$(15$ Points$)$ A channel has a trapezoidal cross$-$section, with a width of $40$ feet across the top

and a maximum depth of $6$ ft $.$ The inclination on the side of the channel is $25.$ You are

interested in estimating the velocity of water flowing in the channel. According to the

empirical Manning's Formula, the velocity $V=\frac{C}{n}{R}^{\frac{2}{3}}{S}^{\frac{1}{2}},$ where n is a roughness

coefficient, S is the slope along the axis of the channel, C is a constant that depends on units,

and R is the hydraulic radius of the channel. Manning defined the hydraulic radius as the

cross$-$sectional area divided by the length of the wetted perimeter. Draw a sketch of the

problem. Determine the hydraulic radius.

Add Sketch $+$ Show Calculations!!!!!!!!: