For a cold gas propulsion rocket engine, where gas is expelled without combustion or significant temperature increase, the velocity of the exhaust gases at the nozzle exit can be determined using the continuity equation, A1V1=A2V2, which is based on the conservation of mass.
The formula indicates that the product of the cross-sectional area and velocity remains constant between the nozzle inlet and exit for an incompressible flow (assuming no losses). As the cross-sectional area decreases, the velocity must increase to maintain mass flow continuity.
For cold gas propulsion, the working fluid is usually a gas stored at ambient temperature. The performance of such systems is often limited compared to engines that involve combustion. Real-world design considerations include the specific properties of the gas used and the geometry of the rocket nozzle. Engineers use more detailed analyses and simulations to optimize the design for efficiency and performance.
The continuity equation is given by:
where:
- and are the cross-sectional areas at the nozzle entrance and exit, respectively,
- and are the velocities at the nozzle entrance and exit, respectively.
which gives
where,
- A1 is the Cross-sectional area at the throat of the nozzle in m2
- A2 is the Cross-sectional area at the exit of the nozzle in m2
- V1 is the Velocity of the exhaust gases at the throat in m/s
- V2 is the Velocity of the exhaust gases at the nozzle exit in m/s