fall_2003_pset14 - Massachusetts Institute of Technology...

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Massachusetts Institute of Technology Department of Aeronautics and Astronautics Cambridge, MA 02139 16.01/16.02 Unified Engineering I, II Fall 2003 Problem Set 14 Name: Due Date: 12/9/03 Time Spent (min) F18 F19 F20 M19 M20 M21 M22 U4 Study Time Announcements:
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Unified Engineering Fall 2003 Fluids Problems F18-20 F18. Wind with velocity V is flowing over a mountain ridge have the shape Y ( x )= Cx . The flow is to be modeled by superimposing a uniform flow with a source located at some location x, y =( d, 0). ψ ( x, y )= V y + Λ l n ( x d ) 2 + y 2 4 π x y d V r θ Λ a) Determine both the source’s location d , and the strength Λ, with the conditions: u =0 at x, y =(0 , 0) v/u = dY /dx at x, y =( d, Cd ) The second condition simply requires that the flow direction on the ridge surface directly above the source is parallel to the ridge surface. b) A sailplane flying in the slope lift upwind of the ridge requires a vertical velocity of at least v 1m / s tos tay a lo f t . F o r aw ind speed o f V = 15m / s (33 mph) and ridge size scale C = 500m, determine the maximum flyable radius r ( θ ) inside which the sailplane can sustain flight. Plot the r ( θ ) boundary superimposed on a plot of the ridge. F19. Determine the C p variation along the x and + y directions for a) Freestream V with source of strength Λ b) Freestream V with vortex of strength Γ c) Freestream V with doublet of strength κ . At large distances, where does a lifting airfoil cause the strongest disturbance to the flow (as measured by C p ),
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

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fall_2003_pset14 - Massachusetts Institute of Technology...

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