CIVE 445 - ENGINEERING HYDROLOGY

SPRING 2004 - MIDTERM 1 - SOLUTION

PROBLEM 2

fc = 1.4 mm/hr

f = 2.75 mm/hr for t = 1 hr

f = 1.85 mm/hr for t = 2 hr


Horton equation:

f = fc + (fo - fc) e-kt

f - fc = (fo - fc) e-kt

2.75 - 1.4 = (fo - 1.4) e-k

1.85 - 1.4 = (fo - 1.4) e-2k

1.35 = (fo - 1.4) e-k

0.45 = (fo - 1.4) e-2k

Dividing these two equations:

3.0 = ek

k = ln (3.0) = 1.0986 hr-1    ANSWER.

Solving for fo:

fo = 1.35 ek + 1.4

fo = (1.35 × 3.0) + 1.4 = 5.45 mm/hr    ANSWER.

fc = 1.4 mm/hr    ANSWER.


Verification:

f = 1.4 + (5.45 - 1.4) e-1.0986 = 2.75 mm/hr   OK

f = 1.4 + (5.45 - 1.4) e-2 × 1.0986 = 1.85 mm/hr   OK

Problem 3

 
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