Characteristic velocity

${\displaystyle c_{Actual}^{*}={\frac {p_{c}A_{t}}{\dot {m}}}}$

• ${\displaystyle c^{*}}$ is the characteristic velocity (m/s, ft/s).
• ${\displaystyle p_{c}}$ is the chamber pressure (Pa, psi).
• ${\displaystyle A_{t}}$ is the area of the throat (m², in²).
• ${\displaystyle {\dot {m}}}$ is the mass flow rate of the engine (kg/s, slug/s).

${\displaystyle c_{Theoretical}^{*}={\frac {I_{sp}g_{0}}{C_{F}}}={\frac {c}{C_{F}}}={\sqrt {{\frac {RT_{c}}{\gamma }}{\Bigl (}{\frac {\gamma +1}{2}}{\Bigr )}^{\frac {\gamma +1}{\gamma -1}}}}}$

Alternative Imperial form:

${\displaystyle c_{Theoretical}^{*}={\frac {I_{sp}g_{0}}{C_{F}}}={\frac {c}{C_{F}}}={\frac {\sqrt {g_{0}\gamma RT_{c}}}{\gamma {\sqrt {{\frac {2}{\gamma +1}}^{\frac {\gamma +1}{\gamma -1}}}}}}}$

• ${\displaystyle I_{sp}}$ is the specific impulse(s).
• ${\displaystyle g_{0}}$ is the gravitational acceleration at sea-level (m/s²).
• ${\displaystyle C_{F}}$ is the thrust coefficient.
• ${\displaystyle c}$ is the effective exhaust velocity (m/s).
• ${\displaystyle \gamma }$ is the specific heat ratio for the exhaust gases.
• ${\displaystyle R}$ is the gas constant per unit weight (J/kg-K).
• ${\displaystyle T_{c}}$ is the chamber temperature (K).

• Characteristic length (L*)
• Thrust coefficient (C_F)