FIGURE $7\mathrm{.}58$: Gate$/$weir combination

A weir is to be placed downstream of a gate to con$-$trol submergence of the gate discharge. Consider the

condition shown in Figure $7\mathrm{.}58,$ where the water depth upstream of the gate is $3m$ and the gate opening

is $0\mathrm{.}5m.$ The width of the channel is $4m$ and the weir is at a suf$-$ ficient distance downstream of the gate

such that flow conditions immediately upstream of the weir are subcrit$-$ ical. Determine the minimum

height of the weir required to ensure that the gate discharge is submerged.