Question 1.1: A jet aircraft is flying at an altitude of 15,500 m, where t...
A jet aircraft is flying at an altitude of 15,500 m, where the air temperature is 239 K. Determine whether compressibility effects are significant at airspeeds of (a) 220 km/h and (b) 650 km/h.
The test for compressibility effects requires calculating the Mach number,M, which, in turn, requires that the acoustic velocity at each airspeed, be evaluated.
For air, k = 1.4, R = 0.287 kJ/kg⋅K, and
C=(k R T)^{1 / 2}
=\left[1.4(0.287 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K})(239 \mathrm{~K})(1000 \mathrm{~N} \cdot \mathrm{m} / \mathrm{kJ})\left(\mathrm{kg} \cdot \mathrm{m} / \mathrm{N} \cdot \mathrm{s}^{2}\right)\right]^{1 / 2}
=310 \mathrm{~m} / \mathrm{s}
(a) At v = 220 km/hr (61.1 m/s)
M=\frac{v}{C}=\frac{61.1 \mathrm{~m} / \mathrm{s}}{310 \mathrm{~m} / \mathrm{s}}=0.197The flow may be treated as incompressible.
(b) At v = 650 km/hr (180.5 m/s)
M=\frac{v}{C}=\frac{180.5 \mathrm{~m} / \mathrm{s}}{310 \mathrm{~m} / \mathrm{s}}=0.582Compressible effects must be accounted for.
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