioseusuille’s equation
PRESENTATION OF RESULT AND CALCULATION
Volume (liters)
Time(s)
Water man. Reading (mm)
Mercury man. reading (mm)
Area of test section =
of test section =
Length of test section =
Water temperature =
Compute and tabulate the value of friction head hf, as head of system
fluid (water).
From the experiment obtain the value of volume, time and cross
sectional area of test section, calculate and tabulate the values of the
mean flow velocity V.
Compute and tabulate V2, Log hf, Log V, Log Re, Log F.
Given that
Graph 1. Plot Log hf against Log V
Graph 2. Plot Log F against Log Re
29
Flow Profile
From the above graphs assess the value of the critical velocity VC
below which flow is laminar.
Graph 3. For V > VC, plot hf against V
Graph 4. Fro V < VC plot hf against V
Determine the empirical relations hf = KVn from graph 1
Determine the empirical relations from graph 2.
Obtain the average value of F for turbulent flow in pipe from graph 3.
Obtain the value of from graph 4
CONCLUSION Does the experiment evidence indicate that two different flow regimes
are occurring?
Does the evidence support the relation for laminar flow and f
= 0.079, Re-0.25 for turbulent flow
Give reason for any discrepancies if experimental average value of
and f do not agree with value found from reference data.
30
Impact of Jets
CHAPTER SEVEN
EXPERIMENT 7.1
FLOW CONDITION
AIMTo observe Laminar, Transitional, Turbulent flow and there velocity
profile.
APPARATUS 1. Hydraulics bench
2. Osborne Reynolds apparatus
3. Vegetable dye
THEORY Laminar Flow: Is a steady conditional flow where the stream lines
are parallel. If the fluid is under this condition, the dye will be easily
identified as a solid core.
Turbulent Flow: Is an unsteady condition where the stream lines
interact causing shear plane collapse and mixing of the fluid. During
this condition, the dye will be totally mix up.
Transitional Flow: Is the period where the flow changes from
laminar to turbulent flow as the velocity of flow increases.
PROCEDURE Position the apparatus on the bench and fill the dye reservoir with dye
and lower the injector until it is just above the bellmouth inlet.
Close the flow control valve with bench inlet valve open slowly fill
head tank to the overflow level and close inlet valve.
31
Impact of Jets
To admit water to the flow visualization pipe open and close flow
control valve. The apparatus should be allowed to stand for at least
Fig
. 7.
1 O
sbor
ne
Rey
nol
ds A
ppar
atu
s
32
Impact of Jets
ten minutes before proceeding. Open the inlet valve slightly until
water trickles from the outlet pipe.
Fractionally open the control valve and adjust dye control valve until
slow flow with dye indication is achieved. When the flow rate is low,
the dye is drawn through the centre of the pipe. If the flow rate is
constantly increased, the flow rate produce eddies in the dye until the
dye completely disperses into the water.
For the velocity profile, open the dye reservoir needle for a drop of
dye to deposit in the pipe and you will observe that the drop will take
a three dimensional paraloid profile.
33
Impact of Jets
EXPERIMENT 7.2
OSBORNE REYNOLD’S EXPERIMENT
AIMTo reproduce the classical experiments conducted by Professor
Osborne Reynolds concerning fluid flow condition
APPARATUS 1. Hydraulics bench
2. Osborne Reynolds Apparatus
3. Measuring cylinder
4. Stop watch,
5. Vegetable Dye
6. Thermometer
See fig. 7. 1 above
THEORY Internationally, Reynolds number Re is recognised as a criterion
for denoting fluid flow condition
PROCEDURE Measure the temperature of the water. Slightly open the inlet
valve until water trickles from the outlet pipe. Fractionally open
the control valve until slow flow with dye indication is achieved.
Measure and note the flow rate. Repeat the experiment for
increasing flow rate by opening the flow control valve. Take a
specific measurement of flow rate at the critical condition.
34
Impact of Jets
Also repeat the procedure for decreasing flow rates, taking a
specific measurement of flow at the critical condition.
PRESENTATION OF RESULT AND CALCULATION
Visual dye condition Volume of water Time
Internal diameter of visualization pipe=
Temperature of water =
Viscosity of water =
Calculate volume flow rate and Re for each setting. Compare flow
conditions indicated by dye stream with value of Re
CONCLUSION Do the results obtained agree with the statement under analysis if
not account for any discrepancies.
35
Flow Visualization
CHAPTER EIGHT
EXPERIMENT 8.1
OPEN CHANNEL FLOW VISUALIZATION
AIMTo demonstrate phenomena associated with open channel flow.
APPARATUS 1. Hydraulics bench
2. Flow visualization channel
THEORY The primary purpose of this piece of apparatus is to demonstrate
visually a wide range of hydraulic effects associated with flow in
open channels. The intention is to complement lecturers
associated with the subject and not to form the basic for
theoretical analysis. No theoretical analyses or detailed
procedures are included. However, any of the effects may be
studied independently in detail.
PROCEDURE The apparatus should be installed over the bench top open
channel. It is important that the apparatus is sited as far as
possible from the volumetric tank, along the channels, to ensure
that water discharging from the apparatus is contained within the
volumetric tank. Connect the inlet pipe to the bench supply and
open the bench flow control valve.
36
Flow Visualization
37
Flow Visualization
The overshot weir may be adjusted in height by releasing both the
38
Flow Visualization
39
Flow Visualization
The overshot weir may be adjusted in height by releasing both the
thumb screw and the screw on the weir support. The plate may be
moved to the required position. The two screws should be re-
tightened to compress the sealing gasket. The undershot weir is a
push fit and height may be adjusted by sliding up or down.
