Q$8.$ A long rectangular channel, $2\mathrm{.}5$ m wide, bed slope $1$:$1000$ and Manning roughness coefficient $0\mathrm{.}02$ discharges $4\mathrm{.}5\frac{m^3}{s}$ freely to atmosphere at the downstream end. Noting that at the end of the channel, the flow depth approximates closely to the critical depth. Compute the distance from the channel end to the place where the flow depth is $10$ percent lower than the uniform flow depth.