Fluid Mechanics Laboratory Manual

poisonmammeringMechanics

Oct 24, 2013 (3 years and 5 months ago)

102 views

Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

1

Fluid Mechanics
Laboratory Manual


Irrigation and Hydraulics Department
2010 – 2011


Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

2
Table of Contents
Description of the Hydraulic Bench ………………………………………………… 3
1. Weir Experiment (Rectangular and Triangular)…………….……………………….. 5
2. Impact of Jet ……………………..…………………………….. .……………………9
3. Flow through Sharp Edged Orifice ………………………………………………….13
4. Bernoulli’s Theorem Demonstration ………………………………………………..18





Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

3
The Hydraulics Bench

The standard Hydraulics Bench is used for all the laboratory experiments carried out during this
course. The Bench has a closed water circulating system to facilitate mobility. Water is stored in an
enclosed tank at the bottom of the bench then pumped up to the experimental setup situated on top of
the bench from which water flows into the upper tank. The upper tank has a drain controlled by a plug
to collect and gauge the water in the upper tank after which water is drained to the bottom tank. The
volume of water collected in the upper tank (in liters) can be measured using the graduated scale fixed
at the side of the Hydraulics Bench. The switch of the water pump and the control valve that regulates
the amount of water that flows to the experimental setup are at the front side of the Hydraulics Bench
(Please see the attached photographs).




Scale of
the volume
(liter)
Control
Valve
Pump
Switch
Upper tank of
the bench
Plug and sink
to drain water
to the lower
tank

Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

4




Scale of
the volume
(liter)
Control
Valve
Pump
Switch
Upper
tank of the
bench
Plug and sink to
drain water to the
lower tank
Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

5
1. Weir Experiment (Rectangular and Triangular)

Objectives of the Experiment
1. To demonstrate the flow over different weir types.
2. To calculate the coefficient of discharge for different weir types.
3. To study the variation and dependence of the relevant parameters.

Theory

For the rectangular weir:
2
3
d
H.g2.B.
3
2
.CQ =




For the triangular weir:
2
5
.2.
2
tan.
15
8
.HgCQ
d




=
θ

where C
d
= Coefficient of discharge
B = width of the rectangular weir (3 cm)
H = head above the weir crest or apex θ = angle of the triangular weir
g = acceleration of gravity

Experimental Setup



Weir Plate
(V-notch)
Stilling
Baffle
Point
Gauge
Open
Channel
Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

6

1. The rectangular or triangular weir plate is attached to the regular Hydraulic Bench as shown
in the photographs.
2. A stopwatch, a hook or a point gauge are also needed with the experiment.

Procedures and Readings
1. Make sure that the Hydraulic Bench is leveled.
2. Set the Vernier on the point gauge to a datum reading by placing the tip of the gauge on the
crest or the apex of the weir. Take enough care not damage the weir plate and the point
gauge.
3. Put the point gauge half way between the stilling baffle plate and the weir plate.
4. Allow water to flow into the experimental setup and adjust the minimum flow rate by
means of the control valve to have atmospheric pressure all around water flowing over the
weir. Increase the flow rate incrementally such that the head above the weir crest increases
around 1 cm for each flow rate increment
5. For each flow rate, wait until steady condition is attained then measure and record the head
(H) above the weir.
6. For each flow rate, measure and record the initial and final volumes in the collecting tank
and the time required to collect that volume. For each flow rate, take 3 different readings of
the volumes and time and record the averages.


Calculations and Results Interpretation
A. Rectangular weir:

Fill the following table of observations
Reading Crest level
(C.L.) (mm)
Water level
(W.L.)(mm)
Initial volume
(I.V.) (liter)
Final volume
(F.V.) (liter)
Time (T)
(sec)
1
2
3
4
5

Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

7
Fill the following table of results
Reading Volume = F.V.-I.V.
(liter)
H = C.L.-
W.L. (cm)
Time
(sec)
Q= volume/time
(cm3/s)
Log Q Log H
H
1.5
Cd
1
2
3
4
5


Plot Q against H, Q against H
1.5
, log Q against log H, C
d
against H, and obtain the C
d
from the slopes
of the two linear graphs. Compare the three obtained values of the C
d


B. Triangular weir:

Fill the following table of observations
Reading Crest level
(C.L.) (mm)
Water level
(W.L.)(mm)
Initial volume
(I.V.) (liter)
Final volume
(F.V.) (liter)
Time (T)
(sec)
1
2
3
4
5

Fill the following table of results
Reading Volume = F.V.-I.V.
(liter)
H = C.L.-
W.L. (cm)
Time
(sec)
Q= volume/time
(cm3/s)
Log Q Log H
H
2.5
Cd
1
2
3
4
5


Plot Q against H, Q against H
5/2
, Log Q against Log H, C
d
against H, and obtain the C
d
from the slopes
of the two linear graphs. Compare the three obtained values of the C
d



Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

8
Suggestions for Conclusions and Comments

1. Is C
d
constant? Give comments.
2. Can the Q-H relation be described by an empirical formula? If so, assume the relation
is in the form of
n
kHQ = and find the constants k and n.