Open channel hydraulics demonstrations include the following:
1. Discharge beneath a sluice gate (undershot weir).
2. Drowning of a sluice by an obstacle downstream (broad
crested weir).
3. The Hydraulic Jump, i.e. energy degradation in transition
from fast to slow flow.
4. Fast and slow, flow over a broad crested weir.
5. Fast and slow flow over a narrow crested weir.
40
Flow Visualization
EXPERIMENT 8.2
VISUALIZATION OF FLOW OVER OR AROUND
IMMERSED OBJECT
AIMTo visualize the flow pattern over or around an object immersed
in a fluid.
APPARATUS 1. Hydraulics bench
2. Flow visualization channel
3. Vegetable dye.
THEORY The primary purpose of this piece of apparatus is to demonstrate
visually a wide range of hydraulic effects associated with flow in
open channels. The intention is to complement lecturers
associated with the subject and not to form the basic for
theoretical analysis. No theoretical analyses or detailed
procedures are included. However, any of the effects may be
studied independently in detail.
PROCEDURE The apparatus should be installed over the bench top open
channel. It is important that the apparatus is sited as far as
possible from the volumetric tank, along the channels, to ensure
that water discharging from the apparatus is contained within the
volumetric tank. Connect the inlet pipe to the bench supply and
open the bench flow control valve. Models used in the channel
should be positioned using the tongs provided and installed by the 41
Flow Visualization
appropriate retaining screw. A blanking plug is provided for each
of the holes on the wall and floor when not in use.
The flow visualization technique involves the use of dye injected
at the hypodermic tubes. In operation, the overshot weir should
42
Flow Visualization
be raised fully and the undershot weir should be removed. The
model under investigation should be installed on its retaining
screw and the dye injection system installed in its retaining clip.
The dye reservoir should be filled with vegetable dye. Flow rate
through the channel should be adjusted at bench control valve.
Density of the dye streams may be adjusted using the control
valve at the base of the reservoir. With the overshot weir in the
raised position, the channel will run full of water enabling flow
patterns around and over submerged objects to be demonstrated.
DEMONSTRATIONS Demonstrations include flow around small or large cylinders and
symmetrical or asymmetrical aerofoils. Patterns of flow over
submerged broad and narrow crested weirs may also be demonstrated.
43
Impact of Jets
CHAPTER NINE
EXPERIMENT 9.1IMPACT OF JETS
AIMTo investigate the validity of theoretical expression to the force
exerted by jet on targets of various shapes. e.g. jet of water
directed on the vane of turbine with an output of 100,000 H.P and
with efficiency of 90%
APPARATUS 1. Jet impact apparatus2. Hydraulic bench3. Flexible hose4. Stop watch5. Vernier caliper 6. Weight
THEORY If a jet of fluid at the rate of 0m3/s along the x-axis with velocity V0
m/sec and is deflected by it tangent through angle B so that the
fluid leaves the tangent with velocity V1m/sec inclined at an angle
B to the axis, then the force F on the tangent in the direction of x is
equal and opposite to the force in the direction of x on the jet.
F = Q(V – Vcos B)
But
For the case of a flat plate, assume B = 900, so that
Since cos 900 = 0
44
Impact of Jets
Since the case of hemispherical tangent assume b = 1800
so that cosB = 1
.
45
Impact of Jets
For the case of a 1200 target, assume B= 1200 and Cos B = hence
PROCEDURE
Fig
. 9.1
Im
pact
of
Jet a
ppar
atu
s
46
Impact of Jets
First level the apparatus. Set the lever to the balanced position (as indicated by the tally) by placing the jockey weight at its zero position and then adjusting the knurled nuts above the spring. Admit water through the bench supply valve and centralize the jet on the flat plate by adjusting the four screws at the base. This screw adjustment should be done simultaneously by equal amount in opposite directions. Increase the rate of flow to the maximum and note the jockey weight which restores the lever to the balanced position, measure the discharge volume in the tank. Take six readings with roughly equally spaced positions of the jockey weight. Repeat the experiment using the 1200 target and the hemispherical target.The diameter of the nozzle, the height of the vane above the tip of the nozzle where the lever is balanced, the distance between the centre of the vane and the pivot of the lever, and the jockey weight
should be noted.
PRESENTATION OF RESULTS AND CALCULATION
1. Results should be tabulated as follows:-
Mass on weight pan
Volume of water Time Flow rate
Q
Q2
Nozzle diameter = g = 9.81 m/s2,
=
2. Repeat table for 1200 target and hemispherical target.47
Impact of Jets
3. For each target plate, compute and tabulate Q and Q2 and plot
mass M on weight pan against Q2 and measure the slope.
4. From the analysis, the slopes of the graph should be as follows
Flat target
1200 ,,
Hemispherical target
Account for any discrepancies between the slopes obtained from
the measured values and the theoretical slopes.
48
Pressure Gauge Calibration
CHAPTER TEN
EXPERIMENT 10.1PRESSURE GAUGE CALIBRATION
AIM:To accurately calibrate a Commercial Bourdon tube pressure
gauge using a dead weigh tester.
APPARATUS:Equipment consists of a stainless steel piston which is free to
move vertically in a closely fittings brass cylinder. A transparent
flexible hose connects the cylinder to the pressure. This gauge is
of the Bourdon tube type and, like the cylinder, is mounted on the
cast base of the unit integral with the piston is a loading plat-form
upon which known weights are placed during test. All air is
expelled from the system by means of a purge hole in the upper
part of the cylinder.
THEORY: Gauge reading can be shown as a function of true (applied)
pressure. Gauge error can also be shown as a function of true
pressure. By graphically representing the results in this way, the
two possible kinds of gauge error-that due to combination of
hysteresis, friction and backlash and that due to graduation errors
can be shown.
