For a reciprocating water pump having cylinder diameter d and crank radius r, if W is the weight of water lifted, the coefficient of discharge is
- A. $\frac{W}{\pi d² r}$
- B. $\frac{2W}{\gamma \pi d² r}$
- C. $\frac{W}{\gamma d² r}$
- D. $\frac{W}{\gamma \pi d²}$
Answer: B. $\frac{2W}{\gamma \pi d² r}$
Explanation: $C_d = \frac{Q_{act}}{Q_{th}}$. Theoretical volume $V = Area \times Stroke = \frac{\pi d²}{4} \times 2r$. Weight $W_{th} = \gamma \frac{\pi d² r}{2}$. So $C_d = \frac{W}{W_{th}} = \frac{2W}{\gamma \pi d² r}$.