HW_19_Soln

HW_19_Soln - ME 309 Fall 2008 Section 2 (Merkle) Homework #...

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ME 309 Fall 2008 Section 2 (Merkle) Homework # 19 Due Mon 13 Oct 2008 Problem 19-1 . The drag coefficient associated with a particular aircraft wing section is measured in a wind tunnel using a 1/4-scale model with a span , S, of 2 m and a chord, C , of 0.6 m . The full-size aircraft flies at 130 miles/hr (58.1 m/s) at an altitude of 6000 m where the temperature and pressure are nominally 250 K and 47 kPa, respectively. a) The model is tested at 300 K and 100 kPa. What wind-tunnel speed is required for the Reynolds number of the model to match that of the full-size aircraft? b) In a particular test with a velocity of 60 mph (26.8 m/s ) and 300 K and 1 atm , the drag force F D on the model is measured to be 2.15 N . Determine the drag coefficient, D D 2 / . 1 2 F CS c V ρ = and the Reynolds number based on chord length for this test. c) Assuming the drag coefficient is independent of Reynolds number, determine the drag force on the full-size wing for the flight conditions given in part a. Assume the viscosity is independent of pressure and increases with temperature as: 4 / 3 T μ Solution: Sketch: Assumptions: steady flow, ideal gas, viscosity a function of temperature only a) Given: T m = 300 K, p m = 100,000 N/m 2 , L m = L p /4, u p , = 130 mph = 58.1 m/s , T p = 250 K , p p = 47,000 Pa Find: Wind tunnel speed to match Re # of full size wing Analysis : Evaluate the Reynolds number: p p p p m m m m C u C u = Solve for velocity in wind-tunnel (model): p m m p m p p m m m p p p p m C C u C C u u = = Use perfect gas law and temperature dependence of viscosity:
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HW_19_Soln - ME 309 Fall 2008 Section 2 (Merkle) Homework #...

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