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Osmosis in Selectively Permeable Membrane

If the value ...

Question

If the value of initial infiltration rate is 20 mm/hr, final infiltration rate is 12 mm/hr and value of constant is 0.9 $h r^{- 1}$ then value of infiltration depth of storm lasting for 6 hr is_________mm.
80.84

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Solution

The correct option is A 80.84
Hortons's equation gives infiltration rate as :

$I = I_{F} + (I_{0} - I_{F}) e^{- k t}$
$= 12 + (20 - 12) e^{- 0.9 t}$
= $12 + 8 e^{- 0.9 t}$

Infiltration depth = $\int_{0}^{t} I d t = \int_{0}^{6} 12 + 8 e^{- 0.9 t} d t$
$= 80.84 m m ≃ 80.85 m m$

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