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)
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)
Show Hint
Correct Answer: 1.08
Solution and Explanation
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 = \(3 + 2.5 + 4 + 3 + 2 + 5 = 19.5 \, {km}\). 2nd order streams:
The lengths of the 2nd order streams are 10 km, 15 km, and 7 km. Total length of 2nd order streams = \(10 + 15 + 7 = 32 \, {km}\). 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 length of 1st order + Total length of 2nd order + Total length of 3rd order \[ L = 19.5 + 32 + 30 = 81.5 \, {km} \] Step 4: Calculate drainage density
The area of the watershed is 74 km\(^2\). Using the drainage density formula: \[ D_d = \frac{L}{A} = \frac{81.5}{74} \approx 1.10 \, {km/km}^2 \] Step 5: Final answer
The drainage density of the watershed is approximately \(1.10 \, {km/km}^2\).
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