Derive the expression for Bernoulli’s equation

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Derivation of Bernoulli’s expression

• Considering a moving incompressible liquid, if the viscosity is negligibly small, there are no frictional forces to overcome.
• In this case the work done by the pressure difference per unit volume of a fluid flowing along a pipe steadily is equal to the gain of kinetic energy per unit volume plus the gain in potential energy per unit volume.
• Assuming the area is constant at a particular place for a short time of flow; the work done by a pressure in moving a fluid through a distance

= force x distance moved

= (pressure x area) x distance moved

= pressure x volume moved,

• At the. beginning of the pipe where the pressure is , the work done per unit volume on the fluid is thus P₁
• At the other end, the work done per unit volume by the fluid is likewise, P₂
• Hence the net work done on the fluid per unit volume = P₂ – P₁

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