Problem $3(50$ points$)$

The centrifugal pumps whose performance curves for water are given in figure $1$a$)$ and $1$b$)$ will be used in the water system of the figure $2.$ The friction factor and the pipe diameter are $0\mathrm{.}010$ and $150mm$ throughout, respectively. Minor losses are negligible.

a$)$ What water flow rate, in gallons per minute, will result in pump $1$a and $1$b$?$

b$)$ What is the pump head $1$ a and $1$ b$?$

c$)$ What is the efficiency $1$a and $1$b$?$

d$)$ Determine the head loss for $1$ a and $1$ b

Figure $1.($Esposito$,1998)$

Figure $2.($Esposito$,1998)$

$\frac{P_1}{}+\frac{V_1^2}{2g}+z_1-h_{\text{l}\text{o}\text{s}\text{s}}+h_{\text{p}\text{u}\text{m}\text{p}}=\frac{P_2}{}+\frac{V^{2}2}{2g}+z_2$

$Q=AV,A=\frac{}{4}{d}^2,h_{\text{l}\text{o}\text{s}\text{s}}=f(\frac{L}{d})\frac{V^2}{2g}$

$1gpm=0\mathrm{.}00223\frac{f{t}^3}{s},1ft=0\mathrm{.}3048m$