49
Pressure Gauge Calibration
PROCEDURE: Remove the piston and completely fill the system with water. Ensure
that all air has been purged by tilting the unit. Replace the piston.
Fig. 10.1 Pressure gauge calibration apparatus
Add weights in increments of kg. And at each increment observe
the pressure gauge reading. Do not apply more than 6kg weight50
Pressure Gauge Calibration
on the calibration platform. During the test, slightly rotate the
piston to avoid sticking. Decrease the weights in decrement of
kg. And at each decrement observe the pressure gauge reading.
Note the weight of the piston and its cross-sectional area.
PRESENTATION OF RESULT AND CALCULATIONS1. Reading should be tabulated as follows:
Weight added to piston (kg)
Total load on piston (kg)
True pressure kg/mm2
Gauge reading (bar)
Increasing pressure
Decreasing pressure
2. Plot a graph of gauge reading against true pressure (Pressure
gauge calibration).
3. Plot a graph of gauge error against true pressure
(Gauge error = True pressure Gauge reading).
4. Comment on the Results obtained.
51
Losses in Bends
CHAPTER ELEVEN
EXPERIMENT 11.1 LOSSES IN PIPE BENDS
AIM To determine losses in small bore piping systems.
APPARATUS: 1. Hydraulic bench
2. Losses in bend apparatus
3. Stop watch
Fig. 11.1 Losses in bends apparatus
DARK BLUE CIRCUIT1. Gate valve
2. Standard Elbow bend.
3. 90° Mite bend
4. Straight pipe
52
Losses in Bends
LIGHT BLUE CIRCUIT5. Globe valve
6. Sudden expansion 13.7mm to 2 diameter
7. Sudden 26.4mm to 13 diameter
8. 152.4mm 900 radius bend
9. 101 .6mm 900 radius bend
10. 50.8mm 90° radius bend
THEORY:For an incompressible fluid flowing through a pipe, the following equations apply: Q = A1V1 =A2V2 (continuity)
(Bernoulli)
Where hl12 is the head loss1. The head loss along a length L of a straight pipe of constant
diameter d is given by where f = friction factor
2. Head loss at a sudden expansion is
3. Head loss at a sudden contraction is given by
where K depends on the ratio
4. Head loss due to a bend , K depends On
ratio
5. Head loss due to a valve where K depends upon
the type of valve and the degree of opening.
PROCEDURE:Open fully the water control valve on the hydraulic bench. With the globe valve closed, open the gate valve fully to obtain
53
Losses in Bends
maximum flow through the Light Blue circuit. Record the readings on the piezometer tubes and the U-tube. Collect a sufficient quantity of water in the weighing tank to ensure that the weighing takes place over a minimum period of 60 seconds. Repeat the above procedure for at least six different flow rates; obtain by closing the gate valve, equally spaced over the full flow range.Record the water temperature in the sump tank of the hydraulic bench each time a reading is taken. Close the gate valve, then open the globe valve and repeat the experimental procedure for the Dark Blue circuit.Close both the globe valve and gate valve before switching off the pump.
PRESENTATION OF RESULTS AND CALCULATIONS
1. Results should be tabulated as follows:
a. Dark Blue Circuit
Test no. Time to collect 15kg water (sec)
Piezometer tube readings (cm) water
U-Tube (cm) Hg
1. 1 2 3 4 5 6 Gate valve2.
b. Light blue circuit
Test no. Time to collect 15kg water (sec)
Piezometer tube readings (cm) water U-Tube (cm) Hg
1. 7 8 9 10 11 12 13 14 15 16 Globevalve
2.2.(i) For the straight pipe, obtain the following relationship
(a) Head loss as a function of volume flow rate.
(b) Friction factor as a function of Reynolds Number.
(ii) For sudden expansion compare the measured rise in
head with the rise calculated on the assumption of
head loss.
54
Losses in Bends
(iii) For sudden contraction, compare the measures fall in
head with the fall calculated on the assumption of head
loss given by
(iv) Obtain values of loss coefficient K for the pipe
55
Steady Uniform Flow
CHAPTER TWELVE
EXPERIMENT 12.1STEADY UNIFORM FLOW
AIMIn most flow problems it is often necessary to predict the rate of
flow through a channel of known physical characteristic (size,
shape, slope, roughness etc.). In this experiment, the theoretical
and empirical relationships of these quantities are compared with
measured values in the channel for steady uniform flow.
APPARATUS:1) 5 metre inclinable flow channel
2) Adjustment sluice Gate/weir
3) Vernier depth gauges
4) Weights
5) Thermometer
THEORY The Chezy equation for steady uniform flow in a channel is given by
Where V = Velocity of flow C = Chezy coefficient
i = slope of channel
Where n = Roughness coefficient.
Where = Density of fluid, = viscosity of fluidV = mean velocity of flow, I = characteristics length
= m for open channel
56
Steady Uniform Flow
PROCEDURE:Set the sluice gate in the closed position and approximately half
fill the channel with water close the delivery valve before
stopping the pump so that W is retained in the channel While
allowing the water to settle, check that the instrument guide rails
are parallel to the channel base by using gauges about 250cm
(100ins.) apart in the mid-length of the channel and tilt the
channel using the hand wheel and screw arrangement until the
depth of water is greater at the down-stream depth gauge
than the upstream one. The channel bed now has a gradient of
.
Open the sluice gate and switch on the pump. Adjust the position
of the sluice gate and the flow rate to obtain a uniform depth of
flow of about 1.25cm over the mid-length of the channel, when
satisfied that the flow is uniform and steady, take measurement of
the flow rate using the weighing mechanism and stop-watch.
