A $20$m wide rectangular channel with a discharge of $10$m$3/$s is to be changed by constructing a broad$-$crested weir. Upstream of the weir, a steady uniform subcritical flow with water depth of $1\mathrm{.}0$m prevails. The weir is designed to produce a flow with a depth of $0\mathrm{.}67$m$.$ Calculate the height of the weir to produce this flow condition.