For the geometry shown in Worked Example 7.2, determine the mass flow rate through the intake and the total pressure recovery for the sub-critical mode of operation when M_∞ = 2.5. Compare these values with those of the critical mode.

Sketc.h the stream tube that enters the intake in the sub-critical mode and prove that the mass flow rate has to be lower based on geometric considerations.

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Example 7.2 Mixed compression supersonic intakes (Fig. 7.5) are widely used in supersonic vehicles, ramjet and scramjet engines owing to their superior off-design performance when compared with internal compression intakes. Here, external com- pression is achieved by means of oblique shocks generated from properly designed ramps and terminated by a normal shock. This is followed by internal compression. The intake shown in Fig. 7.5 is designed for operation at M = 3, P = 15 kPa and T = 135 K. The ramp angles are 15 and 30 respectively. For the critical mode of operation, determine the mass flow rate through the intake, cross-sectional area at the beginning of internal compression and the total pressure recovery.