−M = (GQ/g) (w2r2 − w1r1).
(4)
If α is the angular velocity of the wheel, the work done by the water on the wheel is
T = Ma = (GQ/g) (w1r1 − w2r2) α foot-pounds per second.
(5)
§ 185. Total and Available Fall.—Let Ht be the total difference of level from the head-water to the tail-water surface. Of this total head a portion is expended in overcoming the resistances of the head race, tail race, supply pipe, or other channel conveying the water. Let ɧp be that loss of head, which varies with the local conditions in which the turbine is placed. Then
H = Ht − ɧp
is the available head for working the turbine, and on this the calculations for the turbine should be based. In some cases it is necessary to place the turbine above the tail-water level, and there is then a fall ɧ from the centre of the outlet surface of the turbine to the tail-water level which is wasted, but which is properly one of the losses belonging to the turbine itself. In that case the velocities of the water in the turbine should be calculated for a head H − ɧ, but the efficiency of the turbine for the head H.
§ 186. Gross Efficiency and Hydraulic Efficiency of a Turbine.—Let Td be the useful work done by the turbine, in foot-pounds per second, Tt the work expended in friction of the turbine shaft, gearing, &c., a quantity which varies with the local conditions in which the turbine is placed. Then the effective work done by the water in the turbine is
T = Td + Tt.