Water flows down a trapezoidal channel having a constant longitudinal bed slope of $0\mathrm{.}0005$ and a Manning roughness coefficient of $0\mathrm{.}024.$ The channel cross section has a base width of $15m$ and slide slopes of $1$:$1.$ At a certain point in the channel the depth of flow is found to be decreasing at a rate of $1$ in $10,000$ and at this point the depth is $5m.$ Working with the gradually varied flow equation estimate the discharge in the channel.

$230m^3{s}^{-1}$