Record this against the depth of flow. Repeat the procedure for a
series of flow rates up to the maximum delivery of the pump.
Check the width of the channel with callipers. Also take the
temperature of the water.
PRESENTATION OF RESULTS AND CALCULATION 1. Readings should be tabulated as follows:2. Using Meaning formula and assuming values of n = 0.010,
0.009, 0.008 and 0.0075, calculate C.3. For the first and last tests, calculate the Reynolds number.4. Discuss your results.
57
Hydraulic Jump
CHAPTER THIRTEEN
EXPERIMENT 13.1THE CHANGE IN DEPTH AT A HYDRAULIC JUMP
AIM: To investigate the relationship between the flow rate in the
channel and the depth of flow on either side of a hydraulic jump.
APPARATUS:1) 5 meter inclinable flow channel
2) Adjustable sluice gate
3) Vernier Depth gauge
4) Stop watch
5) Weights.
THEORY: By applying the hydrostatic force and the momentum equations
across an hydraulic jump yields
Where d1 and d2 are depths upstream and downstream of jump.
q = flow per unit width
This equation may be rearranged to include the Froude Number Fr1 of the flow up stream of the Jump. From Continuity,
58
Hydraulic Jump
PROCEDURE. Set up the movable sluice gate about 1 meter from the inlet with the
channel bed set level. Adjust the flow rate and sluice gate opening to
give a range of flow depths upstream and downstream of the jump.
PRESENTATION OF RESULTS AND CALCULATIONS 1. Readings should be tabulated as follows:
Upstream
depth d1
Downstream
depth d2
Quantity W(kg)
Time to
collect
water (sec)
d-
1+
d2
d1d2(d1+d2)
2. Plot a graph of depth variation across a hydraulic jump with
quantity.
i.e. d1d2 (d1+d2) vs
3. Discuss the results obtained
59
Hydraulic Jump
EXPERIMENT 13.2FLOW UNDER A SLUICE GATE WITH A HYDRAULIC
JUMP
AIM:In this experiment, a sluice gate is used to produce rapid flow in a
channel where otherwise the flow would be tranquil. As the flow
reverts from the rapid to tranquil state, a resultant deepening of
the water takes place and is referred to as a Hydraulic jump.
APPARATUS 1. 5M Inclinable flow channel
2. Vernier Depth Gauges
3. Movable sluice gates
4. Stop-clock
5. Weights
THEORY:The energy per unit weight or specific energy E of a fluid above
the base of a channel at a depth d is given by
E is a minimum at the critical depth dc when or
Emin = dc
At the minimum at the critical, the critical velocity
Vc is given by Vc =
The minimum value of E corresponds to a Froude Number of 11
which is the critical condition in determining whether a flow is
rapid or tranquil.
60
Hydraulic Jump
PROCEDURE:
Set up the channel with a small slope on the channel bed of .
Clamp the movable sluice gate to the guide rails at about 1 metre from
the inter end. Check to see that it is squarely placed across the channel
and sealed properly at the edges. Switch on the pump and adjust the
flow rate so that the water is about 102mm (4 ins) deep upstream of
the sluice gate
When the latter is about 38mm from the base of the channel.
Measure the flow rate with the weighing mechanism and stop watch.
Measure the depth of flow upstream of the sluice gate and at 75mm (3
ins) interval downstream.
PRESENTATION OF RESULTS AND CALCULATION 1. Results should be tabulated as follows:
Position Depth d E = d +
Upstream of Gate at Gate
75mm downstream of gate
150mm downstream of gate
2. Plot a graph of depth against specific Energy.3. Plot on another graph paper, depth of flow and specific Energy
against distance from the sluice gate.4. Comment on the position of Emin with respect to that of the
hydraulic jump.
61
Flow over a board
CHAPTER FOURTEEN
EXPERIMENT 14.1FLOW OVER A BROAD - CRESTED WEIR
AIM:To show that the flow over the top of a broad crested weir is
approximately critical
APPARATUS1. 5m inclinable flow channel
2. Depth gauges
3. 3 rectangular plated metal block
4. Stop-watch
5. Weights
THEORYFor a broad-crested weir in a rectangular channel,
Since velocity upstream is small, in
negligible. Therefore E = d0 where do = d0 –d
so that
E = Specific Energy du = Upstream depth of weir
dc = Critical depth do = du - d
d = Heights of weir q = flow per unit width
PROCEDURE:
62
Flow over a board
Adjust the channel bed to a shallow slope of . Place the 3 blocks
end to end about 1 metre from the outlet end of the channel. Adjust
the flow, rate through the channel to the maximum value for which the
flow over the crest is substantially parallel to the crest. Take readings
of the upstream depth du and the depth over the crest (dc + d), while
measuring the flow rate with the weighing mechanism and stop clock.
Reduce the flow rate and repeat the readings.
PRESENTATION OF RESULTS AND CALCULATION 1. Results should be tabulated as follows:
Critical depth
Depth upstream du
Depth at weir dc + d
W kg Time sec
q do dc
2. Plot a graph of calculated critical depth against depth over weir.
3. Comment on the results obtained.
63
Flow through a venture flume
CHAPTER FIFTEEN
EXPERIMENT 15.1FLOW THROUGH A VENTURE FLUME
AIM:To compare the practical and theoretical profiles of the water surface through the venturi and find a coefficient of discharge for the venturi.
APPARATUS:The venturi is made by fitting a pair of double wedge plate inside the channel. The plates are made of 12.7mm ( ½ in.) thick clear Perspex and are shaped so that each tapered section and the throat are 14.3mm(4½ ins) long and in the directions of flow. The plates are held in position at the sides of the channel by a screwed aluminium spacer, which is fitted in the throat above the level of the water surface.
