QUESTION $04-$ Hydro Power Station

$4\mathrm{.}1$ The power crisis has affected every sector in the country, and to try to mitigate the situation, the government has proposed constructing a hydropower generation plant in the Gqeberha area. It is suggested that a turbine develops $15000$ kW at a speed of $120re\frac{v}{m}in$ must be used. The turbine operates under a maximum head of $18$ m $.$ Determine the specific speed at which this turbine will operate.

$4\mathrm{.}2$ Three identical, double$-$jet Pelton wheels operate under a gross head of $400$ m $.$ The nozzles have $75$ mm diameters and a velocity coefficient of $0,9.$ The pitch of the bucket is $1,2m$ in diameter. The bucket deflects the jet through $165$ and

Due to friction, the relative velocity is reduced by $18\%.$ The water from the

reservoir is supplied at $5\frac{m}{s}$ via a pipeline of $0,5m$ diameter and $450$ m long with

a coefficient of friction of $0\mathrm{.}0075.$ The overall efficiency is $82\%.$ Determine:

$4\mathrm{.}2\mathrm{.}1$ The head loss due to friction.

$4\mathrm{.}2\mathrm{.}2$ The

velocity.

jet

$4\mathrm{.}2\mathrm{.}3$ The rotational speed of each turbine when it operates under max.

$(4)$

$4\mathrm{.}2\mathrm{.}4$ The

total

power

output.

$4\mathrm{.}2\mathrm{.}5$ The efficiency.

$(6)$

$[30]$