Final Bernoulli

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    BERNOULLISEQUATION

    BY

    AISHWARYA NAIR[2013A1PS411H]

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

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    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/

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    Derivation

    Fs = -Adp Fb = -gAdz

    Using the momentum equation,

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    Momentum flux = VA dV

    Substituting in momentum equation,

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

    By integrating,

    P/+ V2/2 + gz = constant

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    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.

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    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.

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    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.

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    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,

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    Pitot Tube

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    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.

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    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.

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    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.

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    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.

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    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.