Q$-3.$ A $1$ km long concrete$-$lined tunnel connects two reservoirs with the water surface elevation in the

lower reservoir being $23m$ below to that in the upper reservoir. Roughness height of concrete lining is

given as $1\mathrm{.}5mm.$ Determine the diameter of the tunnel if the flow has to be maintained at $2\frac{m^3}{s}.$ Ignore

all minor losses. Assume kinematic viscosity of water $={10}^{-6}\frac{m^2}{s}.($Hint: Since this is the type $3$ problem

with unknown D$,$ start with an assumed friction factor and find D$,$ then solve iteratively. Use Moody

Diagram from Lecture $5$ or your textbook.$)$