QUESTION $1$

$1\mathrm{.}1.$ You have been tasked to estimate rationally the penstock length of a small$-$

scale hydro$-$power plant $($SSHP$)$ in a reach of one of the Vaal River tributaries.

The head of the reach is assumed to be $0\mathrm{.}05$ km $.$ The hydro$-$electric power

produced will be used by a small community $(B)$ that has grown from $200$ people

a year back, at a constant rate of $150\%.$ Assume roughly hypothetically $10$

people per household. The transmission line is double is double that of another

community $($B$)$ situated at $1$ km from the hydropower project. The material of

the penstock is ductile steel.

The cross section of the penstock $(A)$ and the flow velocity $(V)$ satisfy Equations

$(1)$ and $(2)$ below, respectively:

$A^2+0\mathrm{.}006067=0\mathrm{.}1558A$

$\frac{1}{4}-\frac{1}{V^2}=0$

$Eq.2$

$1\mathrm{.}2.$ Determine the penstock length, if the hydropower power plant was rather meant

to supply electricity to community B such that other considerations remain

unchanged.

$1\mathrm{.}3.$ Without making any calculation, predict logically which penstock will have the

minimum head losses.

$1\mathrm{.}4.$ Make a rational initial selection of the type of turbine$($s$)$ for the hydropower