Question

During a rocket launch from Sea Level to Space, a fixed-geometry nozzle that is over-expanded at the launch pad will eventually become

• A. More over-expanded as it gains altitude
• B. Perfectly expanded, then under-expanded as back pressure drops
• C. Subsonic at the throat
• D. Extremely separated at high altitudes

Hint:

As altitude increases, \[ P_b\downarrow \] Hence, \[ \boxed{ \text{Over-expanded} \rightarrow \text{Perfectly Expanded} \rightarrow \text{Under-expanded}. } \]

Answer 1

The Correct Option is B

Step 1: Recall the nozzle expansion conditions. For a rocket nozzle,
• Over-expanded nozzle: \(P_eP_b\) where \[ P_e=\text{exit pressure},\qquad P_b=\text{back pressure}. \]

Step 2: Determine the effect of increasing altitude. As the rocket ascends, \[ P_b \] continuously decreases while the nozzle geometry remains fixed. Thus, \[ \boxed{ \text{Over-expanded} \rightarrow \text{Perfectly expanded} \rightarrow \text{Under-expanded}. } \] Therefore, \[ \boxed{\text{Perfectly expanded, then under-expanded as back pressure drops}} \] is the correct answer. Thus, \[ \boxed{(B)} \] is the correct answer.