# Characteristic Velocity

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Characteristic velocity, abbreviated as U, measure the effectiveness of the combustion of a rocket engine at high temperature and pressure, seperate from nozzle performance.  It is used to compare different propellant and propulsion systems.

## Characteristic Velocity formulas

 $$\large{ U = \frac { p_c \; A } { \dot m_f } }$$ $$\large{ U = \sqrt { 2 \; Ec \; c \; \Delta T } }$$ (Eckert number) $$\large{ U = \sqrt { \frac{\Delta p}{Eu \; \rho} } }$$ (Euler number)

### Where:

$$\large{ U }$$ = characteristic velocity

$$\large{ A }$$  (Greek symbol rho) = area of throat

$$\large{ \rho }$$  (Greek symbol rho) = density

$$\large{ Ec }$$ = Eckert number

$$\large{ Eu }$$ = Euler number

$$\large{ \dot m_f }$$ = mass flow rate

$$\large{ \Delta p }$$ =  pressure differential

$$\large{ p_c }$$ =  pressure of chamber

$$\large{ c }$$ = specific heat

$$\large{ \Delta T }$$ = temperature change