QUESTION No$.2$

$($a$)$ State and Define D'arcy Formula for the flow of water through pipes and then find the loss of head due to friction in a $50mm$ diameter pipe that is $30m$ long when the velocity of flow is $2\frac{m}{s}$ and the coefficient of friction of the pipe material is $0\mathrm{.}007.($g $=9\mathrm{.}81\frac{m}{s^2})$

$(2+4+2$ marks$)$

$($b$)$ Explain what a Short Circuit is and define the terms in the Short$-$Circuit Formula $t=\frac{K^2{S}^2}{I^2}$ and then calculate the thickness required for a fusible link, allowing for a $2$ minutes and $7$ seconds fault detection period at $k$ value of $750$ for a maximum allowable current of $200,000mA.$

marks$)$

$($c$)$ Define the Pump Laws and provide any assumptions made and then calculate the new Discharge and the new Power Absorbed when a centrifugal pumping set that absorbs $2kw$ and discharges $4\mathrm{.}0\frac{l}{s}$ at $800rpm$ has the angular velocity of its impeller increased to $1000rpm.$

$(3+2+4$ marks$)$

$($d$)$ Define the terms in the Thomas Box Formula for pipe sizing $Q=[\frac{d^{5}H}{25Lx{10}^5}{]}^{\frac{1}{2}}$ and then calculate the head of water necessary to provide a discharge of $2\mathrm{.}0\frac{L}{s}$ through a $100mm$ distribution pipeline $2km$ long.

$(4+4$ marks$)$