A trapezoidal channel with a bottom width of \(3.0 \mathrm{~m}\) and sides with a slope of 2:1 (horizontal:vertical) is lined with fine gravel \((n=0.020)\) and is to carry \(10 \mathrm{~m}^{3} / \mathrm{s}\). Can this channel be built with a slope of \(S_{0}=0.00010\) if it is necessary to keep the velocity below \(0.75 \mathrm{~m} / \mathrm{s}\) to prevent scouring of the bottom? Explain.