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101911 hw3-f011

101911 hw3-f011 - tive to the atmosphere at the entrance...

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f-l W 3 C 1 -\ £ --t, e )t' t bwk p vobie Wl 4-·7b , 4 .w 1.76 It.. Newtonian llqwd fiows slowly into a pia- - nar channel, as shown in Fig. P4 . 76. The planes that confine the flow are parallel, and very wide In the direction perpendicular to the page. Hence the ·flow is two-dimensional. The upper plane "floats" freely in suCh a way that it remains paral- lel to the lower, fixed plane. A weight w sits on the' upper plane. The upper plane itself may be considered weightless. The volume flowrate per width Wentering the system is QIW, and the entrance region is a plane parallel region of 'Ierigth Le and thickness 2B. It width is the same ~Uhat of the upper region. The pressure (rela-
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Unformatted text preview: tive to the atmosphere) at the entrance plane A is Po. Derive an expression for the plane half-. -... . separation H, in terms of w and the other param-eters. ' ~ A pair of viscous liquids is initially layered \ ~~een two large parallel planes, as shown in I :PI8. P4.20. The lower surface is stationary, and I -lhe upper surface moves in its own plane at uni- ' ·Jorm velocity U. Find the steady state velocity I ~:pr{)files in the two fluids. H«B . H«l. FIpre P4.76 Flow into a planar two-dimensional .channel. y=8----------------------•• U ViscositYJl 1 y = IcB ------------,..0 · _______ _ .Figure P4.20 Drag flow in parallel layers. ;...
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