Chapter 12.3, Problem 68E

a.

To determine

To show: The energy loss in moving the fluid from P to S via Q is $L=\frac{k{d}_1}{R^4}+\frac{k{d}_2}{r^4}$.

b.

To determine

To show: The value of $d_1\text{ and }{d}_2$ in terms of a and b and also to prove $E=k\left(\frac{a-b\cot \theta }{R^4}+\frac{b\csc \theta }{r^4}\right)$.

c.

To determine

To show: The E is minimized when $\cos \theta =\frac{r^4}{R^4}$ is satisfied.