A liquid flows through a piping system from $P1$ to the top of a structure at P$2$ The entire piping system is $0\mathrm{.}75$ sch $40$ pipe

The piping system supply pressure at $P1$ is $26$ psig

The piping system is intended to provide liquid at a rate of $14gpm$ while maintaining a P$2$ pressure of $28$ psig.

The flowrate at P$1$ and P$2$ are the same. $($ie$..$ there is no splitting or branching of the flow$)$

The friction factor, $f($fanning$),$ can be assumed to be $0\mathrm{.}007$

Given:

The density of water is $62\mathrm{.}4lb\frac{m}{f}t3$

The specific gravity of the fluid is $0\mathrm{.}8$

The viscosity of the fluid is $15cP$

The piping system is shown above and contains the following fittings:

$1490$ degree bends; $K=11f$

$12$ gate valves ;$K=8f$

$4$ check valves ;$K=30f$

$10$ tee runs ;$K=17f$

$4$ tee branches ; $K=40$ f

The piping system dimensions are as follows: $A=21ft$;$B=175ft$;$C=80ft$

What is the volumetric flow, $ft\frac{3}{s},$ through the pipe?

What is the velocity, $f\frac{t}{s}?$

What is the pressure drop, psi, due to the pipe?

What is the pressure drop, psi, due to the pipe and fittings?

What is the pressure drop, psi, due to the elevation change?

What is the required $TDH,ft,$ of the pump?

What is the required hydraulic horsepower, hp$?$