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
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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
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