Problem #$6$

Schematic of a pump and piping system is given below. The pump is used to deliver hot water at $140F$ from a geothermal reservoir of lower elevation $(z1-0)$ to a tank at a higher elevation $(22-45ft).$ The suction line before the pump has a total length of $L_1-80ft$ fitted with a foot valve $(K_L-0\mathrm{.}8)$ at the entrance and a regular, flanged $90$ elbow $(K_L-0\mathrm{.}31).$ The discharge line after the pump has a total length of $L_2-720ft,$ fitted with two $90$ elbows and a fully open gate valve $(K_L-0\mathrm{.}15).$ The loss coefficient of the exit from the pipe to the tank is $K_L-1\mathrm{.}0.$ Both suction line and discharge line are made of $6$ nominal schedule $40$ galvanized steel pipe. To simplify the analysis, the friction factor $(f)$ inside the pipe can be approximately treated as a constant at $f-0\mathrm{.}02.$ The atmospheric pressure is approximate$]$y $14\mathrm{.}7$ psi. You are asked to do the following:

$3\mathrm{.}1.$ Apply the energy equation to the entire pump and piping system to find an cquation for the system resistance $($also called system head, $H_{syst})$ as a function of the flow rate $(Q)$ in the pipe.

$3\mathrm{.}2.$ Apply the energy equation to the suction line before the pump to find an equation for the available net positive suction head of the system, $NPS{H}_A,$ as a function of the flow rate $(Q)$ in the pipe.

$3\mathrm{.}3.$ Determine the system head $(H_{\text{e}\text{n}\text{a}\text{r}})$ and the available net positive suction head $($NPSHA$)$ of the given pump and piping system for the flow rate of $Q-800gpm.$