Question

The air inlets on both sides of a fuselage are designed to slow the airflow through the inlets to a lower Mach number before feeding into the engine inside the fuselage. Consider a case where the flow entering the inlet is at Mach 0.6 where the inlet cross-sectional area is 3ft^2. At a given location inside the inlet, the cross-sectional area is 4ft^2. Calculate the flow Mach number at this location.

Answer 1

The Mach number is the ratio of the speed of the object (in this case, air) to the speed of sound, it is therefore proportional to the speed. Consider a tube where the cross-sectional area varies across the tube. At a given location, let the cross-sectional area be , speed be and density of air be . Then the amount of air flowing through that cross-section per unit time (the mass current) is . This has to be the same at all points on the tube, unless air is injected or removed in between (not applicable in this case). Further, we may assume air density remains the same at different points on the tube. Therefore, between two points 1 and 2,

Thus,

Let 1 correspond to the inlet and 2 correspond to the location inside. Hence, mach number at 2 is

0.6*(3/4)=0.45.