Question

A flow is steady, inviscid and one-dimensional, with no shaft work or body forces. Which of the following is/are possible under the given conditions?

• A. Oblique shocks
• B. Sound propagation
• C. Rayleigh flow
• D. Fanno flow

Hint:

Match each phenomenon's defining mechanism, friction, heat addition, flow turning, or wave propagation, against the four stated restrictions: steady, inviscid, one-dimensional, no shaft work/body force.

Answer 1

The Correct Option is B, C

The question gives four restrictions on the flow: steady, inviscid, one-dimensional, no shaft work, no body force. The fastest way to solve it is to go through each phenomenon and ask which restriction, if any, it breaks.

1. Oblique shocks: An oblique shock turns the flow through a nonzero deflection angle, so a velocity component appears perpendicular to the original flow direction. A flow with two velocity components is not one-dimensional anymore, so this option fails the "one-dimensional" condition and is ruled out. (A normal shock, which does not turn the flow, would have been fine.)
2. Sound propagation: Treat the sound wave in a frame that travels with it. In that frame, the wave front looks like a fixed thin control surface with steady flow crossing it: gas goes in on one side and comes out on the other with a tiny jump in pressure, density and velocity, and no friction, work input or body force is involved. Every condition in the question is satisfied, so sound propagation is allowed.
3. Rayleigh flow: By definition, Rayleigh flow is frictionless (inviscid), one-dimensional, constant-area duct flow driven purely by heat transfer, with no mechanical work device in the duct and gravity ignored. It matches all four conditions in the question exactly, so it is allowed.
4. Fanno flow: By definition, Fanno flow is constant-area, adiabatic duct flow WITH wall friction as the driving mechanism. Friction means the flow cannot be inviscid, which directly violates the question's stated condition, so Fanno flow is ruled out.

Only sound propagation and Rayleigh flow survive all four restrictions, so options B and C are correct.

Let's summarize:

• Anything that turns or splits the flow direction (like an oblique shock) breaks the one-dimensional assumption.
• Anything driven by friction (Fanno flow) breaks the inviscid assumption; heat-driven (Rayleigh) and acoustic phenomena do not.

The correct options are B and C.