8/11/2019 Final Bernoulli

1/16

BERNOULLISEQUATION

BY

AISHWARYA NAIR[2013A1PS411H]

DEEKSHA REDDY[2013A1PS701H]GAMINI SINGH[2013A1PS740H]

8/11/2019 Final Bernoulli

2/16

Castro-Orgaz, O. & Chanson, H. (2009). "Bernoulli Theorem, Minimum Specific

Energy and Water Wave Celerity in Open Channel Flow".Journal of Irrigation

and Drainage Engineering.

REFERENCES:

Wikipedia.org

MIT PSDAM LAB 2002 COPYRIGHT

http://www.grc.nasa.gov/WWW/k-12/airplane/wrong1.html

http://prezi.com/idfwgkmwhpfk/bernoullis-principle-

music/

8/11/2019 Final Bernoulli

3/16

Derivation

Fs = -Adp Fb = -gAdz

Using the momentum equation,

8/11/2019 Final Bernoulli

4/16

Momentum flux = VA dV

Substituting in momentum equation,

-Adp gAdz = VAdV-dp/gdz = Vdv = d(V2/2)

By integrating,

P/+ V2/2 + gz = constant

8/11/2019 Final Bernoulli

5/16

Bernoullis Equation: Assumptions_______________________________________________

1) Steady State Flow2) No Friction, ie inviscid Flow

3) Flow Along Streamline

4) Incompressible flow

Bernoullis equation cant be used through regions where

fluids mix:

i. Mixed jets & wakes (flow breaks up, swirls resulting

in shear stresses which dissipates energy)

ii. Pumps & motorsiii. Other areas where the fluid is turbulent or mixing.

8/11/2019 Final Bernoulli

6/16

8/11/2019 Final Bernoulli

7/16

8/11/2019 Final Bernoulli

8/16

Lift Explained by Bernoulli Principle

In reality, the velocity on the upper surface of a lifting wing is much higher

than the velocity which produces an equal transit time.

8/11/2019 Final Bernoulli

9/16

Lift Explained by Newtons III Law

The upper airfoil surface doesn't enter into the theory at all. So using this

theory, we would expect two airfoils with the same lower surface but very

different upper surfaces to give the same lift.

In fact, there are devices on many airliners called spoilers, ailerons which are

small plates on the upper surface. They are used to change the lift of the

wing to manoeuvre the aircraft by disrupting the flow over the upper

surface. This theory does not predict or explain this effect.

8/11/2019 Final Bernoulli

10/16

Static Pressure:

Pressure we used to derive Bernoulliequation(thermodynamic pressure).

Pressure experienced by fluid particle as it moves.

Stagnation Pressure:

Generated when a flowing fluid decelerated to zero

speed by frictionless process.

=Dynamic Pressure

So we have,

8/11/2019 Final Bernoulli

11/16

Pitot Tube

8/11/2019 Final Bernoulli

12/16

On The actual tube several small holes are drilled around the outside of the tube and a

centre hole is drilled down the axis of the tube.

The outside holes are connected to one side of a device called a pressure transducer. The

centre hole in the tube is kept separate from the outside holes and is connected to the other

side of the transducer. The transducer measures the difference in pressure in the two groups of tubes by measuring

the strain in a thin element using an electronic strain gauge. The pitot-static tube is mounted

on the aircraft, or in a wind tunnel , so that the center tube is always pointed in the direction

of the flow and the outside holes are perpendicular to the center tube.

Bernoulli's principle is used to calibrate the airspeed indicator so that it displays

the indicated airspeed appropriate to the dynamic pressure

On some airplanes the pitot-static tube is put on a longer boom sticking out of the nose of

the plane or the wing.

8/11/2019 Final Bernoulli

13/16

Cavitation in Pipelines

Cavitation refers to the formation of air bubbles in fluid inlow-pressure condition.It is a potentially damaging condition

in which the fluid in pipes or sewers is at high velocities.

By Bernoullis Equation, at high flow velocities, the pressure

head of fluid is reduced accordingly. As a result dissolved

gases are released from the fluid and these air bubbles will

suddenly collapse when the flow enters into a region of higher

pressure. This high dynamic pressure causes damage to the

pipelines due to its high frequency.

8/11/2019 Final Bernoulli

14/16

Bernoullis principle is applied in the functioning of

carburetor which blends fuel and air in an internal

combustion engine

The carburetor contains a venturi which is

Used to draw all the fuel to the combustion

Chamber.here the bernoullisequation comes

to play .

The venturi contains a very small crosssectionalarea which allows high velocity of gases in thereby

decreasing the pressure.

8/11/2019 Final Bernoulli

15/16

Bernoullis equations application in

music:

Have u ever given a thought to flute and

Trumphet producing sound of different

Pitches when same amount of air is blown

Into them?

The flute and the trumphet are of different sizes.the

trumpet has higher Crosssectional area.

so the velocity of air entering the trumphet would be

Less than that of air entering the flute.according to

bernoullisequation the pressure is inversely

proportional to the velocity.therefore,more pressure is

built up in the flute there by producing a higher pitch.

8/11/2019 Final Bernoulli

16/16

Recent Development

Some confusion exists about the applicability

of the Bernoulli theorem and its generalization

to open-channel hydraulics.

A detailed analysis of the Bernoulli theorem

and its extension to flow in open channels has

been developed recently (2009). This is

generalized depth-averaged Bernoullitheorem.