The document discusses Bernoulli's equation and its applications. (1) Bernoulli's equation states that for an incompressible and inviscid fluid, the total mechanical energy of the fluid is constant. (2) It describes how fluid pressure decreases as velocity increases according to the conservation of energy. (3) Some applications of Bernoulli's equation include Bunsen burners, flow sensors, ejectors, carburetors, aircraft wings, and spoilers on cars.

1. BERNOULLI EQUATION
&
APPLICATIONS OF BERNOULLI
EQUATION
Presented By:
Prakher singh.
Roll no. 2011058 Sec-A

2. Equation of motion :-
By Newton’s 2nd law;
Fx=m.ax
But in fluid flow,
Fx=(Fg)x+(Fp)x+(Fv)x+(Ft)x+(Fc)x …….( I )
Now, if we assume a flow to be ideal, then the equation ( I ) becomes
“Euler’s equation”.)
i.e,
𝑑𝑃
𝜌
+ 𝑔. 𝑑𝑧 + 𝑣. 𝑑𝑣 = 0
This is the required Euler's equation for motion as in the form of a
differential equation.

3. WHAT IS BERNOULLI EQUATION ?
It was Proposed by the Swiss scientist Daniel
Bernoulli
(1700–1782).
“Bernoulli's equation states that for an
incompressible and inviscid fluid, the total
mechanical energy of the fluid is constant” .
An increase in the velocity of a fluid that is
accompanied by a decrease of pressure. Swiss
scientist, Daniel Bernoulli (1700-1782),
demonstrated that, in most cases, the pressure in a
liquid or gas decreases as the liquid or gas moves
faster.
Bernoulli's principle :-

4. BERNOULLI’S EQUATION :-
From Euler’s equation;
𝑑𝑃
𝜌
+ 𝑔. 𝑑𝑧 + 𝑣. 𝑑𝑣 = 0
This is the required bernoulli’s equation
The following assumptions must be met for this Bernoulli equation to apply;
The flow must be steady, i.e. the fluid velocity at a point cannot change
with time,
The flow must be incompressible – even though pressure varies, the density
must remain constant along a streamline;
Friction by viscous forces has to be negligible

5. ENERGY FORM :-
𝑷𝟐 𝑷𝟏
𝑽𝟐 𝑽𝟐
𝝆 𝟐 𝝆 𝟐
+ 𝟐
+g𝒛𝟐 = + 𝟏
+g𝒛𝟏
Pressure energy + Kinetic energy + potential energy = constant
HEAD FORM :-
𝐏𝟐 𝐕𝟐
𝐏𝟏 𝐕𝟐
𝛒𝐠 𝟐𝐠 𝛒𝐠 𝟐𝐠
+ 𝟐
+𝐳𝟐 = + 𝟏
+𝐳𝟏
Pressure head + kinetic head + potential head = constant
PRESSURE FORM :-
𝑽𝟐
𝝆𝑽𝟐
𝟐 𝟐
𝑷𝟐+ 𝛒 𝟐
+𝝆g𝒛𝟐 =𝑷𝟏+ 𝟏
+ 𝝆g𝒛𝟏
Static pressure + dynamic pressure + hydrostaticpressure = constant

6. WHAT IS BERNOULLI EQUATION ?

7. APPLICATIONS:
 Bunsen Burner
 Flow sensors
 Ejectors
 Carburetor
 Aerofoil (lift)
 Pitot tube

8. APPLICATION IN BUNSEN
BURNER :-
When the burner is connected to a gas
supply, the gas flows at high velocity
through a narrow passage in the narrow
nozzle, creating a region of low pressure.
The outside air, which is at atmospheric
pressure is drawn in and mixes with the
gas. The mixture of gas and air enables
the gas to burn completely to produce
a clean, hot, and smokeless flame.

9. EJECTORS:
Ejectors are designed to convert the
pressure energy of a motivating fluid to
velocity energy to entrain suction fluid
… and then to recompress the mixed
fluids by converting velocity energy
back into pressure energy.
Ejectors are composed of three basic
parts: a nozzle, a mixing chamber and
a diffuser.
The diagram illustrates a typical ejector

10. PITOT TUBE
Pitot tube is a pressure measurement instrument
Used to measure fluid flow velocity.
Pitot tubes can be used to indicate fluid flow
velocity by measuring the difference between
the static and dynamic pressures in fluids.
The principle is based on the Bernoulli Equation.
2
𝑃 +
2
2
2 1
𝜌𝑉2
𝜌𝑉2
2
+ g𝜌𝑧 =𝑃 + + gρ𝑧
1 1
𝑃2= 𝑃1+
1
𝜌𝑉2
2
1
𝑉 =
2(𝑃𝑡− 𝑃𝑠)
𝜌

11. CARBURETOR:
The carburetor works on Bernoulli principle:
the faster air moves, the lower its static
pressure, and the higher its dynamic
pressure.
The throttle (accelerator) linkage does not
directly control the flow of liquid fuel.
Instead, it actuates carburetor
mechanisms which meter the flow of air
being pulled into the engine. The speed of
this flow, and therefore its pressure,
determines the amount of fuel drawn into
the airstream.

12. Application - LIFT
The flight of an aeroplane is based on the
principle regarding to the effect of the flow of
air around its wings, which is, the aerofoil.
An aerofoil shape has a rounded front edge
and pointed (sharp) trailing edge. The top
surface is arched (curved) and the bottom is
flat.
When a wing in the form of aerofoil moves
through air, the flow of the air over the top
has to travel faster to cover the longer
distance- i.e region of low pressure. The flow
of air below the wing is slower resulting in a
region of high pressure.

13. Spoiler provides better stability and avoids lift in cars.

14. THANK YOU !
Have Questions in mind ?