Question

A drainage basin of fourth order covers an area of 40 sq. km. Within the basin, total length of 1st order drainage is 12.5 km, 2nd order drainage is 8.8 km, 3rd order drainage is 4.7 km and 4th order drainage is 4.0 km. The drainage density of the basin is ........ km\(^{-1}\) (give answer in two decimal places).

Hint:

To calculate drainage density, sum the lengths of all streams within the basin and divide by the area of the basin.

Answer 1

Correct Answer: 0.75

Step 1: Understanding drainage density.
Drainage density is defined as the total length of all streams (in km) in a drainage basin divided by the area of the basin (in km\(^2\)). The formula for drainage density \( D \) is: \[ D = \frac{\text{Total length of streams}}{\text{Area of basin}} \] Step 2: Calculating the total length of streams.
The total length of streams is the sum of the lengths of the 1st, 2nd, 3rd, and 4th order drainages: \[ \text{Total length of streams} = 12.5 + 8.8 + 4.7 + 4.0 = 30.0 \, \text{km} \] Step 3: Calculating the drainage density.
The area of the basin is given as 40 sq. km. Therefore, the drainage density is: \[ D = \frac{30.0}{40} = 0.75 \, \text{km}^{-1} \] Step 4: Conclusion.
The drainage density of the basin is 0.75 km\(^{-1}\).