__BERNOULLI'S THEOREM AND APPLICATION__

__BERNOULLI'S THEOREM AND APPLICATION__

## In steady flow of fluid, the Bernoulli principle state that at any point of time the sum of all form of energy along the streamline is same. It means that the kinetic energy, potential energy and the internal energy of fluid is constant.

## Consider a case of fluid flow,where the speed of fluid increases. With the increase in speed it gains kinetic energy and dynamic head. But at the same time there is decrease in potential energy, internal energy and also static head.

Observe the above figure carefully, the fluid enters through section"1" of venturimeter and moves out through section "2". As you can see inlet section is of larger diameter and and outlet section is smaller in diameter.

__At section "1" the fluid has high pressure and less velocity. But as it enters section "2" the pressure energy gets converted to kinetic energy and the fluid gains speed__. The difference in pressure is depicted by difference in manometric head "h" (AS SHOWN IN FIGURE).

__Hence one form of energy is converted to another. This is basic idea of BERNOULLI'S principle__.

NOTE -Bernoulli's principle is valid for incompressible fluid only

## Where,

p1 - pressure at section 1

v1 - velocity at section 1

z1 - height of fluid at section 1.

## P2 - Pressure at section 2

V2 - velocity at section 2

## Z2 - height at section 2

g - acceleration due to gravity.

p

*-*density of fluid at all point.__APPLICATION OF BERNOULLI'S THEOREM:-__

## PITOT TUBE

INVENTED BY-HENRI PITOT(18th century)

A pitot tube is a instrument which is used to measure pressure by determining fluid flow velocity. In the modern times it is widely used in industrial application for measuring air speed an in aircraft to measure speed of air.

## A pitot tube has a pointing tip which is exposed directly to fluid flow. The flowing fluid in tube enters the tube, since the other end is closed and connected to pressure measuring device, the fluid is brought to rest (static). The pressure at this moment is known as pitot pressure.

PITOT PRESSURE

*=*STATIC PRESSURE + DYNAMIC PRESSURE

Static pressure is obtained from static ports available in pitot tube and dynamic pressure is obtained by fixing a diaphragm in pitot tube. When fluid flows there is diaphragm present between the static and stagnation side. The movement of diaphragm determines the dynamic pressure.

## Once the dynamic pressure is known the speed can be easily determined by the means of mechanical levers.

## APPLICATION:-

- Determine mach number, speed.
- Determine both static and dynamic pressure.

VENTURIMETER

A venturimeter is a device that helps to create velocity head by restricting the pressure through the restricted area. The venturimeter was first coined by an Italian physicist Gaiovanni Battista Venturi in 18th century. In order to maintain continuity the fluid must flow with increase in speed through the reduced cross section in order to balance the pressure. The decrease in pressure or pressure drop determines the flow rate. The tube has length varying from 100 mm to 1000 mm and the inlet portion has angle of around 30 degree and exist section has angle of about 5 degree. Its use is avoided if the flow of fluid has Reynold's number less than 1.5*10^5.

Note- In venturimeter density of the fluid is assumed to be constant even though its pressure changes.

__Numerical questions__

1) Velocity of discharge is given by relation V = QA, where Q is discharge and A is area.

1) The state is correct

2) The statement is incorrect

3) Can't be justified.

2) The total head is equal to _______________.

1) Pressure head - Velocity head

2) Velocity head - Pressure head

3) Pressure head + Velocity head

4) Pressure head * Velocity head

3) According to Bernaulli's theorem, which statement holds good?

1) Pressure energy gets converted to kinetic energy.

2) Kinetic energy gets converted to pressure energy.

3) No energy transfer takes place.

4) Bernaulli's theorem is applied only for?

1) Real fluid

2) Ideal fluid

3) Viscous fluid

4) All of them

5) According to Bernaulli's theorem, Pressure head + Velocity head + Height = ____________?

1) Variable

2) Constant

6) In Bernaulli's theorem, frictional losses are neglected.

1) True

2) False

7) The unit of discharge of flow is given by?

1) m^2/sec

2) m^3/sec

3) m^3/sec^2

4) m^2/sec^2

Thankyou.