THEORY: For a rectangular cross section flume.
Where E = Specific Energyd = Depth of flowV = Mean Velocity of flow b = Breadth of flowQ = Quantity (rate of flow)
If the flow conditions are critical in the throat, then
Where is the depth of flow in the throat. If there is a large change in the cross sectional area between the upstream and the throat sections, then the upstream velocity head may be neglected and equation (2) becomes
64
Flow through a venture flume
Where do = upstream depth.If we consider the velocity distribution to be uniform at all sections then we may combine (1) and (2) or (1) and (3) so that
Where = Breadth at the throat
Or ………………………………….(4)
Putting E d0
…………………………….……….(5)
or ………………………………….(6)
Where Cd is the coefficient of discharge.PROCEDURE:
Adjust the channel bed to a slope of 1 in 400. Insert and secure the
venturi plates in a position about meter from the outlet end of
the channel. Care should be taken to see that the plates are positioned exactly opposite to one another so that throat positions corresponds. Switch on the pump and adjust the flow rate to the maximum for which the critical condition exists in the
throat (i.e. the depth at some point in the throat should be of
that upstream of the venture). When the flow rate is set, use the depth gauges to measure the depths of flow at 25mm intervals along the length of the venture. Repeat the procedure for series of flow rates being careful that the flow is always critical in the throat.
PRESENTATION OF RESULTS AND CALCULATIONS1. Reading could be recorded as
65
Flow through a venture flume
2.5c
m U
pstr
eam
Sta
rt o
f ve
ntur
e (A
)
2.5c
m f
rom
(A
)
5.0c
m f
rom
(A
)
7.5c
m f
rom
(A
)
10cm
fro
m (
A)
12.5
cm f
rom
(A
)
15.0
cm f
rom
(A
)
17.5
cm f
rom
(A
)
20.0
cm f
rom
(A
)
22.5
cm f
rom
(A
)
25.0
cm f
rom
(A
)
27.5
cm f
rom
(A
)
30.0
cm f
rom
(A
)
32.5
cm f
rom
(A
)
35.5
cm
fro
m (
A)
37.5
cm
fro
m (
A)
40.0
cm f
rom
(A
)
2. Using the Upstream reading, calculate E from
With this derive an expression for each flow rate such that
---------------------------------(b)
Where
Compute values of the left hand side of equation (b) for various values of d and plot these against d.3. Draw the theoretical and practical water surface pr through the
venturi for a given flow rate.4. Using equations (4) and (5) determine the coefficient of discharge
for each flow rate. Draw a graph of theoretical discharge
against practical discharge Qp and comment on your results.
66
Characteristics of Pump(s) at Single Speed
CHAPTER SIXTEEN
EXPERIMENT 16.1PERFORMANCE CHARACTERISTICS OF A SINGLE
PUMP AT A SINGLE SPEED
AIM:To determine the head/flow rate characteristic of a single
centrifugal pump at a single speed.
APPARATUS: 1. Hydraulics bench
2. Series/parallel pump test accessory.
Power sw itch
Hydraulics bench
Fig. 16.1 Series/parallel pump test accessory THEORY:
In this experiment we are concern with head/flow rate
relationship. If we note the inlet and outlet head, the total head
will be the difference between outlets head and the inlet head.
67
Characteristics of Pump(s) at Single Speed
From our gauge reading, if the inlet head is P1 and the outlet
head is P2, then Total head = P1-P2
PROCEDURE With the auxiliary pump on the floor of the left hand side of the hydraulics bench, position the apparatus manifold in the bench channel and connect the bench with the apparatus using the appropriate hoses as shown. Switch on the electrical power supply. Open the drain valve and open the discharge control valve. Switch on the pump.Record inlet pressure, outlet pressure and flow rate using the volumetric tank. Close discharge valve slowly. Tabulate your result at different discharge.
PRESENTATION OF RESULT AND CALCULATIONManifold
pressure mH2OInlet
m.H2ODatum head correction m
Total Head
m.H2O
Vol.(l)
Time(sec.)
Flow rate Q l/s
0 0.82.0 0.84.0 0.86.0 0.88.0 0.810.0 0.812.0 0.814.0 0.816.0 0.8
Plot a graph of head against flow rate
68
Characteristics of Pump(s) at Single Speed
EXPERIMENT 16.2PERFORMANCE CHARACTERISTICS OF SIMILAR PUMP IN PARALLEL
AIM:To determine the head/flow rate characteristics of two similar pumps operating in a parallel at the same speed.
APPARATUS: 1. Hydraulics bench
2. Series/parallel pump test accessory
Pow er sw itch
Hydraulics bench
Fig. 16.2 Series/parallel pump test accessory (with Y-connector i.e. in parallel)
THEORY: When two or more similar pumps are connected in parallel, the head across each pump is the same but the flow rate Q is showed equally between the pumps. It should be noted that flow rate does not increase according to the number of pump switch on.
PROCEDURE: With the auxiliary pump on the floor of the left hand side of the hydraulics bench, position the apparatus manifold in the bench channel and connect the bench with the apparatus using the
69
Characteristics of Pump(s) at Single Speed
appropriate hoses as shown. Switch on the electrical power supply. Open the drain valve and open the discharge control valve. Switch on the pump.Record inlet pressure, outlet pressure and flow rate using the volumetric tank. Close discharge valve slowly. Tabulate your result at different discharge.
PRESENTATION OF RESULT AND CALCULATION Manifold
pressure mH2OInlet
m.H2ODatum head correction m
Total Head
m.H2O
Vol.(l)
Time(sec.)
