Question $5.[30$ marks$]$

The $($simplified$)$ topology of a small catchment is shown in the below figure. The dotted lines represent the contour lines with the contour heights shown in italics. The outlet of the catchment is shown by the round black dot. A small stream flows through the bottom part of the catchment $($shown by the black line$).$ Assume the stream is a rectangular channel, $1$ m wide, $0\mathrm{.}2$ m deep and with Manning's n of $0\mathrm{.}035.$ Distances are shown on the left of the figure, the catchment is $200$ m wide. There are no road$/$buildings

The roughness coefficient, n$^(**),$ of the catchment is $0\mathrm{.}1$ for the scrub area and $0\mathrm{.}4$ for grassland. The below table shows the intensity$-$duration$-$frequency table for the catchment.

Table : Intensity$-$Duration$-$Frequency for question T$3($in mmhr$^(-1))$

Duration ARI$($y$)$ aep $10$m $20$m $30$m $60$m $2$h $6$h $12$h $24$h $48$h $72$h $1\mathrm{.}580\mathrm{.}63322\mathrm{.}216\mathrm{.}814\mathrm{.}210\mathrm{.}67\mathrm{.}84\mathrm{.}73\mathrm{.}42\mathrm{.}51\mathrm{.}51\mathrm{.}120\mathrm{.}524\mathrm{.}618\mathrm{.}615\mathrm{.}611\mathrm{.}88\mathrm{.}65\mathrm{.}13\mathrm{.}72\mathrm{.}71\mathrm{.}61\mathrm{.}250\mathrm{.}233\mathrm{.}625\mathrm{.}221\mathrm{.}416\mathrm{.}111\mathrm{.}66\mathrm{.}94\mathrm{.}93\mathrm{.}52\mathrm{.}11\mathrm{.}6100\mathrm{.}141\mathrm{.}431\mathrm{.}226\mathrm{.}419\mathrm{.}814\mathrm{.}28\mathrm{.}35\mathrm{.}94\mathrm{.}22\mathrm{.}61\mathrm{.}9200\mathrm{.}0550\mathrm{.}438\mathrm{.}132\mathrm{.}224\mathrm{.}217\mathrm{.}1107\mathrm{.}1532\mathrm{.}3300\mathrm{.}03356\mathrm{.}442\mathrm{.}63627\mathrm{.}119\mathrm{.}111\mathrm{.}17\mathrm{.}85\mathrm{.}53\mathrm{.}42\mathrm{.}5400\mathrm{.}02561\mathrm{.}246\mathrm{.}23929\mathrm{.}420\mathrm{.}711\mathrm{.}98\mathrm{.}45\mathrm{.}93\mathrm{.}62\mathrm{.}7500\mathrm{.}0265\mathrm{.}449\mathrm{.}241\mathrm{.}631\mathrm{.}22212\mathrm{.}68\mathrm{.}96\mathrm{.}33\mathrm{.}82\mathrm{.}8600\mathrm{.}0176951\mathrm{.}643\mathrm{.}832\mathrm{.}923\mathrm{.}113\mathrm{.}29\mathrm{.}36\mathrm{.}543800\mathrm{.}01274\mathrm{.}456\mathrm{.}147\mathrm{.}435\mathrm{.}624\mathrm{.}914\mathrm{.}21074\mathrm{.}23\mathrm{.}21000\mathrm{.}0179\mathrm{.}259\mathrm{.}750\mathrm{.}437\mathrm{.}926\mathrm{.}515\mathrm{.}110\mathrm{.}57\mathrm{.}44\mathrm{.}53\mathrm{.}3$

$($a$)$ Explain the concept of partial area calculation and why it is necessary for the catchment in the

above figure.

$[5$ marks$]$

$($b$)$ Using the topological map in the above figure, calculate the time of concentration for

AEP $=0\mathrm{.}05.$

$[10$ marks$]$

$($c$)$ Use the Rational method to calculate the flow $($m$3$ s$-1)$ through the outlet for AEP $=0\mathrm{.}05.$

$[10$ marks$]$

$($d$)$ The entire area will be redeveloped. After recalculation your time of concentration reduces by

$25\%.$ Explain why you should not be directly comparing the peak flow from the redeveloped

catchment with the peak flow calculated under part c of this question. $($a$)$ Explain the concept of partial area calculation and why it is necessary for the catchment in the above figure.

$[5$ marks$]$

$($b$)$ Using the topological map in the above figure, calculate the time of concentration for $\backslash (\backslash$mathrm$\{$AEP$\}=0\mathrm{.}05\backslash ).$

$[10$ marks$]$

$($c$)$ Use the Rational method to calculate the flow $\backslash (\backslash$left$(\backslash$mathrm$\{$m$\}^\{3\}\backslash$mathrm$\{$~s$\}^\{-1\}\backslash$right$)\backslash )$ through the outlet for $\backslash (\backslash$mathrm$\{$AEP$\}=0\mathrm{.}05\backslash ).$

$[10$ marks$]$

$($d$)$ The entire area will be redeveloped. After recalculation your time of concentration reduces by $\backslash (25\backslash \%\backslash ).$ Explain why you should not be directly comparing the peak flow from the redeveloped catchment with the peak flow calculated under part c of this question.