Laminar flow in a narrow slit (see Fig. 2B.3).

(a) 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: In these expressions P = *p* + *pgh* = *p* – *pgz*.

(b) What is the ratio of the average velocity to the maximum velocity for this flow?

(c) Obtain the slit analog of the Hagen-Poiseuille equation.

(d) Draw a meaningful sketch to show why the above analysis is inapplicable if B = W.

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