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)
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)
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Solution and Explanation
Drainage density is a measure of the total length of streams per unit area of the watershed. The formula to calculate drainage density (Dd) 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.
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