For incompressible fluid

(9)

This equation is also called Bernoulli’s equation. Note that this equation is in terms of unit mass of fluid flowing

Frictional losses
Application of equation 10 requires the evaluation of frictional forces in various flow systems. Frictional losses for the flow of fluid in circular tubes can be evaluated by the Fanning equation.

(10)

                                                                                  
f is friction factor, L is length and D is diameter of the pipe. Note that  is the velocity of fluid in the pipe. It is different than velocity of fluid at plane 1. The velocity in equation 11 is equal to V₂ when the plane 2 is at just at the exit of the system. If the plane 2 is downstream the exit than V₂ is not equal to the fluid velocity in the pipe. Friction factor depends on type of flow: Laminar or turbulent flow. For the laminar flow of fluid in a pipe

(11)

Where Re is Reynold’s number and is defined as

(12)

Here  is the velocity of fluid,  is density and  is viscosity.
In the turbulent region friction factor in a smooth pipe

(13)