Interrelation of slit and annulus formulas. When an annulus is very thin, it may, to a good approximation, be considered as a thin slit. Then the results of Problem 2B.3 can be taken over with suitable modifications. For example, the mass rate of flow in an annulus with outer wall of radius R and inner wall of radius (1)R, where is small, may be obtained from Problem 2B.3 by replacing 2B by R, and W by 2(121)R. In this way we get for the mass rate of flow: w=6L(P0PL)R43(121) Show that this same result may be obtained from Eq. 2.4-17 by setting equal to 1 everywhere in the formula and then expanding the expression for w in powers of . This requires using the Taylor series (see C.2) ln(1)=212313414 and then performing a long division. The first term in the resulting series will be Eq. 2B.5-1. Caution: In the derivation it is necessary to use the first four terms of the Taylor series in Eq. 2B.5-2. f flow is w=R2(12)vz, or w=8L(P0PL)R4[(14)ln(1/)(12)2]