Show that the infiltration volume estimated using Horton's infiltration equation between times t1 and t2 is given by;
F =f_{c}(t_{2}t_{1})+(f_{1}f_{c})(1e^{k(t2t1)})/k
Use the above concept in answering the following question.
F_{1} = f_{c} +(f_{0}f_{c})ekt_{1}
In a small watershed with homogeneous soil, runoff from two storms separated by an interval of 3 hours was monitored. The infiltration capacity of the soil at the beginning of the first storm was observed to be at its maximum capacity. Given the following information, determine the runoff for the first burst and the rate of infiltration recovery between the two storms.
Storm intensities:
Time (hr)

0  1

1  2

2  3

3  4

4  5

5  6

6  7

7  8

8  9

9  10

Rainfall (mm/hr)

16

12

14

7

0

0

0

13

10

8

Infiltration capacity: fo = 14 mm/hr, fc = 4.0 mm/hr, k = 0.6 hr^{1}
The surface runoff for the second storm was measured as Y mm at the outlet of the watershed, where Y is given by:
If your R value is between 45 and 55 (both inclusive), then Y = 15.5 mm
If your R value is between 56 and 66 (both inclusive), then Y = 16.0 mm
If your R value is between 67 and 77 (both inclusive), then Y = 16.5 mm
If your R value is between 78 and 88 (both inclusive), then Y = 17.0 mm
If your R value is between 89 and 99 (both inclusive), then Y = 17.5 mm