Question

A perfect gas stored in a reservoir exhausts through a convergent nozzle. The jet emerges at choked conditions with average velocity $u$. If reservoir pressure $p_0$ increases while $T_0$ remains constant, determine effect on $M, u, T, p, \rho$.

• A. $u, M, p, T, \rho$ increase
• B. $u, p, T, \rho$ increase, $M$ same
• C. $u, M, T$ same, $p, \rho$ increase
• D. $u, M, T$ same, only $p$ increases

Hint:

In choked nozzle flow, velocity and Mach number are locked, while pressure and density scale directly with reservoir pressure.

Answer 1

The Correct Option is C

Step 1: Choked condition.
At throat: $M=1$ (fixed).

Step 2: Temperature.
\[ T_t = f(T_0) \Rightarrow \text{constant since } T_0 \text{ constant.} \]

Step 3: Velocity.
\[ u = M a = a = \sqrt{\gamma RT_t} \Rightarrow \text{constant.} \]

Step 4: Pressure & density.
Ratios $p_t/p_0$ and $\rho_t/\rho_0$ are fixed. Increasing $p_0$ raises both $p_t, \rho_t$. \[ \boxed{u, M, T \text{ constant; } p, \rho \text{ increase.}} \]