Question $6$

A lock gate can be partially raised $($up to a height $2\frac{h}{3}$ above the

channel bed$)$ to control the flow rate $Q$ of water from a large lake

of depth $h$ into an irrigation channel with a rectangular cross$-$

section of width $w($see figure $11).$ You can assume that the

irrigation channel is deep enough to carry any flow that is

supplied to it$.$

Figure $11$: Vertical section through large lake and irrigation channel. The lock gate, which

is shown in the shut position, can be partially raised $($up to a height $2\frac{h}{3}$ above the channel

bed$)$ to control the flow into the irrigation channel, which has a rectangular cross$-$section with

width $w.$

$($b$)$

If $h=0\mathrm{.}5m,w=0\mathrm{.}4m$ and the desired flow rate is $0\mathrm{.}17m^3{s}^{-1},$ calculate the flow depth in the irrigation channel a

short way downstream of the lock gate. Take the gravitational acceleration to be $9\mathrm{.}81m{s}^{-2}.$