# Characteristic Velocity

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 formula

$$\large{ U = \frac{ p_c \; A }{ \dot m_f } }$$
Symbol English Metric
$$\large{ U }$$ = characteristic velocity  $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ p_c }$$ =  pressure of chamber $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ A }$$  (Greek symbol rho) = area of throat $$\large{ft^2}$$ $$\large{m^2}$$
$$\large{ \dot m_f }$$ = mass flow rate $$\large{\frac{lbm}{sec}}$$ $$\large{\frac{kg}{s}}$$

## Characteristic velocity formula

$$\large{ U = \sqrt{ 2 \; Ec \; c \; \Delta T } }$$
Symbol English Metric
$$\large{ U }$$ = characteristic velocity  $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ Ec }$$ = Eckert number $$\large{dimensionless}$$
$$\large{ c }$$ = specific heat $$\large{\frac{btu}{lbm-F}}$$ $$\large{\frac{kJ}{kg-K}}$$
$$\large{ \Delta T }$$ = temperature change  $$\large{F}$$ $$\large{K}$$

## Characteristic velocity formula

$$\large{ U = \sqrt{ \frac{\Delta p}{Eu \; \rho} } }$$
Symbol English Metric
$$\large{ U }$$ = characteristic velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ \Delta p }$$ = pressure differential $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ Eu }$$ = Euler number $$\large{dimensionless}$$
$$\large{ \rho }$$  (Greek symbol rho) = density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ 