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?
Show 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.
Step 1: List the given conditions.
The flow is steady (no time dependence), inviscid (no friction/viscosity), one-dimensional (velocity has only one component, along the flow direction) and has no shaft work (no turbine or compressor exchanging work with the fluid) and no body forces (gravity, etc. ignored). We need to check each listed phenomenon against these four conditions.
Step 2: Check option (A), oblique shocks.
An oblique shock deflects the flow through a finite turning angle, so the velocity vector changes direction across the shock. This means a transverse velocity component appears, which breaks the one-dimensional assumption (a strictly 1-D flow can only have velocity along a single line, as in a normal shock, not turned flow). So oblique shocks are not possible in a flow restricted to be one-dimensional; this option is not correct.
Step 3: Check option (B), sound propagation.
A sound wave is a small, inviscid, one-dimensional disturbance. If we look at it in a reference frame moving with the wave (the same trick used to derive the speed of sound), the wave becomes a stationary, steady control volume problem: the flow enters and leaves at slightly different properties, with no friction, no shaft work and no body force acting on this thin control volume. This matches every given condition, so sound propagation is possible.
Step 4: Check option (C), Rayleigh flow.
Rayleigh flow is the standard model for constant-area duct flow with heat addition and negligible friction, i.e. it is explicitly inviscid, one-dimensional and steady. Heat addition is not shaft work (no mechanical device is doing work on the fluid) and body forces are still neglected, so all four conditions hold. Rayleigh flow is a valid possibility here.
Step 5: Check option (D), Fanno flow.
Fanno flow is the standard model for constant-area, adiabatic duct flow WITH friction; friction is precisely what drives the property changes along the duct in this model. Since the problem states the flow is inviscid (no friction), Fanno flow directly contradicts that condition and is not possible here.
Final Answer:
Only sound propagation and Rayleigh flow are consistent with a steady, inviscid, one-dimensional flow having no shaft work or body forces.
\[ \boxed{\text{(B) and (C)}} \]
An excerpt from the table of Prandtl-Meyer function for air is provided below.
