More About Energy Transfer in Turbomachines

Taking scalar product with it becomes

We have used . With a little rearrangement, we have

Since v is the velocity relative to the rotating frame we can replace it by . Further is the linear velocity of the rotor. Integrating the momentum equation from inlet to outlet along a streamline we have

or,	(2.1)

Therefore, we can say, with the help of Eq. (2.1), that last two terms of Eq. (1.7) represent a change in the static head of fluid.

Energy Transfer in Axial Flow Machines
For an axial flow machine, the main direction of flow is parallel to the axis of the rotor, and hence the inlet and outlet points of the flow do not vary in their radial locations from the axis of rotation. Therefore, and the equation of energy transfer Eq. (1.7) can be written, under this situation, as

	(2.2)

Hence, change in the static head in the rotor of an axial flow machine is only due to the flow of fluid through the variable area passage in the rotor.

Radially Outward and Inward Flow Machines
For radially outward flow machines, , and hence the fluid gains in static head, while, for a radially inward flow machine, and the fluid losses its static head. Therefore, in radial flow pumps or compressors the flow is always directed radially outward, and in a radial flow turbine it is directed radially inward.

Impulse and Reaction Machines The relative proportion of energy transfer obtained by the change in static head and by the change in dynamic head is one of the important factors for classifying fluid machines. The machine for which the change in static head in the rotor is zero is known as impulse machine . In these machines, the energy transfer in the rotor takes place only by the change in dynamic head of the fluid. The parameter characterizing the proportions of changes in the dynamic and static head in the rotor of a fluid machine is known as degree of reaction and is defined as the ratio of energy transfer by the change in static head to the total energy transfer in the rotor.

Therefore, the degree of reaction,

	(2.3)