Question

In a drainage basin, the number of the 1st, 2nd, 3rd, 4th and 5th order streams are 240, 40, 8, 2 and 1, respectively. The average of all calculated bifurcation ratios is ............... [round off to 2 decimal places]

Hint:

In stream ordering problems, always use Horton's law of stream numbers: \(R_b = N_u / N_{u+1}\). The average is taken over all successive pairs of stream orders.

Answer 1

Step 1: Formula for bifurcation ratio.
Bifurcation ratio (\(R_b\)) between two successive orders is defined as: \[ R_b = \frac{N_u}{N_{u+1}} \] where \(N_u\) = number of streams of order \(u\), \(N_{u+1}\) = number of streams of next higher order.

Step 2: Calculate bifurcation ratios for each successive pair.
- Between 1st and 2nd order: \[ R_b = \frac{240}{40} = 6 \] - Between 2nd and 3rd order: \[ R_b = \frac{40}{8} = 5 \] - Between 3rd and 4th order: \[ R_b = \frac{8}{2} = 4 \] - Between 4th and 5th order: \[ R_b = \frac{2}{1} = 2 \]

Step 3: Find average bifurcation ratio.
\[ \text{Average } R_b = \frac{6 + 5 + 4 + 2}{4} = \frac{17}{4} = 4.25 \]

Step 4: Round off to 2 decimal places.
\[ R_b = 4.25 \]

Final Answer: \[ \boxed{4.25} \]