GATE 2017 CE (CE2) – Question 34
Horton infiltration is $f=c_1+c_2e^{-kt}$. Initial and long-term rates are 200 and 25 mm/h. At t = 1 h the rate is 90 mm/h. The decay constant k, to two decimal places, is ______ h⁻¹.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.98 to 1.00
Explanation
The final infiltration rate gives $c_1=25$, and the initial rate gives $c_2=200-25=175$. At one hour, $90=25+175e^{-k}$, so $e^{-k}=65/175$. Therefore $k=\ln(175/65)=0.9904$ h⁻¹, or 0.99 h⁻¹.