Example $4-4$: A trapezoidal channel with a longitudinal slope of So $=0\mathrm{.}005$ is made of fine finished concrete, n$1,$ and rock cuts, n$2,$ and carries a discharge of $15$ m$3/$s$.$ The sidewall slope of the channel is $1$V:$1$H and the bottom width is $6$ m$.$ Calculate:

a$)$ normal depth in the channel, yn;

b$)$ Froude number, F$.$

Note: Use Felkel formula to calculate the equivalent Manning$$s coefficient.

Assume the cannel wall are made of rock cuts to calculate the initial depth of yno and continue the calculations for two iterations.