Q$4.($b$)$ A commonly used shape for concrete lined canals, called the standard lined trapezoidal

canal sections, consists of trapezoidal section with each of its two corners being rounded

off by a circular arc of a radius equal to the full supply depth. Determine the dimensions

of such a standard lined trapezoidal canal to carry a discharge of $200\frac{m^3}{s}$ at a bed slope

of $1$ in $4000.$ The side slopes are $2H$:$1V,$ and Manning's $n=0\mathrm{.}014.$ The limiting velocity in

the channel is $2\mathrm{.}0\frac{m}{s}.$ Also draw the cross sections,