# Volumetric Efficiency

on . Posted in Fluid Dynamics

Volumetric efficiency, abbreviated as $$\eta_v$$ (Greek symbol eta), a dimensionless number, is a measure of how effectively an engine can move air in and out of the cylinders during the intake and exhaust strokes.  It is expressed as a percentage and represents the ratio of the actual volume of air that the engine can move in one cycle to the theoretical maximum volume of air that the engine can move in one cycle.  Theoretical maximum volume of air is the volume of air that the engine could move if it filled and emptied the cylinder completely with each stroke.  Actual volume of air is the volume of air that the engine can move in one cycle under real world operating conditions.  This is affected by factors such as air resistance, valve timing, and engine speed.

A perfectly efficient engine would have a volumetric efficiency of 100%, meaning that it can move the maximum amount of air into and out of the cylinders in one cycle.  However, in practice, no engine can achieve 100% volumetric efficiency due to factors such as air resistance, valve overlap, and other losses.  Volumetric efficiency is an important factor in determining an engine's power output and is used by engine tuners and builders to optimize engine performance.  Improving the volumetric efficiency of an engine can increase its power output without increasing its displacement, which can lead to better performance and fuel economy.

## Volumetric Efficiency Formula

$$\large{ \eta_v = \frac{3456 \; CFM}{CID \; RPM} }$$
Symbol 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 $$\large{in^3}$$ $$\large{mm^3}$$
$$\large{ RPM }$$ = pump revolution per minute $$\large{\frac{r}{min}}$$ $$\large{\frac{r}{min}}$$

## Motor Volumetric Efficiency Formula

$$\large{ \eta_v = \frac{ s \; 100 }{ TS } }$$
Symbol English Metric
$$\large{ \eta_v }$$  (Greek symbol eta) = volumetric efficiency $$\large{dimensionless}$$
$$\large{ s }$$ = speed $$\large{\frac{ft}{sec}}$$   $$\large{\frac{m}{s}}$$
$$\large{ TS }$$ = theoretical speed $$\large{\frac{ft}{sec}}$$   $$\large{\frac{m}{s}}$$

## Punp Volumetric Efficiency Formula

$$\large{ \eta_v = \frac{ GPM \; 100 }{ TF } }$$
Symbol English Metric
$$\large{ \eta_v }$$  (Greek symbol eta) = volumetric efficiency $$\large{dimensionless}$$
$$\large{ GPM }$$ = flow in gallon per minute $$\large{\frac{gal}{min}}$$ $$\large{\frac{l}{min}}$$
$$\large{ TF }$$ = theoretical flow $$\large{\frac{ft}{sec}}$$   $$\large{\frac{m}{s}}$$