Topic: Fluid Mechanics
Gaseous Nitrogen at 30°C is expanded through a converging nozzle from a total pressure of 0.5 MPa to a back pressure chamber. If the back pressure is increased from 0.1 MPa to 0.4 MPa in steps of 0.02 MPa, the trend in mass flow rate through the nozzle
- A. will gradually decrease
- B. will gradually increase
- C. will remain constant till a point and then gradually decrease
- D. will remain constant till a point and then gradually increase
Answer: C. will remain constant till a point and then gradually decrease
Explanation: For an ideal diatomic gas like Nitrogen, $\gamma = 1.4$. The critical pressure ratio is $P_c/P_0 = (2/(\gamma+1))^{\gamma/(\gamma-1)} \approx 0.528$. The critical pressure $P_c = 0.5 imes 0.528 = 0.264 \text{ MPa}$. When back pressure increases from 0.1 MPa up to 0.264 MPa, the flow is choked, and mass flow rate remains constant. Once the back pressure exceeds 0.264 MPa up to 0.4 MPa, the nozzle becomes unchoked, leading to a gradually decreasing mass flow rate.