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6. (10 points) Flow of a viscous fluid over a flat plate surface results in the development of a region of reduced velocity adjacent to the wetted surface as depicted in the figure below. This region of reduced flow is called a boundary layer. At the leading edge of the plate, the velocity profile maybe considered uniformly distributed with a value U. All along the outer edge of the boundary layer,the fluid velocity component parallel to the plate surface is also U. If the x-direction velocity profile at section (2) is \frac{u}{U}=\frac{3}{2}\left(\frac{y}{\delta}\right)-\frac{1}{2}\left(\frac{y}{\delta}\right)^{3} develop an expression for the volume flowrate through the edge of the boundary layer from the leading edge to a location downstream at x where the boundary layer thickness is 8. The widthof the plate is 7.

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