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) 

 

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Tags: Efficiency Equations