Section 4: Soil and Water Conservation Engineering
Watershed Management
Subtopic: Watershed characterization and land use capability classification
Question Statement:
A drainage basin has a perimeter $P = 40\text{ km}$ and a total basin area $A = 75\text{ km}^2$. The Gravelius compactness coefficient $K_c = 0.28 \frac{P}{\sqrt{A}}$ is ________ (round off to 2 decimal places).
Answer Key:
1.29
Step-by-Step Solution & Explanation
Gravelius compactness coefficient $K_c$ is defined as the ratio of basin perimeter to the circumference of an equivalent circular area:
$K_c = \frac{P}{2 \sqrt{\pi A}} \approx 0.282 \frac{P}{\sqrt{A}}$
Given $P = 40\text{ km}$ and $A = 75\text{ km}^2$:
$\sqrt{A} = \sqrt{75} \approx 8.66025\text{ km}$
$K_c = \frac{40}{2 \sqrt{\pi \times 75}} = \frac{40}{2 \sqrt{235.619}} = \frac{40}{2 \times 15.3499} = \frac{40}{30.6998} \approx 1.3029$
Using $0.28 \frac{P}{\sqrt{A}} = 0.28 \times \frac{40}{8.66025} = 0.28 \times 4.6188 \approx 1.293 \approx 1.29$