Question $5$

$($a$)$ A small hydroelectric scheme comprises a storage reservoir, surge tank, and turbine

house hydraulically connected by a single pipeline of $800mm$ diameter with a Darcy

friction factor of $0\mathrm{.}018.$

Under normal operating conditions, water is conveyed to the turbines at a rate of $0\mathrm{.}9\frac{m^3}{s}.$

The surge tank has a cross$-$sectional area of $4m^2$ in plan and is positioned $100m$ upstream

of the turbine house and $1400m$ downstream of the reservoir.

Using Table Q$5$ as a template and time intervals of $20$ seconds, determine the maximum

surge height due to an instantaneous turbine shutdown.

$($b$)$ How would results differ if a smaller timestep is used.Question $5$

$($a$)$ A small hydroelectric scheme comprises a storage reservoir, surge tank, and turbine

house hydraulically connected by a single pipeline of $800$ mm diameter with a Darcy

friction factor of $0\mathrm{.}018.$

Under normal operating conditions, water is conveyed to the turbines at a rate of $0\mathrm{.}9$ m$3$

$/$s$.$

The surge tank has a cross$-$sectional area of $4$m$2$ in plan and is positioned $100$ m upstream

of the turbine house and $1400$ m downstream of the reservoir.

Using Table Q$5$ as a template and time intervals of $20$ seconds, determine the maximum

surge height due to an instantaneous turbine shutdown.

Table: Q$5$

t v $-$dy v$2$ Hf y Hf$-$y $-$dv

t $=$ time interval

v $=$ velocity

dy $=$ change in water level

dv $=$ change in velocity

Hf $=$ headloss due to friction

y $=$ water level in surge tank $($above$/$below reservoir level$)$

$20$ Marks

$($b$)$ How would results differ if a smaller timestep is used.

$5$ Marks