Air enters a 5-cm-diameter, 4-m-long adiabatic duct with inlet conditions of Ma₁ = 2.8, T₁ = 380 K, and P₁ = 80 kPa. It is observed that a normal shock occurs at a location 3 m from the inlet. Taking the average friction factor to be 0.007, determine the velocity, temperature, and pressure at the duct exit.

FIGURE P12–107

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P₁ = 80 kPa T₁ = 380 K Ma₁ = 2.8 L₁=3m- Normal shock