Question Bank • QB_IDE_ADV_048 NAT • 2 Marks

Section 5: Irrigation and Drainage Engineering

Soil-Water-Plant Relationship

Subtopic: Measurement of infiltration, soil moisture and irrigation water infiltration

Question Statement:

Cumulative infiltration into an agricultural soil is modeled by Kostyakov's equation: $I = 18.0 \cdot t^{0.65}$, where $I$ is cumulative depth in millimeters and $t$ is elapsed time in hours. The instantaneous infiltration rate $i = \frac{dI}{dt}$ at $t = 2.0\text{ hours}$ in millimeters per hour ($\text{mm/h}$) is ________ (round off to two decimal places).

Answer Key:

9.18

Step-by-Step Solution & Explanation

1. Kostyakov's equations: $\text{Cumulative infiltration: } I = a t^b$ $\text{Infiltration rate: } i = \frac{dI}{dt} = a \cdot b \cdot t^{b - 1}$ 2. Given parameters: - $a = 18.0\text{ mm/h}^b$ - $b = 0.65$ - $t = 2.0\text{ hours}$ 3. Evaluating terms: $a \cdot b = 18.0 \times 0.65 = 11.70$ $b - 1 = 0.65 - 1.00 = -0.35$ $t^{b - 1} = (2.0)^{-0.35} = \frac{1}{(2.0)^{0.35}}$ $(2.0)^{0.35} = 10^{0.35 \log_{10}(2)} = 10^{0.35 \times 0.30103} = 10^{0.10536} \approx 1.2746$ $t^{-0.35} = \frac{1}{1.2746} = 0.78456$ 4. Infiltration rate $i$: $i = 11.70 \times 0.78456 = 9.1793\text{ mm/h} \approx 9.18\text{ mm/h}$
← Previous (QB_IDE_EXP_100) Next (QB_IDE_ADV_053) →

Practice In Authentic CBT Exam Interface

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

Launch CBT Mock Test