Example (V-notch experiment)

H = C.L. - W.L.
(cm)
volume
(lit)
time
(sec.)
Q
(cm3/s)

H
2.5
Q
2/5

2

5

76

65.79

5.66

5.34

2.3

5

53

94.34

8.02

6.16

2.5

5

41

121.95

9.88

6.83

2.8

5

32

156.25

13.12

7.54


slope = 11.974
0.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
160.00
180.00
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00
H^2.5
Q

C
d
= slope*15/(8*
g2.
2
tan




θ
) = 0.507

Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

9

2. Impact of Jet

Objective of the Experiment
To demonstrate and investigate the validity of theoretical expressions for the calculation of the
force exerted by a jet on objects of various shapes.


Theory

From momentum principle,
)cos.vv(QF
y
θ−ρ= where
A
Q
v =
• For flat plate (90º),
A
Q
F
2
y
ρ=
• For 120º plate,
A
2
Q
3F
2
y
ρ=
• For hemispherical target 180º,
A
Q
2F
2
y
ρ=

90
o
FLAT PLATE HEMISPHERE 120 DEG CONE


Experimental Setup
1. The impact of jet apparatus is placed above the regular Hydraulic Bench as shown in the
photographs.
2. A stopwatcher.

Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

10


Procedures and Readings
1. Remove the stop plate and transparent casing to measure the nozzle diameter and place the
flat plate (90º) on the rod attached to the weight pan. Then, reassemble the apparatus.
2. Connect the inlet pipe of the apparatus to the outlet of the Hydraulic Bench.
3. Level the base of the apparatus using the bubble balance.
4. Screw down the top plate to datum on the spirit level.
5. Adjust the level gauge to suit datum on the weight pan.
6. Add masses to the weight pan. Allow water to flow in the experiment and adjust the flow
by the control valve of the Hydraulic Bench so that the pan will be re-adjacent to the level
gauge.
7. Before taking readings the weight pan should be oscillated upwards and downwards and
rotated to minimize the effect of friction.
8. Take the readings of the initial and final volumes and the time of accumulation.
9. Record the masses on the weight pan.
10. Repeat the experiment for different masses on the weight pan.

Nozzle
Plates with
different shapes
Target Plate
Pointer
(spirit level)
Weight pan
From
Pump
Glass
housing
Weights
Water
bubble
level
Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

11
11. Repeat the previous steps with different shapes of plates (120º and the hemispherical
target).

Calculations and Results Interpretation

For each plate, fill the following table of observations

Reading Mass on weight
pan
M (gm)
Initial volume
(I.V.) (liter)
Final volume
(F.V.) (liter)
Time (T)
(sec)
1
2
3
4
5

Fill the following table of results
Reading
Mass on weight
pan
M (gm)
Volume =
F.V.-I.V.
(liter)
Time
(sec)
Q= volume/time
(cm3/s)
Q
2

1
2
3
4
5

Plot mass M on weight pan with Q
2


From the analysis, verify that the slope of the graphs should be:
Flat plate =
gA
ρ

120º plate =
gA
5.1
ρ

Hemispherical target =
gA
2
ρ

Calculate the Coefficient of Impact = (F
act
/ F
calculated
)


Nozzle Diameter
=
8
mm

g = 9.81 m/s
2

Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

12
Suggestions for Conclusions and Comments
1. Comment on the coefficient of impact.
2. Comment on the results of the computed slope and the shape of the target plate.

Example (flat plate)

m (gm) V (lit) T (sec)
Q
(cm3/s) Q
2

280

5

13

384.6154

147929

230

5

14

357.1429

127551

180

5

16

312.5

97656.25

130

5

20

250

62500


solpe = 0.0019
0
50
100
150
200
250
300
0 20000 40000 60000 80000 100000 120000 140000 160000
Q^2
m


gA
ρ
=0.0202

slope = 0.0019
Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

13

3. Flow through Sharp Edged Orifice.

Objective of the Experiment

1. To study the path of water jets issuing from orifices.
2. To determine the coefficients of discharge, velocity and contraction from a sharp-edged
circular orifice.
3. To study the variation and dependence of the relevant parameters.

Theory
The coefficient of discharge C
d
is the ratio of the actual discharge Q
act
to the theoretical discharge Q
th
.
The theoretical discharge is given by the following relationship where A is the area of the orifice and H
is the total head on the orifice centerline and the actual discharge can be measured.

gH2AQ
th
= &
0.1
Q
Q
C
th
a
d
<=

The Path of the jet from the orifice is given by the following equation where x is the horizontal
distance, y is the vertical distance and v is the flow velocity from the orifice.

tvx
act
=
&
2
50.0 gty =


2
2
50.0
act
v
x
gy =

gHc
x
gy
v
2*
50.0
2
2
=
Hy
x
c
v
**2
=

Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

14
Experimental Setup

The regular Hydraulic Bench is used in this experiment
1. The orifice plate apparatus is placed above the regular Hydraulic Bench as shown in the
photographs.
2. A stopwatch is needed.
3. The adjustable stainless steel overflow pipe near the top of the tank is used to adjust the
level of water in the tank.




