On a topographical map extract drawn at a scale of 1:50,000, the total length of all strea… — JAMB UTME

On a topographical map extract drawn at a scale of $1:50,000$ , the total length of all stream channels within a river basin is measured as $18\text{ cm}$ , while the total area of the basin on the map is $12\text{ cm}^2$ . What is the drainage density of this river basin in $\text{km/km}^2$ ?

Answer: 3 km/km²

Answer

The drainage density of the river basin is

3\text{ km/km}^2

Drainage density is determined by dividing total real stream length by total real area of the drainage basin. Given a map scale of

1:50,000

18\text{ cm}

of stream length translates to

9\text{ km}

, and

12\text{ cm}^2

of area translates to

3\text{ km}^2

. The resulting quotient gives a drainage density of

3\text{ km/km}^2

Step-by-Step Solution

Convert linear map measurement to actual distance in kilometers

18\text{ cm} \text{ on map} = 18 \times 0.5\text{ km} = 9\text{ km}

At a scale of

1:50,000

1\text{ cm}

represents

50,000\text{ cm}

0.5\text{ km}

on the ground.

Convert map area measurement to actual area in square kilometers

12\text{ cm}^2 \text{ on map} = 12 \times (0.5\text{ km})^2 = 12 \times 0.25\text{ km}^2 = 3\text{ km}^2

Area scale ratio is the square of the linear scale ratio (

(0.5\text{ km/cm})^2 = 0.25\text{ km}^2/\text{cm}^2

Calculate drainage density using the formula

D_d = \frac{\sum L}{A}

D_d = \frac{9\text{ km}}{3\text{ km}^2} = 3\text{ km/km}^2

Drainage density is defined as the total length of streams per unit drainage area.

Key Concept

Drainage Density and Scale Conversion

Estimated Time:1m 30s

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