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Problem 2.88

# Problem 2.88 - K = 50 o C it is off scale of Fig A.3...

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Problem 2.88 [Difficulty: 3] Given: Data on supersonic aircraft Find: Mach number; Point at which boundary layer becomes turbulent Solution: Basic equation V M c = and c k R T = For air at STP, k = 1.40 and R = 286.9J/kg.K (53.33 ft.lbf/lbm o R). Hence M V c = V k R T = At 27 km the temperature is approximately (from Table A.3) T 223.5 K = M 2700 10 3 × m hr 1 hr 3600 s × 1 1.4 1 286.9 × kg K N m 1 N s 2 kg m × 1 223.5 × 1 K 1 2 = M 2.5 = For boundary layer transition, from Section 2-6 Re trans 500000 = Then Re trans ρ V x trans μ = so x trans μ Re trans ρ V = We need to find the viscosity and density at this altitude and pressure. The viscosity depends on temperature only, but at 223.5
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Unformatted text preview: K = - 50 o C, it is off scale of Fig. A.3. Instead we need to use formulas as in Appendix A At this altitude the density is (Table A.3) ρ 0.02422 1.225 × kg m 3 ⋅ = ρ 0.0297 kg m 3 = For μ μ b T 1 2 ⋅ 1 S T + = where b 1.458 10 6 − × kg m s ⋅ K 1 2 ⋅ ⋅ = S 110.4 K ⋅ = μ 1.459 10 5 − × kg m s ⋅ = μ 1.459 10 5 − × N s ⋅ m 2 ⋅ = Hence x trans 1.459 10 5 − × kg m s ⋅ ⋅ 500000 × 1 0.0297 × m 3 kg ⋅ 1 2700 × 1 10 3 × hr m ⋅ 3600 s ⋅ 1 hr ⋅ × = x trans 0.327m =...
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