Air enters a circular duct with a Mach number of 3.0.

The friction factor is 0.01 .

(a) How long a duct (measured in diameters) is required to reduce the Mach number to 2.0 ?

(b) What is the percentage change in temperature, pressure, and density?

(c) Determine the entropy increase of the air.

(d) Assume the same length of duct as computed in part (a), but the initial Mach number is 0.5 . Compute the percentage change in temperature, pressure, density, and the entropy increase for this case. Compare the changes in the same length duct for subsonic and supersonic flow.