Question $1$

a$.)$ Using Continuity and Momentum derive the expression the sequent depth relationship between upstream and

downstream depths and upstream Froude Number for the rectangular channel $($width b$).$

b$.)$ Derive the expression for the energy loss, hL$,$ in a hydraulic jump in terms of the upstream and downstream

depths.

c$.)$Estimate the ideal flow rate, QI

$,$ over a spillway with total head upstream of the spillway, THu, the spillway crest

height, Hw$,$ and the channel width B$.$ Hence define a discharge coefficient; CD $=$ QA$/$QI

$.[$hint: flow over a

spillway is similar to flow over a sharp$-$crested weir$].$