Q$1.$ An $8-$ft wide rectangular channel with a bed slope of $0\mathrm{.}0004f\frac{t}{f}t$ has a depth of flow of $2ft.$ Assuming steady uniform flow, determine the discharge in the channel. The Manning roughness coefficient is $n=0\mathrm{.}015.$

Q$2.$ Determine the normal depth $($for uniform flow$)$ if the channel described in Q$1$ has a flowrate of $100cfs.$

Q$3.$ What is the full capacity flow rate $($according to Mannings equation$)$ for a circular channel. Show your derivation. $($i$.$e$.,Q=($:$F(S_0,n,D)\}.$

Q$4.$ For a $1\mathrm{.}5m$ pipe, $n=0\mathrm{.}015,$ and $S_0=0\mathrm{.}02,$ find the full capacity flow rate. What would the height of flow be when the flow rate in the channel is running at its quarter capacity $=\frac{1}{4}{Q}_{\text{f}\text{u}\text{l}\text{l}}).$ Use the Manning equation and $R_h$ and A equations for the circular shape, and then use the monograms, you should get the same answer.

Q$5.$ Top width $($T$)$ is the width of the top of the water surface in a channel. Find a formula that describes the Top width $($T$)$ for a circular channel in terms of $$ and $D.($i$.$e$.,T=F(,D)).$ Check your formula for a half full open channel flow.