Question $3$: $(40$ points$)$

Two large reservoirs at different elevations are connected through a circular pipe as shown in the schematic. The pipe has a uniform diameter of $D_{\text{p}\text{i}\text{p}\text{e}},$ a total length of $L_{\text{p}\text{i}\text{p}\text{e}},4$ elbows $($with loss coefficients of $K_L,$ elbow for each of the elbows$),$ and a fully$-$open valve $($with a loss coefficient of $K_{L,\text{v}\text{a}\text{l}\text{v}\text{e}}).$ The loss coefficients of the entrance and exit of the pipe are $K_L,$ entrance and $K_L,$ exit, respectively. The pipe is made of cast iron, and the roughness of the cast iron pipe is ${}_{\text{c}\text{a}\text{s}\text{t}}$ iron $=0\mathrm{.}00085ft.$ For the volume flow rate within the pipe, Q$.[$use the parameter values given in the image next to the schematic$]$:

$($a$)$ Is the flow in the pipe laminar or turbulent? Show your calculations.

$($b$)$ Calculate the friction factor in the pipe using the Colebrook equation. $[$Iterate until your friction factor value converges to less than $10\%$ between iterations and show the intermediate results of your iterations$].$

$($c$)$ What is the elevation difference between the free surfaces of the two reservoirs $($i$.$e$.$ h in the schematic$)?$

$[$The density and dynamic viscosity of water are $=1\mathrm{.}94$ slug $\frac{?}{f{t}^3}$ and $=0\mathrm{.}204{10}^{-4}$ slug$/$f$-$s$,$ gravity acts downward in the schematic; consider atmospheric conditions outside the reservoirs$].$

$D_{\text{p}\text{r}\text{e}\text{v}}=2$ inches

$L_{\text{p}\text{i}\text{r}\text{e}}=120ft$

$K_{\text{L}\text{e}\text{l}\text{b}\text{o}\text{w}}=0\mathrm{.}3$ gor each elbow

$K_{L,\text{v}\text{a}\text{l}\text{u}\text{e}}=0\mathrm{.}2$

$K_{\text{h}\text{e}\text{n}\text{t}\text{r}\text{a}\text{n}\text{c}\text{e}}=0\mathrm{.}03$

$K_{L,\text{e}\text{x}\text{i}\text{t}}=1\mathrm{.}0$

${}_{\text{c}\text{a}\text{s}\text{t}\text{i}\text{r}\text{a}\text{n}}=0\mathrm{.}00085$

$Q=10f{t}^3\frac{?}{\text{m}\text{i}\text{n}\text{u}\text{t}\text{e}}$