Problem $2$: Consider a watershed area in class B soil of $1000$ acres of which $400$ acres is forest with slope of $\backslash (5\backslash \%,500\backslash )$ acres is flat agricultural land, and $100$ acres is urban.

a$)$ Using the table given, compute the CN parameter for the watershed.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$multirow$[$t$]\{2\}\{*\}\{$Land Use$\}$ & $\backslash$multirow$[$t$]\{2\}\{*\}\{$Slope $(\backslash \%)\}$ & $\backslash$multicolumn$\{4\}\{|$l$|\}\{$Hydrologic Class$\}$ & $\backslash$multirow$[$t$]\{2\}\{*\}\{\backslash$begin$\{$tabular$\}\{$l$\}$

Drainage $\backslash \backslash$

Length $($m$)$

$\backslash$end$\{$tabular$\}\}\backslash \backslash$

$\backslash$hline & & A & B & C & D & $\backslash \backslash$

$\backslash$hline $\backslash$multirow$[$b$]\{3\}\{*\}\{\backslash$begin$\{$tabular$\}\{$l$\}$

Agricultural $\backslash \backslash$

land

$\backslash$end$\{$tabular$\}\}$ & $<mtext></mtext><mn>3</mn>$ & $62$ & $72$ & $79$ & $82$ & $\backslash \backslash$

$\backslash$hline & $3-8$ & $64$ & $76$ & $84$ & $88$ & $10\backslash \backslash$

$\backslash$hline & $\backslash (>8\backslash )$ & $70$ & $80$ & $87$ & $90$ & $\backslash \backslash$

$\backslash$hline $\backslash$multirow$\{3\}\{*\}\{$Pasture$\}$ & $<mtext></mtext><mn>3</mn>$ & $32$ & $51$ & $72$ & $79$ & $\backslash \backslash$

$\backslash$hline & $3-8$ & $44$ & $65$ & $77$ & $82$ & $25\backslash \backslash$

$\backslash$hline & $\backslash (>8\backslash )$ & $59$ & $74$ & $83$ & $87$ & $\backslash \backslash$

$\backslash$hline $\backslash$multirow$\{3\}\{*\}\{$Forest$\}$ & $<mtext></mtext><mn>3</mn>$ & $24$ & $54$ & $68$ & $76$ & $\backslash \backslash$

$\backslash$hline & $3-8$ & $33$ & $59$ & $73$ & $79$ & $20\backslash \backslash$

$\backslash$hline & $\backslash (>8\backslash )$ & $44$ & $66$ & $78$ & $83$ & $\backslash \backslash$

$\backslash$hline Urban & Dense & $73$ & $83$ & $88$ & $90$ & $5\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

b$)$ For the same watershed above, use the Curve Number Method to calculate the flow rate $($Q$)$ at the discharge point for the rainfall data below. $($Hint: The table below shows the steps of calculations$).$

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Time $($min$)$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Cumulative rain $\backslash \backslash$

$($P$)($in$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Runoff $($R$)\backslash \backslash$

$($in$)$

$\backslash$end$\{$tabular$\}$ & $\backslash (\backslash$Delta $\backslash$mathrm$\{$t$\}(\backslash$mathrm$\{$min$\})\backslash )$ & $\backslash (\backslash$Delta $\backslash$mathrm$\{$R$\}\backslash )($in$)$ & $\backslash (\backslash$mathrm$\{$Q$\}(\backslash$mathrm$\{$cfs$\})\backslash )\backslash \backslash$

$\backslash$hline $30$ & $0\mathrm{.}04$ & & & & $\backslash \backslash$

$\backslash$hline $60$ & $0\mathrm{.}38$ & & & & $\backslash \backslash$

$\backslash$hline $90$ & $1\mathrm{.}07$ & & & & $\backslash \backslash$

$\backslash$hline $120$ & $1\mathrm{.}54$ & & & & $\backslash \backslash$

$\backslash$hline $150$ & $1\mathrm{.}72$ & & & & $\backslash \backslash$

$\backslash$hline $180$ & $1\mathrm{.}80$ & & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$