Change within kinetic energy of mass:

The change within kinetic energy of mass m is given by:

Δ KE = 1/2 m v₂² - 1/2 m v₁²                                                                                                        

To obtain an expression for the work done on the liquid due to pressure at points A and B, now let the pressure force at A displaces the fluid by a distance δ x₁ and the corresponding displacement at point B is δ x₂. So, the work done at A = p₁ a₁ δ x₁ and work done at point B = - p₂ a₂ δ x₂. The negative sign indicates in which at point B, a pressure force p₂ a₂ is directed opposite to the displacement δ x₂. So, the net work done on the liquid due to pressure forces is (p₁ a₁ δ x₁ -p₂  a₂  δ x₂ ) . Now, since a1 δ x₁ and a₂ δ x₂ are the volumes of equal mass m, we may write, a1 δ x₁= a₂ δ x₂= m/ ρ. Thus, the net work done on the liquid of mass m by the liquid pressure can be written as:

(p₁- p₂ ) m/ρ

There is yet another kind of force acting on the fluid: the gravitational force, which contributes to the work done on the liquid of mass m.