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VERIFICATION OF BERNOULLI’S THEOREM EXPERIMENT NOTES

 VERIFICATION OF BERNOULLI’S THEOREM

Aim:To verify the validity of Bernoulli’s equation for incompressible flow

Introduction: A fluid motion can be completely analyzed by the application ofcertain fundamental equations. These equations are

1) the continuity equation   2) the energy equation  3) the momentum equation.

The above three equations are based on the three fundamental laws normally the law of conservation of mass flow, the law of conservation of energy and the law of conservation of momentum

A fluid body can possess the following types of energy namely potential energy, pressure energy and kinetic energy.

Potential energy or Datum energy: This is the energy possessed by a fluid body byvirtue of its position or location in space. Suppose we consider a fluid of ‘W’ Kg at a height of ‘Z’ in m above a datum plane. The potential energy of the fluid is equal to W Z Kg-m. Thus, the potential energy per Kg of the fluid body is equal to Z Kg-m per Kg or we say the potential head is Z in m.

Pressure energy: This is the energy possessed by a fluid body by virtue of thepressure at which it is maintained the pressure at the point is ‘P’ and w is specific

weight of the fluid the pressure head is wP  in m.
Kinetic energy: This is the energy possessed by a fluid body by virtue of itsmotion. Suppose, a fluid of ‘W’ Kg be moving at a velocity of ‘V’ m/ s.

Then,

Kinetic energy of  fluid =
WV
2
N










2g













V 2

Therefore, Kinetic head  =




m










2g


Thus, we find that if a fluid body of weight ‘W’ Kg be at a height of ‘Z’in m above a datum and at a pressure intensity of ‘P’ Kg /m2 and at a velocity of ‘V’ m /s , then,

the total energy of the fluid body
æ


P


V
2  ö


= WçZ
+


+



÷
Kg-m







ç


w



2g
÷


è





ø













æ
P

V 2



ö


The total energy head = ç

+




+ Z ÷
m







ç
w


2g



÷


è





ø














Object:To verify Bernoulli’s theorem (Law of Conservation of Energy )

Theory: Bernoulli’s theorem is a form of the well known principle of conservation ofenergy. The theorem is stated as “In a steady continuous flow of a frictionless incompressible fluid, the sum of the potential head, the pressure head and the kinetic head is same at all points. i.e.;
P1
+
V1
+ Z1
=
P2
+
V2
+ Z

=  ----------Constant

w
2g
w
2g
2



















23



The above equation is applicable to the following assumptions
1)  The flow of the fluid is steady   2) The flow is frictionless
3) The fluid is incompressible         4)The flow is continuous
Description:

The present apparatus is a self – contained unit operated on a closed circuit basis consisting of sump tank, and supply tank. Collecting tank (delivery tank) connected to Venturimeter with connections to piezometer tubes at different sections. A constant steady supply of water with a means of mono block pump set with outlet delivery valve for flow control. There is also provision for measurement of flow rate thus, the velocity.




















Procedure:

1)  Fill in the sump tank with clean water, and add some quantity of coloured ink to it.
2)    Keep the delivery valve open.

3)    Switch on the pump. Now, you will find water flowing to the collecting tank through Venturimeter.

4)    Now, you find the different piezometric heads for corresponding points of Venturimeter for constant supply head and delivery head.

5)    Note down all the piezometric readings and velocity head at particular point is also noted separately by bringing the inserted probe to that point.

6)    Note down height of water at supply tank and delivery tank

7)    Change the delivery head by pushing down the overflow pipe and repeat the experiment.

8)    Also, change flow rate and repeat the experiment.


Observations:
m2

Ac= Area of Collecting Tank = 0.3x0.4

w = Specific Weight of Water = 9810
N/m3












24
Table of Readings
S.No   No. of
Area of
Piezometer
Water collected
Time taken for
Datum Head
Points
points
Reading
in collecting
‘r’ rise of water




tank




‘i’
‘Ai’

P



‘t’

Z













w

‘r’








































UNIT

m2
cm


m
cm

m
sec
cm

m

1.
1.
5.50x 10 -4












2.
2.
4.75x 10 -4












3.
3.
3.50x 10 -4












4.
4.
2.50x 10 -4












5.
5.
3.00x 10 -4












6.
6.
   3.50x 10 -4












7.
7.
   4.25x 10 -4












8.
8.
4.70x 10 -4












9.
9.
5.00x 10 -4
















Table of Calculations:



S.No
No. of
Area of
Discharge
Velocity(V)

Kinetic head
Total Head

Points
points





                                                                                                              p/w



V=
Q
V 2

P

V 2











+


+ Z





Ai






‘i’
‘Ai’
Q

2g

w

2g













UNIT

m2
m3/sec
m/sec


m



m

1
1
5.50x 10 -4














2
2
4.75x 10 -4














3
3
3.50x 10 -4














4
4
2.50x 10 -4














5
5
3.00x 10 -4














6
6
   3.50x 10 -4














7
7
   4.25x 10 -4














8
8
4.70x 10 -4














9
9
5.00x 10 -4































Graph:

The following curves are drawn on the same graph X-axis: direct points (1, 2, 3, 4, 5, 6, 7)

Y-axis:   pressure head, velocity head, elevation head and total head



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