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.

Impulse water turbine (Pelton turbine or Pelton wheel) is the standard type of turbines that are widely used nowadays. It is also called a free jet turbine. Pelton turbine operates under the high head of water and therefore, requires a comparatively less quantity of water.

In this chapter, the components of hydro-electric power plants using this type of turbine are presented with neat sketches. Theory of power, all mathematical calculations using velocity diagrams, solutions for single or multi-sets, power regulation components, supply, and discharge systems are also presented. Finally, solved problems are illustrated in detail at the end of this chapter.

In a reaction turbine, the runner utilizes both potential and kinetic energies. As flows through the stationary part of the turbine, the whole of its pressure energy is not transformed into kinetic energy and when the water flows through the moving parts, there is a change both in pressure and in the direction and velocity of flow of water. As the water gives up its energy to the runner, both its pressure and absolute velocity were reduced. The water, which acts on the runner blades is under a pressure above atmospheric and the runner passages are always completely filled with water.

The important reaction turbines are Francis and Kaplan which are discussed in this chapter according to their specification related to hydro–electric power plant. Theory for each type presented with sort notes and solved problems.

It is possible that a hydraulic machine will not give the desired result for which it has been designed. Such a machine is costly for manufacture and once it is made, it is difficult to change its components. Therefore, it is required to predict the performance of a prototype hydraulic machine before it is manufactured. This is done by making its model. Experiments are first performed on models from their results the performance of the prototype machine is predicted chapter on "Dimensional and Model Analysis" given in Fluid Mechanics will be useful for the prototype. Here prototype and its model are two similar machines having different specifications, which are to be compared. The concept of "Unit and specific Quantities" is a prerequisite for comparison of hydraulic machines. In addition, in this chapter a brief discussion about cavitation in turbine, turbine section, marking types of turbine and hydraulic turbine classification and section according to hydraulic power plants.

A pump is a machine that provides energy to a fluid in a hydraulic system. It assists to increase the pressure energy or kinetic energy, or both, in the fluid by converting the mechanical energy. The basic difference between a turbine and the pump, from a hydrodynamic point of view, is that in the former flow takes place from the high-pressure side to the low-pressure side, whereas in pump flow takes place from the low pressure forwards the higher pressure. Thus in a turbine, there is accelerated flow while in a pump the flow is decelerated. Accelerated flow throughout the hydraulic turbines is less subjected to turbulence therefore the runner passages are relatively short and high efficiency is available for this machine due to reduced values for the friction losses. Decelerated flow throughout the centrifugal pumps is sensitive to separation and vortices therefore impeller passages are relatively long and gradually increased in cross-section area for lowering the friction losses – "centrifugal pumps" efficiency is normally lower comparing to the turbines.

At the beginning of this chapter, one presents a classification of centrifugal pumps, reciprocating pumps – (Fig. 5.1) and pump turbines. In addition, basic centrifugal pump theory and a brief analysis of the net positive suction head (NPSH) that are very useful for the design and selection of the pumps are detailed. In the next sections similarity laws, specific speed, cavitation and selection of the pumps are available. All these items are illustrated by solved problems.

Chapters on "similarity law, specific speed and cavitation and pumps section" acquiring great efficiency in using the tool of mathematics and at the solved problems are available.