Bernoulli's equation of fluid flow:

Bernoulli's equation of fluid flow: Consider an ideal fluid incompressible and nonviscous of density p flowing along a flow tube of varying cross section. The system under consideration is the flow tube between points 1 and 2, and the Earth (Fig. 2.37) From the continuity equation it follows that pressure and speed must be different in regions of different cross section. If the height also changes, there is an additional pressure difference.

The fluid enters the system at point 1 through a surface of cross section A, at speed . The point 1lies at a height hy, with respect to anarbitrary reference level y = 0, and the local pressure there is p₁. Thefluid leaves the system at point 2where the corresponding quantitiesare A2 , h2 and p2.

Consider a small fluid element, of

volume ΔV and mass Δm = p ΔV, that enters at point 1 and leaves at point 2 during small time interval Δt. In the absence of internal fluid friction, it can be shown that the wor done on the fluid element by the surrounding fluid is

 ΔW= (p1-p2)ΔV.

This is sometimes called the pressure energy. During This is sometimes called the pressure energy. During Δt, the changes in the kinetic energy and potential energy are