Orifice
Pointers
(thin pins)
Constant
head tank
Metal piece
for over flow
Scale
Paper
Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

15




Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

16
Procedures and Readings
1. Turn on the pump of the hydraulic bench and allow water into the constant head tank to
build up above the orifice. Wait until steady condition is achieved.
2. You can control the level of the water into the constant head tank by pulling up and down
the adjustable stainless steel overflow pipe as shown in the photograph.
3. Measure the head (H) above the orifice using the graduated scale.
4. By setting the thin pins so that they just touch the issuing water jet, draw the path of the
water jet on the given graph paper.
5. Measure and record the initial and final volumes and the time of accumulation for each
reading of head (H).
6. Repeat the previous steps for at least four more different heads (H) by changing the position
of the adjustable stainless steel overflow pipe.

Calculations and Results Interpretation
For each reading of head (H), fill the following table of observations

Point(1)

Point(2)

Point(3)

Point(4)

Point(5)

Point(6)

H (cm)

Initial
volume
(liter)
Final
volume
(liter)
X(cm)


Y(cm)




1. Calculate the theoretical flow rate using the measured head and the area of the orifice.
2. Calculate the actual flow using the volume and time recorded.
3. Calculate the coefficient of discharge C
d
.
4. draw x
2
-y relationship and determine the coefficient of velocity
5. Repeat the above mentioned steps for various values of measured head
6. Plot Q
a
against (H)
0.5

7. Comment on the graphs and on the slope of each graph.
8. Is the coefficients of the orifice is constant with change of water head

Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

17
Example


point
1
point
2
point
3
point
4
point
5
point
6
H
(mm) V (lit)

T (sec)
X (cm) 5

10

15

20

25

30

Y (cm) 0.2

0.7

1.5

1.8

4.2

5.7

X
2
25

100

225

400

625

900

Cv = (X
2
/4YH)
0.5
0.88

0.94

0.97

1.18

0.96

0.99

400 7 150

D
orifice
= 6mm

v
th
= (2gH)
0.5 =
280.14

cm/sec

Q
act
= V/T = 46.67

cm3/s
Q
th
= a
orifice
* v
th
= 79.17

cm3/s

Cd = Q
act
/Q
th =
0.589



Cv = (X
2
/4YH)
0.5

SLOPE = 4HCv
2 =
158.28


Cv = 0.995


Cc = Cd/Cv = 0.592



slope = 158.28
0
100
200
300
400
500
600
700
800
900
1000
0 1 2 3 4 5 6
Y
X^2



Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

18
4. Bernoulli’s Theorem Demonstration

Objective of the Experiment
1. To demonstrate the variation of the pressure along a converging-diverging pipe section.
2. To verify the Bernoulli’s Theorem.

Theory
For ideal flow at any section on the pipe,






++ Z
g
p
g
v
ρ
2
2
= constant.
In the experimental setup, the pipe is horizontal (i.e. Z = constant). Therefore along the pipe,
g
p
g
v
ρ
+
2
2
= constant

Experimental Setup


The Bernoulli’s experimental setup is placed on the top of the regular Hydraulic Bench.


Control
Valve
Glass
Venturimeter
Water
Manometer
From the
Pump

To the
Venturi

Air
inlet
Pitot
Tube
Air
bubble
Cairo University Fluid Mechanics
Faculty of Engineering 2
nd
Year Civil Engineering
Irrigation and Hydraulics Department 2010 - 2011

19
Procedures

1. Level the Bernoulli’s experimental apparatus on the Hydraulic Bench by adjusting the
screw legs.
2. Switch on the pump and open the flow control valve to fill the entire apparatus and
manometers with water. Ensure that no air is entrapped in the apparatus or any of the
manometers by opening the air valve at the right end of the air chamber connecting the top
ends of the manometers. Make sure to close the air valve again.
3. Adjust the flow rate into the experiment by the flow control value in the apparatus.
4. To make visible the water levels in the manometers, connect and work the hand air pump at
the air inlet (shown in the photograph) to raise the air pressure in the air chamber, thus
pushing the manometer columns down into the glass tubes.
5. Carefully adjust both flow control valves in the apparatus and in the Hydraulic Bench to
provide the combination of flow rate and pressure within the pipe such that the pressure
difference between the highest and the lowest manometer levels is reasonable.
6. Observe the variation of the scale readings of the water levels in each manometer tube.
7. Push the stainless steel probe (pitot-tube) at the right end of the horizontal transparent
section of the pipe into the tapered portion of the pipe. Position its end at stations adjacent
to the manometer openings in the pipe one station at a time. For each position, observe the
corresponding scale reading of the manometer to the probe. Compare the pitot-tube reading
to the manometer reading connected to the same position.
8. Repeat the previous steps with different flow rates at high and low static pressure for
different combinations of valve opening.