---
title: "Drainage density, form factor, channel slope"
subject: "Engineering Hydrology"
chapter: 4
key: "semester_5/engineering_hydrology:drainage-density-basin-140km2"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/drainage-density-basin-140km2
site: BCT Engineering
---

# Drainage density, form factor, channel slope

Engineering Hydrology · Chapter 4: Surface Runoff

- Asked in: 2081 Baisakh, 4 marks; 2072 Chaitra, 4 marks (asked 2 times)
- Video: [Hydrology: Horton's Law & Drainage Density Example](https://www.youtube.com/watch?v=EYA9WU6hh2A) — Simmy Sigma
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/drainage-density-basin-140km2
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-4

## Question

Find the drainage density, average length of overland flow, form factor and channel slope for a basin with the following data:

Area of basin (A) = 140 km$^2$
Distance between the outlet to the farthest point (L) = 21 km
Elevation difference between the outlet and the farthest point (h) = 1090 m
Total length of channels of all order ($L_s$) = 654 km

## Short answer

Drainage density = 4.67 km/km²; average overland flow length = 0.107 km; form factor = 0.317; channel slope = 0.052 (5.2%).

## Answer

**Data:** $A = 140$ km$^2$, $L = 21$ km, $h = 1090$ m, total channel length $L_s = 654$ km.

#### Drainage density
$$
D_d = \frac{L_s}{A} = \frac{654}{140} = 4.67\ \text{km/km}^2
$$

#### Average length of overland flow
$$
L_o = \frac{1}{2D_d} = \frac{1}{2\times4.671} = 0.107\ \text{km} = 107\ \text{m}
$$

#### Form factor
$$
R_f = \frac{A}{L^2} = \frac{140}{21^2} = \frac{140}{441} = 0.317
$$

#### Channel slope
$$
S = \frac{h}{L} = \frac{1090}{21\,000} = 0.0519 \;(5.19\ \%) \approx 51.9\ \text{m/km}
$$

**Answer: $D_d = 4.67$ km/km$^2$; $L_o = 0.107$ km; form factor $= 0.317$; channel slope $= 0.052$ (5.2 %).**

The high drainage density and steep slope show a well-drained basin with quick runoff. The low form factor shows an elongated basin, which gives lower and flatter peak flows than a circular basin.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the drainage density?
   A. 21/140
   B. 654 x 140
   C. 654/140 = 4.67 km/km2
   D. 140/654
   Answer: C. D_d = total channel length / area. (Key point: Drainage density)

2. What is the average length of overland flow?
   A. 2 D_d
   B. D_d/2
   C. 1/D_d = 0.21 km
   D. 1/(2 D_d) = 0.107 km
   Answer: D. L_o = 1/(2 D_d) = 1/9.34 = 0.107 km. (Key point: Overland flow length)

3. What is the form factor?
   A. A/L = 6.7
   B. L^2/A
   C. A/L^2 = 0.317
   D. L/A
   Answer: C. 140/441 = 0.317. (Key point: Form factor)

4. What is the channel slope?
   A. h/L = 1090/21000 = 0.052
   B. 21/1090
   C. 1090/140
   D. 1090 x 21
   Answer: A. Elevation difference over length, about 5.2 %. (Key point: Channel slope)

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