Problem $1.$

A water pump is used to pump water from one large reservoir to another large reservoir that is at a higher elevation. The free surfaces of both reservoirs are exposed to atmospheric pressure, as sketched in the figure below. The dimensions and minor loss coefficients are provided in the figure. The pump's performance is approximated by the expression $H_{\text{a}\text{v}\text{a}\text{i}\text{l}\text{a}\text{b}\text{l}\text{e}}=H_0-a{V}^{}{?}^2,$ where shutoff head $H_0=24\mathrm{.}4m$ of water column, coefficient $a=0\mathrm{.}0678\frac{m}{(Lpm{)}^2},$ available pump head $H_{\text{a}\text{v}\text{a}\text{i}\text{l}\text{a}\text{b}\text{l}\text{e}}$ is in units of meters of water column, and capacity $V^{}$ is in units of liters per minute $($Lpm$).$ Estimate the capacity delivered by the pump. Show your detailed calculation procedures in MS Excel. The water temperature is $20C,$ assume the density and dynamic viscosity are $1000k\frac{g}{m^3}$ and $0\mathrm{.}001k\frac{g}{m}s,$ respectively.

$z_2-z_1=7\mathrm{.}85m(elevation$ difference$)$

$D=2\mathrm{.}03cm(pipe$ diameter$)$

$K_{L_{\text{e}\text{n}\text{t}\text{r}\text{a}\text{n}\text{c}\text{e}}}=0\mathrm{.}50(pipe$ entrance$)$

$K_L$ valve $=17\mathrm{.}5(valve)$

$K_{L_{\text{e}\text{l}\text{l}\text{o}\text{w}}}=0\mathrm{.}92(each$ elbow$-$there are $5)$

$K_{L_{\text{e}\text{x}\text{i}\text{t}}}=1\mathrm{.}05(pipe$ exit$)$

$L=176\mathrm{.}5m(total$ pipe length$)$

$=0\mathrm{.}25mm(pipe$ roughness$)$