$1\mathrm{.}1.$ Derive expressions for the flow area, $A,$ wetted perimeter, $P,$ hydraulic

radius, $R,$ top$-$water surface width, $B,$ and hydraulic depth, $D,$ for the following

channel cross sections:

i$.$ Rectangular $($bottom width $=B_o)$

ii$.$ Trapezoidal $($bottom width $=B_o,$ side slopes $=$

iii. Triangular $($side slopes $=1V$:$sH)$

iv$.$ Partially$-$full circular $($diameter $=D)$

v$.$ Standard horseshoe$($Fig$.1-17).$

Fig. $1-17.$ Horseshoe section