Assertion (A): A convergent-divergent nozzle may give supersonic orsub...
Assertion (A): A convergent-divergent nozzle may give supersonic or subsonic flow at the exit even if the throat is choked.
Reason (R): Depending on the back pressure ratio Pb/Po, the divergent part of the nozzle may act as a supersonic nozzle or a subsonic diffuser.
The correct answer is option 'A', which means that both the assertion and the reason are individually true, and the reason is the correct explanation of the assertion.
Explanation:
To understand this assertion and reason, let's first review the basics of a convergent-divergent nozzle.
A convergent-divergent nozzle is a device used to accelerate the flow of a fluid (usually a gas) to supersonic speeds. It consists of three sections: the convergent section, the throat, and the divergent section. The convergent section narrows down the flow area, increasing the velocity of the fluid. The throat is the smallest cross-sectional area of the nozzle, and it is designed to achieve choked flow conditions. The divergent section gradually expands the flow area, further accelerating the fluid to supersonic speeds.
Now, let's analyze the assertion and reason:
Assertion (A): A convergent-divergent nozzle may give supersonic or subsonic flow at the exit even if the throat is choked.
This assertion is true. When the throat of the nozzle is choked, it means that the mass flow rate through the nozzle is at its maximum value, and the flow velocity at the throat is sonic (i.e., equal to the speed of sound). However, the flow conditions at the exit of the nozzle can be either supersonic or subsonic, depending on the back pressure ratio (Pb/Po). If the back pressure ratio is greater than the critical value, the flow at the exit will be subsonic. If the back pressure ratio is less than the critical value, the flow at the exit will be supersonic.
Reason (R): Depending on the back pressure ratio Pb/Po, the divergent part of the nozzle may act as a supersonic nozzle or a subsonic diffuser.
This reason is the correct explanation of the assertion. The divergent section of the nozzle plays a crucial role in determining the flow conditions at the exit. If the back pressure ratio is greater than the critical value, the divergent section acts as a subsonic diffuser, decelerating the flow and causing it to exit the nozzle at subsonic speeds. If the back pressure ratio is less than the critical value, the divergent section acts as a supersonic nozzle, further accelerating the flow and causing it to exit the nozzle at supersonic speeds.
In conclusion, a convergent-divergent nozzle can have supersonic or subsonic flow at the exit even if the throat is choked, and this is determined by the back pressure ratio. The divergent section of the nozzle acts as either a supersonic nozzle or a subsonic diffuser depending on the back pressure ratio.
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.