A drainage basin outlined on a topographic map with a scale of 1:50,000 has a total stream… — JAMB UTME

A drainage basin outlined on a topographic map with a scale of $1:50,000$ has a total stream network length of $45\text{ cm}$ and a basin area of $36\text{ cm}^2$ measured directly from the map sheet. What is the actual drainage density of the basin in $\text{km}/\text{km}^2$ ?

Answer: 2.5 km/km²

Answer

The actual drainage density of the river basin is

2.5\text{ km}/\text{km}^2

To calculate the true drainage density, map linear measurements and area measurements must first be converted to ground units using the scale

1:50,000

(

1\text{ cm} = 0.5\text{ km}

1\text{ cm}^2 = 0.25\text{ km}^2

). Total ground stream length is

45 \times 0.5 = 22.5\text{ km}

and total ground basin area is

36 \times 0.25 = 9\text{ km}^2

. Dividing stream length by basin area yields

2.5\text{ km}/\text{km}^2

Step-by-Step Solution

Convert the measured total stream network length from map units (cm) to real-world kilometers.

Ground stream length

L = 45\text{ cm} \times 0.5\text{ km/cm} = 22.5\text{ km}

At a scale of

1:50,000

1\text{ cm}

on the map represents

50,000\text{ cm} = 0.5\text{ km}

on the ground.

Convert the measured basin area from square centimeters to square kilometers.

Ground basin area

A = 36\text{ cm}^2 \times (0.5\text{ km})^2 = 36 \times 0.25\text{ km}^2 = 9\text{ km}^2

The areal scale factor is the square of the linear scale factor (

1\text{ cm}^2 = 0.25\text{ km}^2

Divide the total ground stream length by the total ground basin area.

Drainage density

D_d = \frac{22.5\text{ km}}{9\text{ km}^2} = 2.5\text{ km}/\text{km}^2

Drainage density measures stream channel length per unit area within a river basin.

Key Concept

Drainage Density and Scale Conversion in Basin Analysis

Estimated Time:2m 0s

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