(Solved): a) The supersonic passenger jet, Concorde, had a cruising speed of Mach 2 at ...

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a) The supersonic passenger jet, Concorde, had a cruising speed of Mach 2 at an altitude of \( 16 \mathrm{~km} \), where air temperature is typically \( -50^{\circ} \mathrm{C} \). Calculate the cruising speed in \( \mathrm{km} / \mathrm{h} \). Take \( R=286.9 \mathrm{~J} / \mathrm{kgK} \) and \( \gamma=1.4 \) [6 marks] For frictionless flow of an ideal compressible gas through a duct, the rate of change of velocity, \( v \) with cross-sectional area, \( A \), is given by \[ \frac{\mathrm{d} A}{\mathrm{~d} v}=\frac{A}{v}\left(M^{2}-1\right) \] Discuss the implications of the above equation for the flow Mach number through of a converging-diverging duct where the upstream flow is i) Subsonic ii) Supersonic [10 marks] c) Explain how turbulent fluctuations in a fluid can act to increase heat transfer above what might be found in purely laminar flow. [4 marks] d) Use the following expression for convective heat transfer in the fluid to illustrate why turbulent flows are inherently more difficult to model than laminar flows. \[ q=-c_{\mathrm{P}} \rho\left(a+\varepsilon_{H}\right) \frac{\mathrm{d} T}{\mathrm{~d} y} \] [5 marks]