What is Bernoulli's Equation and its Limitations.

In Hydrodynamics the Motion of Liquid and the Forces causing Flow are covered.In this post,I will cover some topics of Hydrodynamics.

Energy of a Liquid in Motion.

Energy means the capacity to do work.Mainly three important Energy Forms are possessed by a Liquid,these are as follows.

01)Potential Energy:-
It is the Energy possessed by a Liquid particle,by virtue of its position.

02)Kinetic Energy:-
It is the Energy possessed by a Liquid particle,by virtue of its Motion or Velocity.

03)Pressure Energy:-
It is the Energy possessed by a Liquid particle,by virtue of its existing Pressure.

Bernoulli's Equation:-
It states that "For a perfect Incompressible Liquid,flowing in a continuous Stream,the total Energy of a particle remain the same,while the particle moves
from one point to another".There is one assumption that "there are no Friction Losses in Pipe".

Limitation of Bernoulli's Equation:-

01)The Velocity of Liquid particle in the centre of a pipe is maximum and gradually decreases towards the walls of the pipe due to friction.
Thus while using Bernoulli's Equation,only the Mean Velocity of the Liquid should be taken into account because the Velocity of Liquid particles is not
uniform.As per assumption it is not practicle.

02)There are always some external Forces acting on the Liquid,which affects the Flow of Liquid.Thus while using Bernoulli's Equation,all such external
forces are neglected which is not happened in actual practise.If some Energy is supplied to or extracted from the Flow,same should also taken into account.

03)In Turbulent Flow some Kinetic Energy is converted into Heat Energy and in a Viscous Flow some Energy is lost due to Shear Forces.Thus while using
Bernoulli's Equation all such losses should be neglected,which is not happened in actual practise.

04)If the Liquid is Flowing through curved path,the Energy due to Centrifugal Forces should also be taken into account.

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