Dimensional analysis is used to derive the efficiency, η of a pump or a turbine, which is represented by the “drag coefficient, CD.” The efficiency of a pump, ηpump = (Pp)out/(Pp)in =...

Dimensional analysis is used to derive the efficiency, η of a pump or a turbine, which is represented by the “drag coefficient, CD.” The efficiency of a pump, ηpump = (Pp)out/(Pp)in = γQhpump/ωTshaft,in (Equation 4.197) expresses the ratio of a real/actual flow variable (hydraulic power output from the pump) to its corresponding ideal flow variable (shaft power input to the pump). And, the efficiency of a turbine, ηturbine = (Pt)out/(Pt)in = ωTshaft,out/γQhturbine (Equation 4.217) expresses the ratio of a real/actual flow variable (shaft power output from the turbine) to its corresponding ideal flow variable (hydraulic power input to the turbine). Explain Step 3 in the five-step procedure to derive a functional relationship between the n physical variables in the fluid flow situation and thus the n-m dimensionless numbers (π terms) for a given flow situation.

Equation 4.197

Equation 4.217