Flow rate Q l/s
0 0.82.0 0.84.0 0.86.0 0.88.0 0.810.0 0.812.0 0.814.0 0.816.0 0.8
Plot a graph of head against flow rate
Compare this graph with graph of experiment 16.1
Comment on your flow rate and give reasons why the flow rate
does not increase in proportion to the number of pumps used.
70
Characteristics of Pump(s) at Single Speed
EXPERIMENT 16.3
PERFORMANCE CHARACTERISTICS OF TWO SIMILAR PUMP IN SERIESAIM:
To determine the head/flow rate characteristics of two similar
pumps operating in series at the same speed.
APPARATUS: 1. Hydraulics bench
2. Series/parallel pump test speed
Power switch
H yd raulics b en ch
Fig. 16.3 Series/parallel pump test accessory (in series)
THEORY:If two or more similar pumps are connected in series, the discharge passes through each pump in turn and undergoes a head boost
D = Number of pumpsH = total head
It two similar pumps are connected in series will give a combined pump characteristics of twice the head P1 + P2
PROCEDURE:
71
Characteristics of Pump(s) at Single Speed
With the auxiliary pump on the floor of the left hand side of the hydraulics bench, position the apparatus manifold in the bench channel and connect the bench with the apparatus using the appropriate hoses as shown in fig. 16.3. Switch on the electrical power supply. Close bench control valve, close discharge valve, and switch on pump. Open discharge valve. With the discharge valve fully open allow the pumps to stabilize for a few minutes and notice that there will be no pressure reading as the valve is fully open.Close the discharge valve slowly to obtain a convenient pressure gauge reading of about 0.5bar. Record pressure and compound gauge readings using the volumetric tank determine flow rate. Repeat above procedure at different pressure until discharge valve is fully closed.
PRESENTATION OF RESULTS AND CALCULATIONS
Times
Vol.l
Flow rate Q
Pressure Compound Velocity head
correction
Datum head
correction
Total head
mH2Ol/s m3s-
1Bar mH2O Bar mH2O
Area of hose = 7.85 × 10-5m2
Velocity Head = , but , g = 9.8ms-2
Distance between gauge centres = (Datum head)Total head = (pressure + velocity head + datum head) – CompoundPlot a graph of total head against flow rate.
72
Characteristics of Pump(s) at Varying Speed
CHAPTER SEVENTEEN
EXPERIMENT 17.1PERFORMANCE CHARACTERISTICS OF A PUMP
AIM:To determine the relationship between head discharge, power
efficiency and speed for a centrifugal pump at various speed.
APPARATUS: 1. Hydraulics bench
2. Pump characteristics test accessory
Fig. 17.1 Pump characteristics test accessory
THEORY: The performance of any pump working at a fixed speed can be
represented by the following relationship
1. Total Head (H) against Discharge (Q)
2. Input Power (P) against Discharge (Q)
3. Efficiency ()against Discharge (Q)
73
Characteristics of Pump(s) at Varying Speed
The above relationship plotted together on a graph sheet is
called the performance characteristics and is always advisable
to plot them on a common base line of discharge (Q).
Total head = Inlet pressure – Discharge pressure (mH2O)
Input Power = Volts ×Amps (W)
Efficiency % =
Water power = gHQ (W)
Where = 1,000kg/m3
g = 9.81 m/s2
PROCEDURE: Position the apparatus manifold block on the working channel
of the hydraulics bench and the pump set on the floor at the left
hand side of the bench. With the appropriate hoses connect the
apparatus to the bench drain valve. Switch on the electrical
supply, and open the drain valve and the discharge control
valve. Switch on pump to run on a speed of 2,000r.p.m
Tabulate reading on gauge and meters, determine flow rate.
Slowly close discharge valve to give a convenient reading on
the gauge and record new reading until valve is totally closed.
Repeat the above procedure for a pump speed of 2,500r.p.m
and 3,000r.p.m
PRESENTATION OF RESULT AND CALCULATIONS
74
Characteristics of Pump(s) at Varying Speed
Tabulate result as shown belowR
.P.M
Suction head
(mH2O)
Pressure head
(mH2O)
Gauge correction
head
Total head
(mH2O)
Vol
l
Tim
es
Q l
/s
Q
m2 /s
Water power P(w)
Am
ps
Vol
ts
Power input
W
Eff
icie
ncy
%
2000 0.8
2000 0.8
2000 0.8
2000 0.8
2500 0.8
2500 0.8
2500 0.8
2500 0.8
3000 0.8
3000 0.8
3000 0.8
3000 0.8
Plot the following performance characteristics curve for each speed
Total head (H) against Discharge (Q)
Input power (P) against Discharge (Q)
Efficiency () against Discharge (Q)
From your graph, at what speed was the operating point of the
pump achieved?
Comment on the effect of suction head on the performance of the
pumps.
See appendix 1 for the performance curve
75
Characteristics of Reciprocating Pump
CHAPTER EIGHTEEN
EXPERIMENT 18.1PRESSURE HEAD AND FLOW RATE AT VARIOUS
SPEED OF A RECIPROCATING PUMP
AIM:To investigate the relationship between pressure head and flow
rate at various reciprocating pump speeds.
APPARATUS: 1. Arm field ram pump test bench
2. Stop watch
Fig. 18.1 Reciprocating Pump
PUMP SPEED RATIO
Pump/Motor pulley teeth ratio
Maximum pump speed Motor @ 1450 rev.min
Bourdon pressure guage
72.14 282 rev/min 0-70m.H2O
76
Characteristics of Reciprocating Pump
Fig. 18.2 Arm field ram pump test bench
PROCEDURE: With the delivery gate valve fully open, switch on the test rig and
raise the motor speed to maximum. Note the reading on the
pressure gauge at this point. Now slowly close the delivery gate
valve and STOP when the pressure gauge reads 5m.H2O.
