Channel section design and excavation estimation

Design a channel section and estimate the total excavation amount for an earthen channel in sandy soil:

Channel bottom slope is $0\mathrm{.}0015$

Design discharge $290$ cfs

Design work:

Select design methos:

$\backslash$table$[[$For an excavated channel, the design criterion should be consided:,,$],[2.$ Choose channel parameters:$],[$For sandy soil, the side slope of the channel should be $m=($use sandy loam$),,],[$For earthen channel, the manning's coefficient should take $n=,0\mathrm{.}026,],[$The maximal allowable velocity for unlined channel is $v_{\text{m}\text{a}\text{x}}=([$US$]$ units given$),3\mathrm{.}6,$ft$/$s$]]$

Size the channel:

a$.$ Determination of hydraulic radius $R_h$ : $($for a logn channel, normal flow will be assumed:$)$

$\backslash$table$[[$Rearranging the Manning equaiton to solve for the hydraulic radius, $R_h=,,f{t}^{-1}$