Let us consider a small portion of fluid over the length at the left side, which is under the pressure P₁ and with a speed v₁. When the same fluid moves over to the right side, the pressure, speed and length of the fluid are respectively P₂, v₂ and .

            The work done by the pressure force P₁A₁ on the system is P₁A₁ and the work done on the system by the pressure force P₂A₂ is  -P₂A₂.The negative sign implies that the work done is done by the system. The work done on the system by gravity is  -mg(y₂. y₁). Here also it is negative, because the work is done by the system against the gravity. The total work done on the system,

                                 ------------------------------(31)

As per work-energy theorem, the above work done on the system is equal to the change in kinetic energy.

                               -------------(32)

Since the mass 'm' of the selected portion of the fluid and its density do not change, we can write,