$3$ problem $3(30$ pts$)$:

A pump system is being designed to transfer water from a river to an elevated water tank as shown in the figure below, using two parallel pipes, each with $2^{\text{'}\text{'}}$ diameter with the Hazen$-$Williams roughness coefficient of $C=110.$ The pump characteristic curve is described as $H_p=45-10000Q^{1\mathrm{.}852}.$ The length of the pipes is $20$ m $.$ Calculate the flow rate that can be pumped to the tank $($ignore all the minor losses and the head loss in the pipe before the pipes split in two$).$

Figure $2$: Problem $3$

Hint:

The Hazen$-$Williams equation in SI unit system is:

$h_f=L\frac{10\mathrm{.}67}{C^{1\mathrm{.}852}}\frac{Q^{1\mathrm{.}852}}{d^{4\mathrm{.}8704}}$

where

$h_f=$ head loss in meters $($water$)$ over the length of pipe

$L=$ length of pipe in meters

$Q=$ volumetric flow rate, $\frac{m^3}{s}($cubic meters per second$)$

$C=$ pipe roughness coefficient

$d=$ inside pipe diameter, m $($meters$)$