Question Bank • QB_SWCE_EXP_023 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Hydrology

Subtopic: Infiltration – indices and equations

Question Statement:

Horton's infiltration equation for a catchment is $f = 10 + 30 e^{-2 t}$, where $f$ is infiltration capacity in $\text{mm/h}$ and $t$ is time in hours. Assuming rainfall intensity always exceeds infiltration capacity, the total cumulative depth of water infiltrated in the first 2 hours in $\text{mm}$ is ________ (round off to 2 decimal places).

Answer Key:

34.73

Step-by-Step Solution & Explanation

Cumulative infiltration depth $F(t) = \int_0^t f(t) dt$: $F(t) = \int_0^t (10 + 30 e^{-2t}) dt = \left[ 10 t - \frac{30}{2} e^{-2t} \right]_0^t = 10 t + 15 (1 - e^{-2t})$ For $t = 2\text{ hours}$: $F(2) = 10(2) + 15(1 - e^{-4}) = 20 + 15(1 - 0.0183156) = 20 + 15(0.98168) = 20 + 14.725 = 34.725\text{ mm} \approx 34.73\text{ mm}$
← Previous (QB_SWCE_ADV_122) Next (QB_SUB_SWCE_0176) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test