S.1 Spacecraft Propulsion Systems Chapter 1: Introduction to ...

Maximum Exhaust Velocity
- 16-
Conservation of energy applied for gas flow in nozzles:
decrease of enthalpy H (H=cpT) is equal to the increase of kinetic energy (½ Mv 2 )
applied to one mole of perfect gas → the velocity of the gas when leaving the nozzle exit
(index E) is given
2
vE = o −
M
( H H )
E
[m/s]
and the theoretical maximum value for vE is for HE=0, that is all enthalpy has been used to
increase the kinetic energy of the expelled gas molecules:
2
M
( H )
vE max = o
=
2κ
κ −1
RT
M
[m/s]
where κ is the ratio of specific heat, R is the universal gas constant, T is the absolute
temperature and M is the molecular mass.
Note that the exhaust velocity is a function of mainly temperature T and molar mass M
T
vE ≈ [m/s]
M