Question

Consider gas flow through a converging-diverging nozzle. Of the five following statements, select the one that is incorrect: (a) The fluid velocity at the throat can never exceed the speed of sound. (b) If the fluid velocity at the throat is below the speed of sound, the diversion section will act like a diffuser. (c) If the fluid enters the diverging section with a Mach number greater than one, the flow at the nozzle exit will be supersonic. (d) There will be no flow through the nozzle if the back pressure equals the stagnation pressure. \((e)\) The fluid velocity decreases, the entropy increases, and stagnation enthalpy remains constant during flow through a normal shock.

Short answer

A) The fluid velocity at the throat can achieve the speed of sound but not exceed it. B) If the fluid velocity at the throat is below the speed of sound, the diverging section acts as a diffuser. C) When the fluid enters the diverging section with a Mach number greater than 1, the flow at the nozzle exit is supersonic. D) When back pressure equals the stagnation pressure, there is no flow through the nozzle. E) The fluid velocity decreases, the entropy increases, and the stagnation enthalpy remains constant during flow through a normal shock. Answer: E) The fluid velocity decreases, the entropy increases, and the stagnation enthalpy remains constant during flow through a normal shock.

Step-by-step solution

Statement A

: It is a fact that the fluid velocity at the throat can achieve the speed of sound (M = 1), but it cannot exceed the speed of sound if the gas flow is choked. Hence, this statement is correct.

Statement B

: If the fluid velocity at the throat is below the speed of sound (i.e., subsonic), the diverging section of the nozzle will indeed act as a diffuser, as it slows down the fluid and increases its pressure. This statement is also correct.

Statement C

: When the fluid enters the diverging section with a Mach number (M) greater than 1, it means that the flow is supersonic. Consequently, the flow at the nozzle exit will also be supersonic. This statement is correct as well.

Statement D

: In the case where back pressure equals the stagnation pressure, there would be no pressure difference and thus no flow through the nozzle. This statement is correct.

Statement E - Incorrect Statement

: Finally, statement (e) states: "The fluid velocity decreases, the entropy increases, and the stagnation enthalpy remains constant during flow through a normal shock." While it is true that during a normal shock, the fluid velocity decreases, and the stagnation enthalpy remains constant, the part "entropy increases" is incorrect. In fact, the entropy of the fluid remains constant during the normal shock, as it is an adiabatic process. So the incorrect statement among the given options is statement (e).