A Newtonian fluid is in laminar flow in a narrow slit formed by two parallel walls a distance 2B apart. It is understood that B<
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A Newtonian fluid is in laminar flow in a narrow slit formed by two parallel walls a distance 2B apart. It is understood that B < < W, so that "edge effects" are unimportant. Make a differential momentum balance, and obtain the following expressions for the momentum-flux and velocity distributions: tau_xz = (P_0 - P_L/L) x upsilon_z = (P_0 - P_L) B^2/2 mu L [1 - (x/B)^2 In these expressions P = p + pgh = p - pgz. What is the ratio of the average velocity to the maximum velocity for this flow? Obtain the slit analog of the Hagen-Poiseuille equation. Draw a meaningful sketch to show why the above analysis is inapplicable if B = W. How can the result in be obtained from the results of section 2.5?
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