Partial Diversion of a Stream through a Slot

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Consider an inviscid uniform fluid flowing with velocity (expressed in ) parallel to a wall. A narrow slot in the wall allows some of the fluid to be diverted. The volumetric flow rate of withdrawn fluid is (expressed in ).

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The Demonstration plots the stream function for this partial diversion problem, which is given by:

.

For small values of or large values of , the velocity profiles approach that of a uniform flow. Far from the slot, the velocity field is again almost that of uniform flow parallel to the wall.

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Contributed by: Housam Binous (March 2011)
Open content licensed under CC BY-NC-SA


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J. O. Wilkes, Fluid Mechanics for Chemical Engineers, Upper Saddle River, NJ: Prentice Hall, 1999.



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