# Mechanical Efficiency

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Mechanical efficiency, abbreviated as $$\eta_m$$  (Greek symbol eta), a dimensionless number, is the ratio of theoretical power the pump needs to operate to the actual power delivered to the pump itself.

## Mechanical Efficiency Formulas

 $$\large{ \eta_m = \frac{ PSI \; 100 }{ TT } }$$ (motor (pressure differential PSI) ) $$\large{ \eta_m = \frac{ PSI \; 100 }{ TP } }$$ (pump (gauge pressure PSI) ) $$\large{ \eta_m = \frac{ P_a }{ P_m } }$$ (DC generator)

### Where:

 Units English Metric $$\large{ \eta_m }$$  (Greek symbol eta) = mechanical efficiency $$\large{dimensionless}$$ $$\large{ CIR }$$ = cubic inch per revolution $$\large{\frac{in^3}{rev}}$$ $$\large{\frac{mm^3}{rev}}$$ $$\large{ PSI }$$ = gauge pressure in pounds per square inch $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ P_m }$$ = mechanical input power $$\large{\frac{ft-lbf}{sec}}$$ $$\large{W}$$ $$\large{ P_a }$$ = converted power in armature $$\large{\frac{ft-lbf}{sec}}$$ $$\large{W}$$ $$\large{ PSI }$$ = pressure differential across motor in pounds per square inch $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ TP }$$ = theoretical pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ TT }$$ = theoretical torque $$\large{lbf-ft}$$ $$\large{N-m}$$ $$\large{ \tau }$$  (Greek symbol tau) = torque $$\large{lbf-ft}$$ $$\large{N-m}$$

### Solve for:

 $$\large{ TT = \frac{ CIR \; PSI }{ 6.28 } }$$ (motor) $$\large{ TP = \frac{ \tau \; 6.28 }{ CIR } }$$ (pump)

Tags: Efficiency Equations