112811 hw6-f011

112811 hw6-f011 - flow? SpecificaUy, what boundary...

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8.1 Give the stream function formulation (Eq. 8.1.6) and find the stream function for the follow- ing flows: L Plane Couette flow Fluid is confined between infinite parallel planes, ' one of which moves at constant speed in its own plane. There is no pressure gradient. Plot stream- lines of equal increments. b. Plane Poiseuille flow Fluid is confined between infinite parallel planes that are stationary. Flow occurs due to imposi- tion of a steady state pressure gradient. Plot streamlines of equal increments. 8.9 One sometimes finds the following expres- sion given as the stream function for steady two- dimensional creeping flow about a cylinder of radius a: (P8.9) q, = Uy [1 - x 2 : f J where x and y are Cartesian coordinates centered· on the axis of the cylinder. How is the stream function defined for this flow? What is the nature of this
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Unformatted text preview: flow? SpecificaUy, what boundary condi-tions are satisfied by u. and u, on the cylinder surface, and far from the surface? 11.3. Find the force (magnitude and direction) required to hold the water nozzle shown in Fig. Pll.3 in place. Assume that the pressure at the entrance to the converging section is 500 kPa (gage), and the exit velocity of the water jet is ISmm 50 m/s. 11.5 A piece of flexible plastic tubing is used to deliver a liquid (water) to a process, as shown in Fig. P11.S. A short nozzle is made by squeezing a glass tube into the flexible tube. Fmd the axial force acting on the glass tube. The tube bas an inner diameter of 1 em and an outside diameter of 1.2 em. t Figure P1L3 A water nozzle. PIIstic IIIbc 01 ," lube ..-L ... ,.----'em T llan -.....------+, ~ T U-I Imm Figure P1L5 Forces acting on a glass tube. I...
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