The formula for the nozzle reaction, also known as the thrust force, is:
*F = ṁ (V<sub>e</sub> - V<sub>0</sub>)**
Where:
- F is the thrust force (N)
- ṁ is the mass flow rate of the propellant (kg/s)
- V<sub>e</sub> is the exhaust velocity (m/s)
- V<sub>0</sub> is the velocity of the vehicle (m/s)
This formula essentially states that the thrust force is equal to the rate of change of momentum of the propellant as it is ejected from the nozzle.
Practical Insights:
- Higher exhaust velocity (V<sub>e</sub>) leads to greater thrust. This is why rocket engines are designed to achieve high exhaust velocities.
- Higher mass flow rate (ṁ) also increases thrust. This is why larger rockets have more powerful engines.
- The velocity of the vehicle (V<sub>0</sub>) has a small impact on the overall thrust, but it is important to consider in certain applications.
Example:
Imagine a rocket engine with a mass flow rate of 10 kg/s and an exhaust velocity of 3000 m/s. If the rocket is stationary (V<sub>0</sub> = 0 m/s), the thrust force would be:
F = 10 kg/s * (3000 m/s - 0 m/s) = 30,000 N
This means the rocket engine would produce a thrust of 30,000 Newtons.
