Question $1$

$($b$)$

$($i$)$ The runoff data measured following a $3-$hour storm are given in Table Q$1.$ If the baseflow is $2\mathrm{.}0\frac{m^3}{s},$ determine the $10$ mm $3-$hour unit hydrograph. Note that the catchment area draining to the river is $2305199m^2.$

Table Q$1$

$\backslash$table$[[$Time $(hr),0,5,10,15,20,25,30,35,40,45,50],[$Discharge $(\frac{m^3}{s}),2\mathrm{.}0,3\mathrm{.}6,4\mathrm{.}8,6\mathrm{.}8,8\mathrm{.}2,6\mathrm{.}4,5\mathrm{.}4,4\mathrm{.}7,4\mathrm{.}0,3\mathrm{.}4,2\mathrm{.}0]]$

Answer: equivalent depth of rainfall $=229mm.$ UH peak of $0\mathrm{.}27\frac{m^3}{s}$@$20hrs$ Hint: subtract baseflow, determine volume of excess rainfail $($area under Q$/$t curve$),$ divide volume by catchment area to determine equivalent depth of rainfall, and use this value to modify QR hydrograph to UH$.$

$(14.$ Marks$)$

$($ii$)$ For a $3-$hr storm of total rainfall $7m\frac{m}{h}r$ and losses of $2m\frac{m}{?}$ hour, derive the quick response runoff using the unit hydrograph obtained in $($i$).$

Answer: hydrograph peak of $0\mathrm{.}41\frac{m^3}{s}$@$20hrs$

Hint: determine effective rainfall and use this value to modify UH$.$

$(5$ marks$)$