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8/11/2019 Final Bernoulli
http://slidepdf.com/reader/full/final-bernoulli 1/16
BERNOULLI’SEQUATION
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 = -ρgAdz
Using the momentum equation,
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Momentum flux = ρVA dV
Substituting in momentum equation,
-Adp – ρgAdz = ρVAdV-dp/ ρ – gdz = Vdv = d(V 2 /2)
By integrating,
P/ ρ + V 2 /2 + gz = constant
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Bernoulli’s Equation: Assumptions _______________________________________________
1) Steady State Flow2) No Friction, ie inviscid Flow
3) Flow Along Streamline
4) Incompressible flow
Bernoulli’s equation can’t 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 Newton’s 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 Bernoulli’s 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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Bernoulli’s 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 “bernoulli’s equation” 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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Bernoulli’s equation’s 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
“bernoulli’s equation” 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.