a$)$ Construct a triangular rainfall hyetograph $($similar to Figure $2\mathrm{.}1)$ for a $25$

$(5$ marks$)$

year$-6$ hour duration in a location given the following information:

$i(m)$

rigure

Average intensity of rainfall of duration $(t_d)$ in minutes: $i=\frac{a}{(L_a+b{)}^c}(m\frac{m}{h}r)$ where $a=81$;$b=7\mathrm{.}7$;$c=0\mathrm{.}724$

Total rainfall of duration $(t_d)$:$P=i{t}_d=\frac{1}{2}{t}_{d}h(mm)$

Advancement coefficient: $r=\frac{t_9}{L_d}=0\mathrm{.}5$

b$)$ Estimate the $2$ ha catchment's time of concentration and calculate its peak

$(10$ marks$)$ runoff rate for a $30$min storm with a return period of $20$ years. Take a Manning's $n$ for overland flow of $0\mathrm{.}25,$ an average overland flow length of $60m,$ and an average slope to the outfall of $0\mathrm{.}5\%.$ You are given the following relationships:

$t_c=6\mathrm{.}99\frac{(nL{)}^{0\mathrm{.}6}}{(i_6{)}^{0\mathrm{.}4}(S_0{)}^{0\mathrm{.}3}}$

$i_{e20}=\frac{150}{(t+8\mathrm{.}96{)}^{0\mathrm{.}78}}$

Where:

$i_{eq}$ is the average excess

rainfall intensity $(c\frac{m}{h}r)$ for a

$20-$year return period

$t$ is the storm duration $($min$)$

Where:

$t_c$ is the time of concentration $($min$)$

$n$ is Manning's overland roughness

coefficient

$L$ is the distance of the overland flow path $($m$)$

$t_e$ is the excess rainfall intensity $(m\frac{m}{h}r)$

c$)$ Given the following $1$ hr unit hydrograph and net rainfall profile, determine

$(10$ marks$)$

$(10$ marks$)$ the surface runoff hydrograph.

Unit Hydrograph data

$\backslash$table$[[$Time $(hr),0,1,2,3,4,5,6,7],[$Discharge $(\frac{m^3}{s}),0,1,4,6,5,3,1,0]]$

Net rainfall profile

$\backslash$table$[[$Time $($hr$),0-1,1-2,2-3$