The inlet of the jet engine of a supersonic aircraft is a carefully shaped flow passage that takes in flow at very high speed ν₁(relative to the engine) (section 1) and discharges the air at much lower velocity ν₂ << ν₁ and higher pressure (section 2) to the inlet of the compressor. Treating the air as a perfect gas with constant specific heats, derive an expression for the temperature T₂ at section 2 in terms of the temperature T₁ at section 1, the inlet velocity ν₁, and constants for the gas. Heat transfer between the air and the walls may be neglected. Use a reference frame attached to the engine.

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T₁ T, P, M Mp vp Po M₁ Workpiece Ap Notation A piston area My piston mass L 8 T P pressure in the cylinder above the piston Pe pressure in the cylinder M device length; see figure T₁ M₁ piston height; see figure gravity acceleration temperature in the cylinder above the piston below the piston mass of gas in the cylinder above the piston inlet temperature inlet mass flow rate pistan downward velocity time