Question $4($Pipe flow$)$

$($Total $30$ marks$)$

a$)$ Water flows between two tanks through two horizontal pipes in series, the first is $125mm$ diameter and $45m$ long pipe, and the second pipe is $90mm$ diameter, and $10m$ 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 $4m,$ determine the flow rate.

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