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A Newtonian liquid is in pressure driven laminar flow in an inclined narrow rectangular slit of height 2B and width W(W>>2B), as illustrated below. The
A Newtonian liquid is in pressure driven laminar flow in an inclined narrow rectangular slit of height 2B and width W(W>>2B), as illustrated below. The pressure at the entry to the section is Po, the pressure at the exit is PL. It may be assumed that gravity acts straight down (and thus acts to promote the flow), and the system is at steady state. Assuming that the x1-axis is aligned with the flow direction, use a shell balance approach to derive expressions for: (a) The shear stress profile (as a function of x2 ). (b) The velocity profile (as a function of x2 ). (c) The volume flow rate. (d) If the pressure differential (P0PL) is zero, derive an expression for the volume flow rate in the pipe
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