Express the Bernoulli equation in three different ways using (a)energies, (b)pressures, and (c) heads.

Consider a small volume of fluid with volume , of length and area of cross section . Also consider the velocity of the fluid is , density is , pressure is , and the height is

Then the kinetic energy is

The potential energy is

And the work done due to the pressure to flow from one side of the volume to the other side fo the volume is

Hence the total energy is

constant (from the conservation of energy)

Now divide the equation with respect to the , we get

constant (1)

This is the Bernoulli's equation in energy terms.