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Bernoulli’s Theorem

It states that in a steady, ideal flow of an incompressible fluid, the total energy at any point of the fluid is always constant.

Total Energy = constant

P/ γ + V2/2g + Z = constant

where

P/ γ   =  pressure energy or pressure head per unit weight

V2/2g  = kinetic energy or kinetic head per unit weight

Z  =  potential energy or datum energy or datum head per unit weight

Assumptions made in Bernoulli’s Equation:

1.    The fluid is ideal.
2.    The flow is steady and continuous.
3.    The flow is incompressible.
4.    The flow is one-dimensional i.e. along steam-line.
5.    Velocity is uniform over the cross-section and is equal to the mean velocity.
6.    The gravity force and pressure force are only considered.
7.    The flow is irrigational.

Limitation of Bernoulli’s Equation:

1.    It is applicable to ideal incompressible flow.
2.    The heat transfer into or out of fluid should be zero.
3.    The temperature remains constant so that internal energy does not change.
4.    The effect of presence of any mechanical device between two sections is ignored.

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