The Momentum Equation and Its Application

The major encountered in the hydraulic machine is to find the power developed (or consumed) by (or in) a particular machine. A turbine produces power while pumps, compressors, and fans consume power to run. The power is determined from the dynamic force or forces which are being exerted by the flowing fluid on the boundaries of the flow passage and which are due to the change of momentum. These are determined by applying "Newton's second law of motion".

In this chapter, we present the momentum equation and fluid dynamics forces in a simple way and a step by step manner related to the types of prime movers, turbines, pumps, water wheels ... etc. The force and power calculations using the velocity diagram for each type are presented too.

The derivation of Bernoulli's equation for relative motion based on consideration of momentum is very useful to present fluid motion inside a turbine runner or pump impeller of a centrifugal pump, which is shown in this chapter with solved problems.

Keywords: Bernoulli`s equation, Momentum equation, Velocity diagram.