Bernoulli Experiment Lab Report






Aim
Aim of this experiment is to compare the behavior of ideal fluid and real fluid 

Objective
1. Use the venture meter apparatus to study the effect of area of the flow velocity and fluid pressure
2. Use the Bernoulli’s equation to compare the behavior of ideal and real fluid






Introduction
According to the Bernoulli’s principle when area available for the fluid to flow decrease then flow velocity of the fluid increase and at the mean while time the fluid pressure or the fluid potential energy decreases (R.K. Bansal (n.d)). This principle was name after the Daniel Bernoulli who first writes this principle in book named Hydrodynamic. 

Following are some of the application of the Bernoulli’s principle
Air-flight
Lift
Baseball
Draft

Sailing

Theory
According to Miller, R.W (1996) Law of conservation of energy was the main deriving factor behind the derivation of the Bernoulli’s principle. Bernoulli’s principle state that the in a steady flowing fluid the sum of all the mechanical energies including kinetic energy, dynamic head, fluid pressure and potential energy should remain same at all the point of the flow. So if any type of energy increase like if kinetic energy increase then the other type of the energy like potential energy, pressure will decrease to make the final sum same as before. 

According to the Bernoulli equation a flowing fluid have three things
Pressure head
Kinetic Energy
Potential Energy

So we have

P+  1/2×ρ×v^2+ ρgh=C

P/ρg+  1/2×v^2/g+h=C

According to the law of conservation of energy, energies at the input should be equal to the output so

P_1/ρg+  (V_1^2)/2g+h=  P_n/ρg+  (V_n^2)/2g+h

In the above equation 
P = fluid pressure
V = flow velocity
Z = height
ρ = density 

From Bernoulli’s principle it can be stated that the density and pressure are inversely proportional to each other’s means high density fluid will apply more pressure while moving than the low density fluids. 

In the horizontal pipe where the inlet and outlet of the are at same height, the z quantity can be removed to give the above mention equation of Bernoulli’s principle a new look from where we can calculate the height at any point of the flow if we have the initial height of flow and velocity at respective positions. 

P_1/ρg+  (V_1^2)/2g=  P_n/ρg+  (V_n^2)/2g

P_1/ρg=h1 and  P_n/ρg=hn 

h_1+  (V_1^2)/2g= h_n+  (V_n^2)/2g

h_n= h_1-[  (v_n^2)/2g-  (v_1^2)/2g]

Apparatus
Venture meter
Supply Hoses
Measuring Tank

Procedure
1. Place the venture meter on to a horizontal surface and note the height of input valve and output valve and make sure they are same.

2. Attach the apparatus with the power supply but keep the supply off

3. Open all the air bleed valves of the manometer present at the top.

4. On the power supply to run the pump and adjust the flow rate control valve until water level in all the manometers is at readable range.

5. Place stop plug in basin

6. Note the time require to fill the basin with specific amount of water

7. Remove the stop plug to drain out all the water from the water

8. Place the dynamic pressure probe with the static pressure port  and measure the manometer data from both of the probes

9. Now place the dynamic pressure probe with next static pressure probe and measure the manometer data from the probes

10. Repeats the above steps for measuring data from all the manometer probes

11. Turn off the pump and set off the power supply


Sample calculations

Mass = 6 Kg

Volume = 6/1000 = 0.006 cubic meter

Time = 13.075 sec

Flow Rate = 0.006/13.057 = 0.000459 cubic meter/sec

V = Q/A

A = 0.000531

V = 0.000459/0.000531

V= 0.865 m/sec

h_n= h_1-[  (v_n^2)/2g-  (v_1^2)/2g]

h_2= 0.274-[  〖1.106529〗^2/2g-  〖0.881013〗^2/2g]

h_2= 0.251131 m


Experimental Results

Calculations
Position
A
B
C
D
E
F
G
H
I
J
K
Diameter mm
26
32.2
18.4
16
16.8
18.47
20.16
21.84
23.53
25.24
26
Area mm^2
530.9
422.7
265.9
201.1
221.7
268
318.8
375
435
500.8
530.9
Area m^2
0.000531
0.000423
0.000266
0.000201
0.000222
0.000268
0.000319
0.000375
0.000435
0.000501
0.000531
Test
Mass Kg
Time sec
Q m^3/sec
Distance from A mm
0
20
32
46
61
76
91
106
121
36
156
1
6
13.075
0.000458891
hn exp m
0.274
0.26
0.166
0.022
0.039
0.121
0.167
0.196
0.214
0.228
0.234
6
12.59
0.000476569
Vn m/s
0.881013
1.106529
1.759045
2.325858
2.109743
1.745261
1.467158
1.24728
1.075241
0.933966
0.881013
hn th m
0.274
0.251131
0.155732
0.037601
0.086509
0.158196
0.203777
0.234228
0.254614
0.269097
0.274
2
6
14.75
0.00040678
hn exp m
0.263
0.252
0.176
0.062
0.074
0.139
0.176
0.198
0.213
0.223
0.228
6
14.66
0.000409277
Vn m/s
0.768559
0.96529
1.534517
2.028981
1.840451
1.522493
1.279887
1.088075
0.937995
0.814752
0.768559
hn th m
0.263
0.245597
0.172997
0.083098
0.120317
0.174872
0.20956
0.232733
0.248247
0.259268
0.263
3
6
19.25
0.000311688
hn exp m
0.24
0.223
0.189
0.12
0.125
0.165
0.188
0.200
0.208
0.214
0.217
6
19
0.000315789
Vn m/s
0.590957
0.742226
1.179914
1.560114
1.415151
1.170668
0.984125
0.836637
0.721239
0.626476
0.590957
hn th m
0.24
0.229711
0.186787
0.133636
0.155642
0.187896
0.208405
0.222106
0.231278
0.237794
0.24


Graphs


Discussion

From the calculation it is very clear that with decrease in area of the flow velocity increase and pressure decrease

As shown in graph of all three test that the decrease in area of flow decrease the height of water in manometer column means they are directly proportional to each other

Difference in the theoretical and measured value it can be said that water is not an ideal fluid 

Height of water in the final column was not equal to the initial values which show that there are friction losses in water particle

This type of information is very use full in the case if nozzles, jets and diffusers


Conclusion

Aim objective of this experiment was to discuss the behavior of ideal and real fluid and on the basis of the test result it can be concluded that the experiment was successful because there is difference in measured and theoretical values. This is because of the friction losses in the real fluid; ideal fluid does not have friction losses. From the experiment it can be conclude that with decrease in area of flow there is an increase in velocity and decrease in the flow pressure of the fluid. 

References

R.K. Bansal (n.d) Chapter 8 flow measurement, A Textbook of Fluid Mechanics

Miller, R.W (1996) Flow Measurement engineering Handbook 3Rd ED. McGraw-Hill Book, New York N.Y

USBR (1996) Flow Measurement Manual. Water Resource Publication LLC Highland Ranch Co

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