Hydrograph Analysis Questions and Answers

Answer: A

The watershed area is about 7.56 km².

Subtract the base flow of 1 m³ s⁻¹ to get direct runoff: 0, 6, 25, 36, 26, 12, 0. The runoff volume is the sum of the ordinates times the 1-hour interval, and it must equal the total excess rainfall (2 + 3 = 5 cm) over the area:

\[ \begin{aligned} V &= (6 + 25 + 36 + 26 + 12)(3600) \\ &= 105 \times 3600 = 378000\ \text{m}^{3} \\ A &= \frac{378000}{0.05} = 7.56 \times 10^{6}\ \text{m}^{2} \end{aligned} \]

That is 7.56 km². Forgetting to remove the base flow adds 7 m³ s⁻¹-hours and gives about 8.06 km²; the other options do not follow from a 5 cm rainfall excess.

Answer: C

The falling limb depends on basin characteristics only.

The falling (recession) limb of a hydrograph begins after the peak, once rainfall has stopped adding to the flow. From then on the discharge is the catchment draining its stored water, from surface, channel and groundwater storage, and its shape is set by the properties of the basin: its size, shape, slope, drainage density, soils and geology. This is why a recession curve can be described by a basin constant and is independent of the storm that produced it.

The rising limb and the peak are the parts that depend on both basin and storm characteristics, such as rainfall intensity, duration and its movement across the basin. Storm characteristics alone, or the direction of the rainfall, do not govern the recession.

Answer: B

The time of concentration is proportional to \(S^{-0.385}\).

Kirpich's formula, the one usually taught for small agricultural watersheds, gives

\[ t_c = 0.0195\, L^{0.77} S^{-0.385} \]

with \(t_c\) in minutes, L the maximum length of travel in metres and S the slope. For a given length, \(t_c\) varies as \(S^{-0.385}\): the steeper the watershed, the quicker water reaches the outlet.

The exponent on L is 0.77, not 1.77, so the options with \(L^{1.77}\) are wrong, and \(S^{0.385}\) has the wrong sign, since a steeper slope shortens the time of concentration.

Answer: C

They are called Natural hydrographs.

A natural hydrograph is plotted directly from the observed discharge of a stream, by measuring runoff rates at the outlet of a watershed over time during and after a storm.

Unit, dimensionless and synthetic hydrographs are derived ones. A unit hydrograph is computed from natural hydrographs for 1 cm of excess rainfall, and a dimensionless hydrograph expresses discharge and time as ratios to their peak values. 'Basic hydrograph' is not a standard type.