Expalation about Bernoulis Equation

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II MODULE
FLUID MOTION
BERNOULIS EQUATION
By
SINY MARY LONA

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Bernoulli’s Principle

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Assumptions by Bernoulli’s Equation:
●Fluid is Ideal
●Flow is Steady
●Flow is Incompressible
●Flow is IrrotationalS

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Bernoulli’s Theorem
●In Fluid Dynamics: Bernoulli’s Principle states that increase in
speed of a fluid occurs simultaneously with decrease in static
pressure or a decrease in fluids Potiental Energy
●Meaning: It states that speed of a moving fluid increases when
pressure decreases.

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Bernoulli’s Principle

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Bernoulli’s Theorem
●It is based on principle of Energy Conservation for Ideal fluid in
steady flow
●The sum of Pressure energy ,Kinetic Energy and Potiental Energy
per unit mass of an Incompressible non viscous fluid ,remains
constant

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Bernoulli’s Principle

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Derivation
●Consider a flow of liquid through pipe AB flowing
●V= Volume of liquid entering At A time’t’=Volume of fluid
leaving Pipe AB in ’t’ sec.
●AA,PA,vA be the Area,pressure and Velocity of fluid through Pipe
A
●Similarly
●AB,PB,vB be the Area,Pressure and Velocity of fluid through pipe
B.

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Pressure Energy
●Force exerted by liquid at A:
●P=F/A FA=PA*AA
●Distance Travelled by liquid in time ’t’sec
●Work done =FA*d
●Since FA=PA*AA*vA*t as vA=d/t
●But AA*d=V
●WA=FA*d=PA*V

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Contd.......
●Pressure Energy per unit Volume
●PA*V/V=PA
●Pressure Energy per unit mass=Pressure energy/mass
● =PA*V/m=PA/(rho)
●Similarly at End B:
●PB*V/m=PB/(rho)
●The pressure energy is the energy in/of a fluid due to the applied
pressure (force per area). So if you have a static fluid in an enclosed
container, the energy of the system is only due to the pressure; if the
fluid is moving along a flow, then the energy of the system is the kinetic

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Pressure Energy

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Example of pressure Energy

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Potiental Energy

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Examples of Potiental energy

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Potiental Energy
●P.EA=m*g*h
●A potential energy is the energy that is stored in an object due to
its position relative to some zero position. An object possesses
gravitational potential energy if it is positioned at a height above
(or below) the zero height.

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Examples of Kinetic Energy

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Kinetic Energy
●K.EA=1/2*m*vA
2
●
Kinetic energy is the energy of mass in motion. The kinetic energy of an object is the
energy it has because of its motion.
●
In Newtonian (classical) mechanics, which describes macroscopic objects moving at a
small fraction of the speed of light, the kinetic energy (E) of a massive body in motion can
be calculated as half its mass (m) times the square of its velocity (v): E = ½mv2. Note that
energy is a scalar quantity, i.e., it does not depend on direction, and it is always positive.
When we double the mass, we double the energy; however, when we double the velocity,
energy increases by a factor of four.

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Kinetic Energy

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●As per Bernoulli’s Theorem
●E A=EB
●PA/(rho)+VA
2/2*g+hA=PB/(rho)+VB
2/2*g+hB=Constant
●The above Equation is consequences of Conservation of energy

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Disadvantages of Bernoulli’s Theorem
●According to law of conservation of energy :
●No Energy is lost ,but energy is lost due to friction.
●In practice Energy is lost in friction ,due to layers of fluid
flowing in layers with different velocity exert frictional force on
each other.This loss of energy is converted into Heat Energy.
●Thus this theorem is basically used for non viscous fluid having
zero viscosity
●When pipe is horizontal ,h=0

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Examples of Bernoulli’s Theorem:

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Examples of Bernoulli’s Theorem

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Thank you