Water at $30\backslash$deg C is pumped from a pressurized reservoir $(5$ psig$)$ to an open storage tank atop a building by means of a centrifugal pump. The level of water in the pressurized reservoir is $35$ ft above the center$-$line of the pump. The piping system consists of $100$ ft equivalent length of$4"$ SCH $40$ steel pipe containing one $(1)$ globe valve $($bevel$-$seat$)$ and four $(4)-90\backslash$deg standard elbows from the pressurized reservoir to the pump; $4$ SCH $40$ pipe follows the pump for an equivalent length of $50$ ft after which the pipe size is decreased to $2$ SCH $40$ steel pipe for an equivalent length of $300$ ff to the tank. The $2\text{'}$ SCH $40$ pipe contains two $(2)-90\backslash$deg standard elbow.If it is desired to maintain a flow of water of $400$ gpm into the storage tank and the level of the liquid in the storage tank is $300$ ft above the center$-$line of the pump, determine the following at the suction and discharge points:

a$.)$ total friction head

b$.)$ suction pressure and discharge pressure $($psig$)$

c$.)$ average velocities $($ft$/$s$)$

Calculate the following:

$1.)$ total discharge head $($ft$)$

$2.)$ total suction head $($ff$)$

$3.)$ total dynamic head $($ft$)$

$4.)$ theoretical power $($hP$)$

$5./$ brake horsepower with n$=65\%($hP$)$

$6.)$ NPSHA $($ft$).$ Will cavitation occur if the NPSH rating of the pump is $15$ ft$?$

Note:

a$.)$ Provide a summary of your answers $[$a to c; $1$ to $6].$ Label appropriately.b$.)$ Use g$=32\mathrm{.}174$ ft$/$s$2$b$.)$ Conversion factor: $1$ f$/3=7\mathrm{.}48$ gal and $1$ g$/$mL $=62\mathrm{.}4$ lbm$/$ft$3$