OUESTION ONE $(30$ MARKS$)$

$($a$)$ In still water of depth $15m,$ determine $($i$)$ the period and its phase speed $($celerity$)$; for a water wave with wavelength $45m$; $($ii$)$ the wavelength and its phase speed $($celerity$)$ for a wave with period $8s.$

$(8$ Marks$)$

$($b$)$ A Pelton turbine is driven by two jets, generating $4\mathrm{.}0MW$ at $375re\frac{v}{m}in$ with overall efficiency ${}_0=91\%.$ The gross head available is $210m$ of water. The water is delivered to the turbine through a pipe $200m$ long and of $0\mathrm{.}5$ diameter having a friction loss of $hf=10\mathrm{.}0m.$ The Nozzle velocity coefficient. $K_N(C_v)=0\mathrm{.}98$ and the axes of the jet are tangent to a circle $1\mathrm{.}5m$ in diameter of the turbine.

$(8$ Marks$)$

Considering only friction losses, determine

$($i$)$ The net head available at the nozzles and the power input to the turbine

$($ii$)$ the flow of water through each nozzle

$($iii$)$ jet speed and the diametor of each jet

$($iv$)$ the specific speed of the turbine $($in $m.kW,r,p,m)$

$($e$)$ Periormance characteristics of a pump is shown in Table Pl$($e$).$ The pipe system is designed to convey water from a lower reservoir located at an elevation of $180m$ through a $40cm$ diameter total length of $1000m$ commercial steel pipe with friction factor, $f=0\mathrm{.}0125$ to a higher reservoir located at an eleyation of $200m.$ determine $($i$)$ the discharge, head and power required if one punip is used $($ii$)$ the discharge, head delivered & total power produced and power consumed by each pump if two identical pumps are connected in series. The system has two gate valves $(k_v=0\mathrm{.}15$ each$)$ and two bends each