Within a fourth order drainage basin, the total lengths of the 1st, 2nd, 3rd and 4th order streams are 10.5 km, 7.5 km, 5.5 km and 1.5 km, respectively. If the drainage density of the basin is 0.5 km-1, the basin area is km2. (In integer)
Correct Answer: 50
Solution and Explanation
To find the basin area given a fourth-order drainage basin's stream lengths and drainage density, we use the formula for drainage density (D) which is defined as the total length of streams (Ltotal) per unit area (A) of the basin: D = Ltotal/A. We are given D = 0.5 km-1.
First, calculate Ltotal by summing the lengths of streams of all orders: Ltotal = 10.5 km + 7.5 km + 5.5 km + 1.5 km = 25 km.
Using the formula, rearrange for A: A = Ltotal/D = 25 km / 0.5 km-1 = 50 km2.
Thus, the basin area is 50 km2.
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