Problem $8\mathrm{.}49($page $436)$: A $150-$ft$-$high $30-$ft$-$long uncontrolled USBR ogee spillway is designed to

have a crest$-$above water depth of $50ft.$ Neglect the approach velocity head. Determine the:

$(1)$ Spillway geometries and draw the profile

$(2)$ Design discharge

$(3)$ Discharge at a crest$-$above water depth of $30ft$

$(4)$ Discharge at a crest$-$above water depth of $65ft$

$(5)$ Discharge at a crest$-$above water depth of $20ft$ if the spillway is controlled by a gate when its

opening height is $6ft$