Question

The optimum expansion in the nozzle occurs when

• A. exit pressure of the nozzle is greater than the atmospheric pressure
• B. exit pressure of the nozzle is less than the atmospheric pressure
• C. exit pressure of the nozzle is equal to the atmospheric pressure
• D. exit pressure is zero

Hint:

Optimum expansion ensures no residual pressure loss or shock formation.

Answer 1

The Correct Option is C

In aerospace engineering, the efficiency of a nozzle is critical for propulsion systems like jet engines and rockets. To achieve optimal performance from a nozzle, the expansion of gases should occur under specific conditions. The concept of "optimum expansion" implies that the pressure conditions at the nozzle's exit are crucial. Here's why the correct option is when the exit pressure equals the atmospheric pressure:

For a nozzle to be optimally expanded: 

• When the nozzle's exit pressure (P_e) is equal to the atmospheric pressure (P_atm), it indicates that there are no additional pressure differences that could cause further expansion or compression of the gases once they exit the nozzle.
• Mathematically, this can be represented as:
  P_e = P_atm
• Equalizing these pressures ensures that the potential energy within the gas is entirely converted into kinetic energy, maximizing thrust.
• If P_e is > P_atm, the nozzle is under-expanded, and the gases continue to expand outside the nozzle, reducing efficiency.
• If P_e is < P_atm, the nozzle is over-expanded, leading to shock waves and a loss of efficiency.

Thus, the optimal condition occurs at exit pressure of the nozzle is equal to the atmospheric pressure.