$(10$ Points$)$ A trapezoidal channel is lined with newly finished concrete as shown the

figure below. The channel slope is $S_0=0\mathrm{.}0014$ and the normal depth is $1\mathrm{.}5m.$ The

flow is uniform and you are to design the channel to have a mean velocity of $3\frac{m}{s}.$

Assume that freshwater flows through the channel.

Figure pertains to Problem $4.$

$($a$)$ Using Manning's Equation, determine the width $b$ of the channel.

$($b$)$ Determine the flow rate of the channel.

$($c$)$ Determine the Froude number of the flow and comment.

$($d$)$ Calculate the Reynolds number, assuming water at $60F(15\mathrm{.}6C),$ and comment.

$($e$)$ Assume that the concrete channel is replaced by a rougher surface, rubble ma$-$

sonry. Assume all other parameters and dimensions are the same. Calculate the

new flow rate in the channel. How does the surface lining of the channel affect

the flowrate?

To estimate the friction factor, $f,$ you can either use the Moody diagram or the

Haaland equation:

$\frac{1}{\sqrt[\phantom{2}]{f}}=-1\mathrm{.}8lo{g}_{10}[(\frac{lo\frac{n}{D}}{3\mathrm{.}7}{)}^{1\mathrm{.}11}+\frac{6\mathrm{.}9}{Re}]$