$($c$)$ A surface irrigation is required to irrigate $5-$acre watermelon plot with a peak water demand of $12m\frac{m}{?}$ day and depletion rate of $0\mathrm{.}8$ on clay loam soil whose infiltration rate is $7\mathrm{.}2m\frac{m}{h}r$ and water holding capacity of $150m\frac{m}{m}.$ Design a $1$:$1$ trapezoidal canal to deliver the irrigation water at $0\mathrm{.}7\frac{m}{s}$ if the irrigation efficiency of $80\%$ is anticipated for $8-$hour irrigation per day. Assume bed$-$slope of $1$:$500$ concrete lined canal with a manning roughness of $0\mathrm{.}015$ and rooting depth of $1\mathrm{.}3m.$

$(15$ marks$)$