Question

A drainage basin of fourth order covers an area of 35 km². Within the basin, the total lengths of the 1st order, 2nd order, and 3rd order drainages are 11.5 km, 8.5 km, and 4.2 km, respectively. If the drainage density of the basin is 0.8 km\(^{-1}\), the total length of the 4th order drainage is \(\underline{\hspace{1cm}}\) km.

Hint:

Drainage density can be used to estimate the total length of drainage channels in a basin based on the area and other drainage orders.

Answer 1

Correct Answer: 3.8

Drainage density is defined as the ratio of the total length of drainage channels to the area of the basin: \[ D = \frac{L}{A} \] where:
- \( D \) is the drainage density,
- \( L \) is the total length of drainage channels, and
- \( A \) is the area of the basin.
Given:
- \( D = 0.8 \, \text{km}^{-1} \),
- \( A = 35 \, \text{km}^2 \).
Thus, the total length \( L \) of the drainage is: \[ L = D \cdot A = 0.8 \cdot 35 = 28 \, \text{km} \] Now, the total length of the 4th order drainage is: \[ L_{\text{4th order}} = 28 - (11.5 + 8.5 + 4.2) = 28 - 24.2 = 3.8 \, \text{km} \]