Question

The areas of drainage basins A and B are 25 km² and 50 km², respectively. The total length of drainages of all orders in basin A is 20 km. If both the basins have the same drainage density, the total length of drainages of all orders in basin B in km is____ (in integer).

Hint:

If drainage density is constant across basins, total stream length scales linearly with basin area: \(L \propto A\).

Answer 1

Correct Answer: 40

Step 1: Define drainage density.
Drainage density \(D_d = \dfrac{\text{Total stream length}}{\text{Basin area}}\). Step 2: Compute \(D_d\) for basin A.
\[ D_d = \frac{20\ \text{km}}{25\ \text{km}^2} = 0.8\ \text{km}^{-1} \] Step 3: Use same \(D_d\) for basin B to get its total length.
\[ L_B = D_d \times A_B = 0.8\ \text{km}^{-1} \times 50\ \text{km}^2 = 40\ \text{km} \] \[ \boxed{40\ \text{km}} \]