$(4$ Marks$)$

$($b$)$ Figure Q$3$ shows water $($kinematic viscosity, $v=1{10}^{-6}\frac{m^2}{s})$ flowing from the reservoir through a $0\mathrm{.}12$ m diameter $($D$)$ inclined pipe of length $L=100m.$ The flow emerges from the pipe as a free jet into the atmosphere.

$($i$)$ Calculate the roughness height, $$ of the pipe if the exit jet velocity $V=1\frac{m}{s}.$

$($ii$)$ Sketch the Total Energy Line $($TEL$)$ and the Hydraulic Grade Line $($HGL$)$ for the flow system.

$[$Hint: Ignore all minor losses in your computation; you need to use the Moody Diagram in the Appendix for your computation.$]$

$(12$ Marks$)$