The Mach number in the mixing of two fluid streams

(a) Show that when the radicand in Eq. 15.3-13 is zero, the Mach number of the final stream is unity. Note that the Mach number, Ma, which is the ratio of the local fluid velocity to the velocity of sound at the local conditions, may be written for an ideal gas as v/v_s = v/√γRT/M (see Problem 11C.1). 

(b) Show how the results of Example 15.3-2 may be used to predict the behavior of a gas passing through a sudden enlargement of duct cross section.