TUTORIAL # $1-$ OPEN CHANNEL FLOW

Question $1$: Open Channels $-$ Normal Depth Flow

$($a$)$ In an open channel, it is noted that the slope of the bed $($s$)$ is parallel to the water

surface profile $($water depth $=Y_1)$ and to the energy grade line $(EL).$ For the sketch shown

below state what this depth of flow is called.

$($b$)$ Also comment on:

i$.$ For this type of flow, is the water depth a function of distance along the channel?

ii$.$ For this type of flow, is the water depth a function of time?

iii. What are the two main forces that are acting on this flow?

iv$.$ Applying a force balance approach over the length considered $($L$),$ develop an expression

for the energy loss $h_f$ in terms of $,L,V,g$ and $m.$

v$.$ Rearrange the equation derived in $($iv$)$ above to give the Chezy Equation.

$($c$)$ Using the Manning Equation, $V=\frac{1}{n}{m}^{\frac{2}{3}}{i}^{\frac{1}{2}},$ design a rectangular channel in formed

unfinished concrete, having a flow discharge of $6\frac{m^3}{sec},$ a bed slope of $1\mathrm{.}2\%$ and normal

depth equal to $\frac{1}{2}$ the width of the channel. Use the table below to get the Manning's

coefficient of roughness.