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external flow example

external flow example - Example Air enters a...

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Example: Air enters a two-dimensional wind tunnel as shown. Because of the presence of the boundary layer, fluid will be displaced away from the surface. In order to maintain a constant velocity inside the tunnel, it is necessary to increase the cross-sectional size of the tunnel. (a) Determine the channel height, H(x), as a function of the distance measured from the inlet of the tunnel, x. The tunnel velocity is 10 m/s and the tunnel inlet height is 5 m. Assume the boundary layer has a profile u(y)=U sin( π y /2δ29. (b) What is the momentum thickness θ (x) of the boundary layer flow. (c) If a sphere has a diameter of 0.1 m is placed in the center of the wind tunnel, what is the drag force exerted on the sphere. ρ air =1.2 kg/m 3 , ν =1.5x10 -5 m 2 /s. C D U =10 m/s 5 m x H(x) Sphere, 0.1 m diameter C D =24/Re, when Re<1 Re=VD/ ν 0.5 400 300,000 C D =24/Re 0.646 , when 1<Re<400
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In order to maintain a constant velocity inside the tunnel, the tunnel wall has to be displaced outward in order to accomodate the growth of the boundary layer.
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