A De Laval nozzle is the hourglass-shaped part of a rocket engine that turns hot, high-pressure gas into a fast exhaust jet. It matters because rocket thrust depends strongly on how quickly mass is thrown out the back of the engine. The nozzle has a converging section, a narrow throat, and a diverging section that work together to accelerate the gas.
This shape is what lets rocket exhaust go from subsonic to supersonic speed.
Key Facts
- Thrust is approximately F = mdot ve + (pe - pa)Ae, where mdot is mass flow rate, ve is exhaust speed, pe is exit pressure, pa is outside pressure, and Ae is exit area.
- At the throat of an ideal De Laval nozzle, the flow reaches Mach 1 when the nozzle is choked.
- Mach number is M = v / a, where v is flow speed and a is the local speed of sound.
- In the converging section, subsonic gas speeds up as the area gets smaller.
- In the diverging section, supersonic gas speeds up as the area gets larger.
- Rocket momentum thrust is F = mdot ve when the exit pressure matches the outside pressure.
Vocabulary
- De Laval nozzle
- A converging-diverging nozzle that accelerates hot gas from subsonic speed to supersonic speed.
- Throat
- The narrowest part of the nozzle where choked flow reaches Mach 1 in an ideal rocket nozzle.
- Mach number
- The ratio of an object's or fluid's speed to the local speed of sound.
- Choked flow
- A flow condition in which the mass flow rate cannot increase because the gas has reached Mach 1 at the throat.
- Exhaust velocity
- The speed of the gas leaving the nozzle, which is a major factor in rocket thrust.
Common Mistakes to Avoid
- Thinking the widest part of the nozzle is where the gas first becomes sonic is wrong because ideal choked flow reaches Mach 1 at the narrow throat.
- Assuming a diverging section always slows gas down is wrong because supersonic gas speeds up when the flow area increases.
- Ignoring pressure thrust is wrong because F = mdot ve is incomplete when the exit pressure does not match the outside pressure.
- Using one constant speed of sound everywhere in the nozzle is wrong because the gas temperature changes, so the local speed of sound changes too.
Practice Questions
- 1 A rocket nozzle expels gas at mdot = 20 kg/s with exhaust velocity ve = 1800 m/s. If pressure thrust is negligible, what is the thrust?
- 2 At a point in a nozzle, the gas speed is 900 m/s and the local speed of sound is 600 m/s. What is the Mach number, and is the flow subsonic or supersonic?
- 3 Explain why a De Laval nozzle must have both a converging section and a diverging section to accelerate rocket exhaust from subsonic speed to supersonic speed.