a$)$ Water flows between two tanks through two horizontal pipes in series, the first is $125$ mm diameter and $45$ m long pipe, and the second pipe is $90$ mm diameter, and $10$ m long. The pipe entrance is sharp edged, and has a $\frac{3}{4}$ open gate valve where the pipes join. The outlet is also sharp edged. The value of $$ for each pipe is $0\mathrm{.}021,$ and shock loss coefficients are shown in Table $1.$ If the difference in water level between the two tanks is $4$ m $,$ determine the flow rate.

$\backslash$table$[[$Fitting$,],[$Sharp edged entrance,$0\mathrm{.}5],[90$ degree elbow,$0\mathrm{.}7],[3/4$ open gate valve,$0\mathrm{.}6],[1/4$ open gate valve,$12\mathrm{.}0],[$sudden enlargement,$1\mathrm{.}0]]$

Table $1$