$****$please upload written workings if possible $*****$ Question $1$

A rectangular concrete channel $(n=0\mathrm{.}02)$ has a bed slope of $0\mathrm{.}0015,$ a width of $7m$

and conveys water at a rate of $15\frac{m^3}{s}.$ The channel cannot be considered 'wide'.

On the upstream side of a broad$-$crested weir, the flow depth is $3\mathrm{.}8m.$ Determine:

$($a$)$ The normal and critical flow depths in the channel.

$($b$)$ The upstream water surface profile classification.

$($c$)$ The length of the upstream backwater curve to normal depth through 'direct step'

calculations. Limit your analysis to two length intervals.

$($d$)$ What would be the benefit of using more than two length intervals for the analysis

in $($c$).$

$($e$)$ Suggest an alternative to the direct step method, outlining any advantages of this

method in 'real world' situations.

The flow depth downstream of the weir was measured at $2\mathrm{.}2m.$

$($f$)$ Explain with the aid of a specific energy diagram why the water surface decreases

from upstream to downstream of the weir.

$(20\%)$A rectangular concrete channel $($n $=0\mathrm{.}02)$ has a bed slope of $0\mathrm{.}0015,$ a width of $7$ m

and conveys water at a rate of $15$ m$3/$s$.$ The channel cannot be considered $$wide$.$

On the upstream side of a broad$-$crested weir, the flow depth is $3\mathrm{.}8$ m$.$ Determine:

$($a$)$ The normal and critical flow depths in the channel. $(20\%)$

$($b$)$ The upstream water surface profile classification. $(10\%)$

$($c$)$ The length of the upstream backwater curve to normal depth through $$direct step$$

calculations. Limit your analysis to two length intervals. $(30\%)$

$($d$)$ What would be the benefit of using more than two length intervals for the analysis

in $($c$).(10\%)$

$($e$)$ Suggest an alternative to the direct step method, outlining any advantages of this

method in $$real world$$ situations. $(10\%)$

The flow depth downstream of the weir was measured at $2\mathrm{.}2$ m$.$

$($f$)$ Explain with the aid of a specific energy diagram why the water surface decreases

from upstream to downstream of the weir. $(20\%)$

Question $2$

$($a$)$ In the context of pump$-$pipeline system analysis, explain the following:

$($i$)$ system curve $($ii$)$ pump characteristic curve

$($iii$)$ duty point $($iv$)$ cavitation $(20\%)$

$($b$)($i$)$ A site contractor wishing to pour the foundations for a large retail development

requires the water level in an excavated site to be lowered. A number of

identical centrifugal pumps are located on site. The head$-$discharge

characteristics for one such pump operating at test speed is in Table $1.$

Table $1$

The static lift in pumping the water from the excavation to an on$-$site water

storage facility can be taken as $5$ m$.$ The excavation and storage facility are

connected by an $800$ m long pipe of diameter $0\mathrm{.}2$ m$.$ The Darcy Weisbach

friction factor for the pipe can be taken as $0\mathrm{.}02$ and local losses through the

pipe total $8$ V$2/2$g$.$

In an attempt to minimise the time required for the removal of the flood water

in the excavated site, the contractor is considering either operating two of the

pumps in parallel at test speed or operating a single pump at $1\mathrm{.}5$ times the test

speed.

Determine the time saving that could be made by choosing one configuration

over the other if the volume of water in the excavation is $12,500$ m$3.(70\%)$

$($ii$)$ Based on assumptions inherent in your analysis, suggest how the accuracy of

your analysis might be improved. $(10\%)$Discharge Q $($l$/$s$)01530405055$

Head $($m$)282521171310\mathrm{.}3$