$5$ cm diameter pipe. The water passes through one gate valve, four bends $(90$ elbows$)$ and a pump. Roughness in the pipe is given as $282\mathrm{.}1m.$ There is no change in height from tank A to B$.$ Ignore sudden contractions and expansions, and assume a constant friction factor, f of $0\mathrm{.}015.$

Given: $\frac{L_e}{D}($gate valve$)$: $7$

L$/$D $(90$ elbow$)$: $15$

$g=9\mathrm{.}81\frac{m^2}{s^2}$

Density: $1000k\frac{g}{m^3}$

a$)$ Fill in the blank: The cross sectional area of the pipe is:

$n^2$

$(1)$

b$)$ Fill in the blank: The change in pressure in the system is:

${?}^{3}a$

$(1)$

c$)$ Fill in the blanks: Derive an expression for the system curve.

$H=[$units in meters$]$

$(5)$

d$)$ Given the pump curve data below, what is the operating head $($in m $)$ of the system $(\frac{m^3}{s})$

$(4)$

e$)$ Given the pump curve data below, what is the operating flowrate $($in $\frac{m^3}{s})$ of the system $(\frac{m^3}{s})$

$(4)$

Pump manufacturers curve data

$\backslash$table$[[Q(\frac{m^3}{s}),H(m)$

Please solve for the head Step by Step