Question

A watershed has an area of 74 km\(^2\). The stream network within this watershed consists of three different stream orders. The stream lengths in each order are as follows: Ist order streams: 3 km, 2.5 km, 4 km, 3 km, 2 km, 5 km
IInd order streams: 10 km, 15 km, 7 km
IIIrd order streams: 30 km
The drainage density of the watershed is _________km/km\(^2\) (Round off to two decimal places)

Hint:

Drainage density is an important indicator of the terrain's permeability. Higher values typically indicate more rugged terrain with faster water runoff, while lower values are indicative of flatter, more permeable areas.

Answer 1

Step 1: Understanding the Drainage Density Formula
Drainage density is a measure of the total length of streams per unit area of the watershed. The formula to calculate drainage density (D_d) is:

\[ D_d = \frac{L}{A} \]
Where:
L is the total length of all streams in the watershed (sum of the lengths of streams of all orders),
A is the area of the watershed.

Step 2: Calculate the Total Length of Streams in Each Order
1st order streams:
The lengths of the 1st order streams are 3 km, 2.5 km, 4 km, 3 km, 2 km, and 5 km.
Total length of 1st order streams = \(3 + 2.5 + 4 + 3 + 2 + 5 = 19.5 \, \text{km}\)

2nd order streams:
The lengths of the 2nd order streams are 10 km, 15 km, and 7 km.
Total length of 2nd order streams = \(10 + 15 + 7 = 32 \, \text{km}\)

3rd order streams:
The length of the 3rd order stream is 30 km.
Total length of 3rd order streams = 30 km

Step 3: Calculate the Total Stream Length
Total stream length (L) = Total of 1st order + 2nd order + 3rd order streams
\[ L = 19.5 + 32 + 30 = 81.5 \, \text{km} \]

Step 4: Calculate Drainage Density
The area of the watershed is 74 km². Using the drainage density formula:
\[ D_d = \frac{L}{A} = \frac{81.5}{74} \approx 1.10 \, \text{km/km}^2 \]

Step 5: Final Answer
The drainage density of the watershed is approximately 1.10 km/km².