# Volumetric Efficiency

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Volumetric efficiency, abbreviated as $$\eta_v$$ (Greek symbol eta), a dimensionless number, is the calculation for an internal combustion engine.  This is the calculation for the volumetric efficiency for an internal combustion engine.  For a thermal engine, the combustion process depends on the air-fuel ratio inside the cylinder.  The more air inside the combustion chamber, the more fuel that can be burned and the higher the output engine torque and power.

## Volumetric Efficiency Formulas

 $$\large{ \eta_v = \frac{3456 \; CFM}{CID \; RPM} }$$ $$\large{ \eta_v = \frac{ s \; 100 }{ TS } }$$ (motor) $$\large{ \eta_v = \frac{ GPM \; 100 }{ TF } }$$ (pump)

### Where:

 Units English Metric $$\large{ \eta_v }$$  (Greek symbol eta) = volumetric efficiency $$\large{dimensionless}$$ $$\large{ CFM }$$ = air flow in cubic feet per minute $$\large{\frac{ft^3}{min}}$$ $$\large{\frac{m^3}{min}}$$ $$\large{ CID }$$ = cubic inch displacement $$\large{in^3}$$ $$\large{mm^3}$$ $$\large{ CIR }$$ = cubic inch per revolution $$\large{\frac{in^3}{rev}}$$ $$\large{\frac{mm^3}{rev}}$$ $$\large{ GPM }$$ = flow in gallon per minute $$\large{\frac{gal}{min}}$$ $$\large{\frac{L}{min}}$$ $$\large{ RPM }$$ = pump revolution per minute $$\large{\frac{rev}{min}}$$ $$\large{\frac{rev}{min}}$$ $$\large{ s }$$ = speed $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$ $$\large{ TF }$$ = theoretical flow $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$ $$\large{ TS }$$ = theoretical speed $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$

### Solve for:

 $$\large{ TS = \frac{ GPM \; 231 }{ CIR } }$$ (motor) $$\large{ TF = \frac{ RPM \; CIR }{ 231 } }$$ (pump) 