Directions: The ordinates of a 2-h unit hydrograph at 1 hour intervals starting from time t = 0, are 0, 3, 8, 6, 3, 2 and 0 m3/s. Use trapezoidal rule for numerical integration, if required.
What is the catchment area represented by the unit hydrograph?
-
1.00 km2
-
2.00 km2
-
7.92 km2
-
8.64 km2
C
Correct answer
Explanation
The volume of the unit hydrograph is the area under the hydrograph curve. Using the trapezoidal rule: Volume = (1/2) * [ (0+0) + 2*(3+8+6+3+2) ] * (1 hour * 3600 s/h) = 22 * 3600 = 79200 m^3. Since it is a unit hydrograph (1 cm of runoff), Area = Volume / Depth = 79200 m^3 / 0.01 m = 7,920,000 m^2 = 7.92 km^2.