Assertion (A): A normal shock wave can occur at any section in aconver...
Ans. (d) A shock wave takes place in the diverging section of a nozzle, in a diffuser, throat of a supersonic wind tunnel, in front of sharp-nosed bodies.
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Assertion (A): A normal shock wave can occur at any section in aconver...
Assertion (A): A normal shock wave can occur at any section in a convergent-divergent nozzle.
Reason (R): A normal shock wave occurs only when the flow of the fluid is supersonic and the subsequent flow after the shock is subsonic.
Explanation:
A convergent-divergent nozzle is a key component in supersonic flow systems, such as jet engines and rocket nozzles. It is designed to accelerate the flow of a fluid (usually air or exhaust gases) to supersonic speeds. In such nozzles, a normal shock wave can occur at any section depending on the flow conditions.
Let's examine the assertion and reason separately to understand why option D is the correct answer.
Assertion (A): A normal shock wave can occur at any section in a convergent-divergent nozzle.
A normal shock wave is a type of shock wave where the flow changes from supersonic to subsonic velocity abruptly. It occurs when the flow speed exceeds the local speed of sound, causing a compression wave to form.
In a convergent-divergent nozzle, the flow undergoes a gradual acceleration in the converging section, reaching a critical point at the throat where the flow velocity becomes sonic (Mach number = 1). After the throat, the flow expands in the diverging section, which further accelerates the flow to supersonic speeds.
Due to the complex flow behavior in supersonic flows, a normal shock wave can occur at any section in the convergent-divergent nozzle. The shock wave forms when the flow speed exceeds the local speed of sound, causing a sudden increase in pressure and temperature.
Reason (R): A normal shock wave occurs only when the flow of the fluid is supersonic and the subsequent flow after the shock is subsonic.
The reason correctly states that a normal shock wave occurs only when the flow is supersonic. In subsonic flows, the flow changes smoothly without any shock wave formation. When the supersonic flow encounters an obstacle or a sudden change in the flow area, it can lead to the formation of a shock wave.
In the case of a convergent-divergent nozzle, the flow is accelerated to supersonic speeds in the diverging section. If the flow conditions are such that the flow speed exceeds the local speed of sound, a normal shock wave can occur. The flow after the shock wave becomes subsonic as it decelerates due to the sudden increase in pressure and temperature across the shock wave.
Conclusion:
From the above explanation, it is clear that both the assertion and reason are true. However, the reason does not provide the correct explanation for the assertion. The reason simply restates the condition for a normal shock wave to occur, which is already mentioned in the assertion. Hence, option D is the correct answer.
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