f18_ps14_fall03

f18_ps14_fall03 - Fall 2003 Unified Engineering Fluids...

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Unformatted text preview: Fall 2003 Unified Engineering Fluids Problem F18 � F18. Wind with velocity V� is flowing over a mountain ridge have the shape Y (x) = Cx. The flow is to b e modeled by superimposing a uniform flow with a source located at some location x, y = (d, 0). �� � (x, y ) = V� y + ln (x − d)2 + y 2 4κ y r V � � x d a) Determine b oth the source’s location d, and the strength �, with the conditions: u=0 at x, y = (0, 0) � v /u = d Y /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 (λ ) inside which the sailplane can sustain flight. Plot the r (λ ) b oundary superimposed on a plot of the ridge. ...
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