fall_2003_pset14

# 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 ln ( 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 to stay aloft. For a wind speed of 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 ), above and below, or fore and aft? Explain. F20. Two very long source panels of strength ± λ are located at distance h apart. Determine the velocities at points A, B, C.
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