NOTE: The delivery gate valve must not be fully closed with the pump
running as serious damage could occur to the equipment.
Note the difference between the maximum pressure reading and minimum pressure reading (5m.H2O) and select six equi-spaced points throughout the pressure range, which will be the pressures at which flow will be measured. The actual pressure head of the
77
Characteristics of Reciprocating Pump
pump is the difference between the pressure gauge reading in m.H2O and the vacuum gauge reading in m.H2O, at a particular rate of flow.At each selected pressure reading, measure the rate of flow using the graduated sight glass on the volumetric tank and the stopwatch. Tabulate this data in the Results Section below.The above procedure is now repeated at two other speeds, e.g. 1000 rev/min and 500 rev/min and the results are tabulated.
PRESENTATION OF RESULTS AND CALCULATIONS
Pump speed =
= Readings Pressure m.H2O Vacuum m.H2O Head m.H2O Flow rate l/sec123456
Pump Speed:………………….
Readings Pressure m.H2O Vacuum m.H2O Head m.H2O Flow rate l/sec123456
Pump speed:………………..
78
Characteristics of Reciprocating Pump
Readings Pressure m.H2O Vacuum m.H2O Head m.H2O Flow rate l/sec
123456
CONCLUSION From the results table construct a family of three graphs for each
speed using common axes of pump head (vertical axis) against flow
rate (horizontal axis).
Compare the characteristics curves and comment upon the
flow/pressure relationship at different speeds.
Suggest any advantages or disadvantages of the ram type pump.
79
Characteristics of Reciprocating Pump
EXPERIMENT 18.2RELATIONSHIP BETWEEN PRESSURE HEAD, FLOW RATE, TORQUE, AND POWER OF A RECIPROCATING PUMP
AIM:To investigate the relationship between pressure head, flow rate,
torque, power consumed for a reciprocating pump.
APPARATUS: 1. Arm field ram pump test bench (see fig. 18.2)
2. Stop watch.
PROCEDURE 1. Ensure that the dynamometer motor torque arm has been
correctly set to zero.2. With the delivery gate valve fully open, switch on the test rig
and set the motor speed to maximum 1450 rev/mm.3. Note the reading on the pressure gauge at this point.4. Now slowly close the delivery gate valve and STOP when the
pressure gauge reads 5m.H2O NOTE: The delivery gate valve must not be fully closed with the pump running as serious damage could occur to the equipment.
5. Note the difference between the maximum pressure reading and minimum pressure reading (5m.H2O and select six equi-spaced points throughout the pressure range, which will be the pressures at which flow will be measured. The actual pressure head of the pump is the difference between the pressure gauge reading in m.H2O, and the vacuum gauge reading in m.H2O, at a particular rate of f low.
6. Adjust the delivery gate valve to the first of the selected pressure gauge readings.
80
Characteristics of Reciprocating Pump
7. Measure the rate of flow using the graduated sight glass on the volumetric tank and the stopwatch. Record flow rate in results.
8. At this particular flow rate, place weights on the weight hanger to return the beam to the balanced (horizontal) position. Note the Torque in the results table.
9. Repeat operations (f) and (h) above, for the five other selected pressure readings.
10. Repeat operations (b) to (i) above for two other motor speeds as required, say 1000 rev/mm and 500 rev/mm.
PRESENTATION OF RESULTS AND CALCULATIONSAll data gathered during the test must be tabulated on the results sheet.
CALCULATIONS Torque T = L.g.W
Where T = Torque Nm L = torque arm length (metres) g = 9.81 m.sec-2
W = load (kg)
Input Power P =
Where P = Power in watts N = Pump rev/mmT = Torque N.m.
Note: The actual pump speed may be calculated using the pump/motor pulley ratio as follows:
Pump Speed = Motor Speed
Hydraulic Power (Pump output power) P/ = .g.Q.H/.10-3 Where P/ = Hydraulic power (watts)
= Density of water g = Gravity 9.81.sec-2
Q = Rate of flow 1/sec H/ = Pump head m.H2O
81
Characteristics of Reciprocating Pump
1. Construct a family of curves for the various speeds at which the tests were carried out, using common axes of Pressure Head (vertical axis) against Flow Rate (horizontal axis).
2. Construct a family of curves for the various speeds at which the tests were carried out, using common axes of Pressure Head (vertical axis) against Torque (horizontal axis).
3. Construct a family of curves for the various speeds at which the tests were carried out, using common axes of Input Power (vertical axis) against Flow Rate (horizontal axis).
QUESTION1. Referring to the Power/Flow graph, should. the pump be
started with its flow control valve open, or closed? Explain why.
2. What are the disadvantages of the ram type pump when compared with centrifugal or gear type pumps?
3. Given that Efficiency = , show the most
efficient operating point for the pump at any one of the operating speeds chosen in the test.
4. State a suitable industrial application for this type of pump. Correlate the industrial application with the test data obtained.
Note: This results table is used for the testing of the pump at ONE speed only. If tests at other speeds are required, further copies of this sheet must be used.
Motor speed:………………….rev/min
Readings Pressurem.H2O
Vacuumm.H2O
Pump Head
m.H2O
Volume(l)
Time(sec.)
Flowl/sec
TorqueN.m
PowerWatts
123456
82
Characteristics of Reciprocating Pump
83
Characteristics of Turbines
CHAPTER NINETEEN
EXPERIMENT 19.1PERFORMANCE CHARACTERISTICS OF PELTON IMPULSE TURBINE
AIM:To determine the operating characteristics of a pelton turbine at
various speeds.
