De Laval Nozzle - Exhaust Gas Velocity

Exhaust Gas Velocity

As the gas enters a nozzle, it is traveling at subsonic velocities. As the throat contracts down the gas is forced to accelerate until at the nozzle throat, where the cross-sectional area is the smallest, the linear velocity becomes sonic. From the throat the cross-sectional area then increases, the gas expands and the linear velocity becomes progressively more supersonic.

The linear velocity of the exiting exhaust gases can be calculated using the following equation:

Some typical values of the exhaust gas velocity v_e for rocket engines burning various propellants are:

• 1,700 to 2,900 m/s (3,800 to 6,500 mph) for liquid monopropellants
• 2,900 to 4,500 m/s (6,500 to 10,100 mph) for liquid bipropellants
• 2,100 to 3,200 m/s (4,700 to 7,200 mph) for solid propellants

As a note of interest, v_e is sometimes referred to as the ideal exhaust gas velocity because it based on the assumption that the exhaust gas behaves as an ideal gas.

As an example calculation using the above equation, assume that the propellant combustion gases are: at an absolute pressure entering the nozzle of p = 7.0 MPa and exit the rocket exhaust at an absolute pressure of p_e = 0.1 MPa; at an absolute temperature of T = 3500 K; with an isentropic expansion factor of γ = 1.22 and a molar mass of M = 22 kg/kmol. Using those values in the above equation yields an exhaust velocity v_e = 2802 m/s or 2.80 km/s which is consistent with above typical values.

The technical literature can be very confusing because many authors fail to explain whether they are using the universal gas law constant R which applies to any ideal gas or whether they are using the gas law constant R_s which only applies to a specific individual gas. The relationship between the two constants is R_s = R/M.