Problem $3(15$ points$)$ Water is discharged from a tank to the atmosphere at C $.$ The volumetric flow rate is $Q=0\mathrm{.}475\frac{m^3}{s}$ with the gate valve A fully open. The pipe is made of galvanized iron with a mean roughness $=0\mathrm{.}15mm.$ The entrance to the pipe is sharp$-$edged with a minor loss coefficient of $0\mathrm{.}5$ and there are two $90-$degree elbows. The free surface $B$ is exposed to air. Neglect the minor loss associated with the exit. Find the pipe diameter d $($Hint: Gate valve and elbow loss coefficient can be found from the table supplied below. You will need first to establish an eqn. relating the diameter to the friction factor. Iterations may be needed to find the solution$).$

$\backslash$table$[[$Loss coefficients for pipe,$],[$fittings$,K_L$