Characteristic Velocity

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	\(\large{\frac{lbm}{ft^3}}\)	\(\large{\frac{kg}{m^3}}\)