CIV E 445 - APPLIED HYDROLOGY
SPRING 2010
SOLUTIONS TO HOMEWORK 2 , CHAPTER 2

Problem 2-1

Since  i = a / (t + b), it follows that:

55 = a / (1 + b); and

22 = a / (2 + b).

Solving for a and b: a = 36.6667; b = -0.3333.  ANSWER.

Problem 2-2

Since at t = ∞, the final infiltration rate is 0.5 mm/h, then: fc = 0.5 mm/h. Therefore, from Eq. 2-13:

3 = 0.5 + (fo - 0.5) e -k; and

1 = 0.5 + (fo - 0.5) e -3k

fo - 0.5 = 2.5 ek

fo - 0.5 = 0.5 e3k

Dividing these two equations:

e2k = 5

From which: k = 0.8047 h-1

Then: fc = 0.5 mm/h; fo = 6.09 mm/h; and k = 0.8047 h-1.   ANSWER.

Problem 2-3

Try several likely values for φ. For instance, assume φ between 1 and 2 cm/h.

Therefore: 2 • (2 - φ) + 2 • (3 - φ) + 2 • (4 - φ) + 2 • (2 - φ) = 10.  

Solving for φ: φ = 1.5 cm/h.   ANSWER.

Therefore, the assumption of φ being between 1 and 2 cm/h was correct.