Due to adiabatic but non-optimal performance of an aircraft engine intake the flow at the intake exit is aligned with the engine axis (x), but sheared with a velocity that varies linearly with distance y across the duct as U=700y. Here y varies from 0 to 0.5−m and U is in meters per second. The flow through the intake is steady. (a) Do you expect the flow to have constant stagnation enthalpy? Explain exactly why? Why is it important to your argument that the flow begin in a free stream? (b) Estimate the magnitude of the gradient of specific entropy in this flow, given that the stagnation enthalpy at y=0 is 4×10 5 J/kg.

Give the units of your result. In what direction is this entropy increasing?