Problem 3.44

# Problem 3.44 - Problem 3.44[Difficulty 3 Given Atmospheric...

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Problem 3.44 [Difficulty: 3] Given: Atmospheric conditions at ground level ( z = 0) in Denver, Colorado are p 0 = 83.2 kPa, T 0 = 25°C. Pike's peak is at elevation z = 2690 m. Find: p / p 0 vs z for both cases. Solution: Governing Equations: dp dz ρ g = p ρ R T = Assumptions: (1) Static fluid (2) Ideal gas behavior (a) For an incompressible atmosphere: dp dz ρ g = becomes pp 0 0 z z ρ g d = or 0 ρ 0 g z = p 0 1 gz RT 0 = (1) At z 2690 m = p 83.2 kPa 1 9.81 m s 2 2690 × m kg K 287 N m × 1 298 K × Ns 2 kg m × × = p 57.5 kPa = (b) For an adiabatic atmosphere: p ρ k const = ρρ 0 p p 0 1 k = dp dz ρ g = becomes dp ρ 0 p p 0 1 k g dz = or 1 p 1 k dp ρ 0 g p 0 1 k dz = But p 0 p p 1 p 1 k d k k1 0 () k = hence k p k p 0 k ρ 0 g p 0 1 k g z = Solving for the pressure ratio

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Problem 3.44 - Problem 3.44[Difficulty 3 Given Atmospheric...

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