APPARATUS:1. Hydraulics bench
2. Pelton impulse turbine
3. Tachometer
Fig. 19.1 Pelton impulse turbine
84
Characteristics of Turbines
THEORY Pump and turbine performance curves are derived in the same
ways. The speed is usually considered as a principle variable when
plotting power, efficiency, torque and discharge.
Mechanical power Pm = Torque angular velocity
= T, where T = Force radius (Nm)
and =
Water power = Where = density of water 1,000kg/m3
g = 9.81 m/s2
H = Inlet head mQ = Flow rate m3/s
Turbine Efficiency % =
PROCEDURES Position the pelton turbine on the hydraulic and connect the bench
supply to the apparatus. Clamp the tachometer and lift the band
brake assembly until it is off the brake drum. Switch on the bench
pump and fully open the bench control valve. Adjust spear control
valve until the maximum rev/min are indicated on the tachometer.
Measure rev/min, flow rate, and inlet pressure. Lower band brake
assembly over brake drum and adjust band until a convenient
reading is indicated on the right hand spring balance loads. Repeat
the procedures above at different applied loads and tabulate the
results.
PRESENTATION OF RESULTS AND CALCULATION
Brake drum radius = 30 10- 3m
D ru m
W2 W1
85
Characteristics of Turbines
Total force = W2 – W1
Fig. 18.2
R.P.M (rad/s)
W1 (N) 0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0W2 (N)
W1-W2 (N)
Drum radius
30 30 30 30 30 30 30 30 30 30 30 30 30 30
Torque (N/m)Pm (W)
Vol. (l)
Time (s)
Flow rate (m3/s)Pressure (mH2O)Pw (W)
Efficiency (%)
1. Plot a graph of power against rotor speed.
2. Plot a graph of torque against rotor speed.
3. Plot a graph of efficiency against rotor speed.
4. Plot a graph of discharge against rotor speed
5. What is the difference between pump and turbine
6. Comment on the graphs.
86
Characteristics of Turbines
Pow er
Pow er
Fig. 1. Head/ flow rate control for single centrifugal pump at single speed
H
Q
2 Pum ps1 Pum p
Pow erQ2
Q2
Fig. ii. Head/flow rate for two centrifugal pump in parallel
H
Q
2 Pum ps
1 Pum p
H2
H2
Fig. iii. Head/ flow rate control for two centrifugal pump in series Discharge
Operating point
Head
Power input
Efficie
ncy
Fig. iv. Performance curve for a centrifugal pump
Discharge
Torque Power
Efficiency
Rotor Speed
Fig. v. Performance curve for a Pelton turbine
87
REFERENCE
Arm Field Instructional Manual, October 1988
Felix J. K. Ideriah: Fluid Machinery, MacMillan Press London (in Preparation)
J. F. Douglas; J.M Gasiovek; J. A. Swaffield, London Fluid Mechanics, Pitman Books Ltd. 1981.
John A. Robertson; Calyton L. Crowe Engineering Fluid Mechanics Washington State University Pullman. 2nd Edition
Lewitt. E. H; Hydraulics and Fluid Mechanics, Pitman and Sons Ltd. London (1966)
Walsaw A. C and Jobson D. A; Mechanics of Fluids, Longmans Green and Co. Ltd, London 1962
88
Index
A
APPARATUS, 3, 5, 9, 12, 15, 33ARM FIELD RAM PUMP TEST BENCH,
72, 73, 76
B
BENCH, 2, 3, 5, 12, 15BENDS, 3BERNOULLI’S THEOREM, 17, 18BOURDON TUBE, 45BRAKE DRUM, 81BUOYANCY, 7
C
CENTRIFUGAL PUMP, 3CHEZY EQUATION, 52CIRCUIT, 50CRITICAL DEPTH, 58, 59
D
DISCHARGE, 37, 69, 70, 71DYE, 33
E
ENERGY, 57, 58, 60
F
FLEXIBLE HOSE, 41FLOW, 3, 19, 30, 35, 38, 40, 43, 64, 66, 68,
74, 75, 77, 78, 80, 81FLUID, 19, 83FRICTION, 3, 28, 50
G
GATE VALVE, 48, 50GAUGE, 45, 47, 71GRAVITY, 6, 77
H
HEMISPHERICAL TARGET, 44HOOK, 20, 23HYDRAULIC BENCH, 8, 17, 20, 23, 26, 41,
48
HYDROSTATIC, 3, 8, 9
J
JOCKEY WEIGHT, 7
L
LOSSES IN BEND APPARATUS, 48
M
MANIFOLD, 64, 66MASS, 11, 43METACENTRIC, 3, 5METRE, 5MOMENT, 8MOVABLE SLUICE GATES, 56
P
PONTOON, 7PUMP CHARACTERISTICS TEST
ACCESSORY, 69
R
ROUGHNESS COEFFICIENT, 52
S
SUMP, 3
T
TACHOMETER, 79TEMPERATURE, 34THERMOMETER, 26, 33, 52TUBE, 19, 50TURBULENT FLOW, 30
U
UPSTREAM DEPTH, 55, 58
V
VEGETABLE DYE, 30, 38VERNIER DEPTH GAUGES, 52VOLUMETRIC, 6, 15, 35, 38, 64, 66, 68,
74, 76
89
Index
W
WATCH, 15, 17, 20, 23, 26, 33, 41, 48, 53, 54, 57, 58, 72, 76
WEIGHT, 1, 2, 6, 43, 44, 47, 56, 77WEIRS, 40
90