Question 1.46: A plane travels at 700 mph at an altitude of 40,000 ft above...

(a) The sonic velocity for air at an altitude of 40,000ft above sea level is read from Table A.1 in Appendix A. The Mach number, assuming the BG system of units, is determined by applying Equation 1.164 \sqrt{C} =M=\frac{\upsilon }{\sqrt{\frac{E_{\upsilon } }{\rho } } } =\frac{\upsilon _{a} }{\nu _{i} } =\frac{\upsilon }{C} as follows:

C:=968.08\frac{ft}{sec}                  v:=700mph=1.027\times 10^{3} \frac{ft}{s}                 M:=\frac{v}{C} =1.061

(b) The sonic velocity for air at an altitude of 40,000 ft (converted to meters) above sea level is read from Table A.1 in Appendix A. The Mach number, assuming the SI system of units, is determined by applying Equation 1.164 \sqrt{C} =M=\frac{\upsilon }{\sqrt{\frac{E_{\upsilon } }{\rho } } } =\frac{\upsilon _{a} }{\nu _{i} } =\frac{\upsilon }{C} as follows:

40000ft=12.192km               c:=295.07\frac{m}{sec}                v:=700mph=312.928\frac{m}{s}
M:=\frac{v}{C} =1.061

(c) First, it is important to note that because the Mach number is dimensionless, its magnitude for a given flow situation will be the same regardless of whether the BG or SI system of units is assumed. Second, because the Mach number, M = 1.061 > 1, the speed of the plane is supersonic. And, finally, because the Mach number, M = 1.061 > 0.5, the flow is compressible; thus, the compressibility effects of the air must be modeled.