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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:
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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- Fall '05