Discussion
A perfect gas stored in a large reservoir exhausts into the atmosphere through a convergent duct. The reservoir pressure is \(P_{0}\) and temperature is \(T_{0}\). The jet emerges from the nozzle at choked conditions with average velocity \(u\), Mach number \(M\), pressure \(p\), temperature \(T\), and density \(\rho\). If the reservoir pressure is increased, then
Answer: C
Raising the reservoir pressure leaves \(u\), \(M\) and \(T\) unchanged, while \(p\) and \(\rho\) increase.
A choked convergent nozzle has \(M = 1\) at its exit, and once choked it stays at \(M = 1\) however high the reservoir pressure goes. With adiabatic flow, the exit temperature is fixed by the reservoir temperature alone, and so is the exit velocity:
\[ \begin{aligned} T &= \frac{2T_{0}}{\gamma + 1} \\ u &= \sqrt{\gamma RT} \end{aligned} \]
Neither depends on \(P_{0}\). The exit pressure, however, is a fixed fraction of the reservoir pressure, \(p = P_{0}(2/(\gamma+1))^{\gamma/(\gamma-1)}\), so it rises with \(P_{0}\); then \(\rho = p/RT\) rises too, and that is how the mass flow of a choked nozzle increases.
Any option in which \(u\), \(M\) or \(T\) increases is therefore wrong, and the option keeping \(\rho\) constant contradicts the ideal gas law with \(p\) rising at fixed \(T\).
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development