102611 hw4-f011

102611 hw4-f011 - these conditions 4.84 A viscous Newtonian...

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I~o A Hw y . . o I Uquid fibn -jBt- FigareP4.77 4. T1 A Newtonian viscous liquid is flowing be- tween two wide planar surfaces, as shown in Fig. P4.77. The surface along y = 0 is fixed in space, and the surface along y = B has a steady speed U parallel to the fixed plane. If U were zero, the liquid film would flow downward under the action of gravity. Derive an expression for the speed U such that the liquid neither falls nor rises. What is the shear force (per unit width . normal to the page) on the fixed surface under
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Unformatted text preview: these conditions? 4.84 A viscous Newtonian fluid is confined be. .: tween large parallel plates, as shown in FigJ P4.B4. The motion is a combination of drag and pressure flow. Derive an expression for the ve-: locity profile. Find an expression for the valuei u ... _-====---JL. .--Fipre P4.84 of U that yields a zero shear stress at th<l fixed · . plate. Draw the velocity profile under these con-aitions. Draw the velocity profile if U is half • this value. . I i I...
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