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.