Question

The approximate relationship between Sediment Delivery Ratio (SDR) and drainage area (A) shows that SDR varies

• A. directly with \(A^{0.2}\)
• B. inversely with \(A^{0.2}\)
• C. directly with A
• D. inversely with A

Answer 1

The Correct Option is B

The Sediment Delivery Ratio (SDR) is an important concept in soil and water conservation engineering. It represents the proportion of eroded soil that is actually delivered to a specific location, typically the outlet of a watershed.

The relationship between SDR and drainage area (A) is generally observed to be inverse, meaning that as the drainage area increases, the SDR decreases. This inverse relationship is often expressed through empirical equations.

Let's analyze the options provided and identify the correct relationship:

1. \(\text{SDR varies directly with } A^{0.2}\): This suggests that SDR increases with the power of the drainage area, which does not align with common empirical observations.
2. \(\text{SDR varies inversely with } A^{0.2}\): This fits the typical inverse relationship between SDR and drainage area. As the drainage area increases, the SDR decreases, which is consistent with empirical findings.
3. \(\text{SDR varies directly with } A\): This suggests a linear relationship where SDR increases with the drainage area, which is contrary to observed data.
4. \(\text{SDR varies inversely with } A\): This suggests a simple inverse relationship, which is plausible, but the question specifically asks about the power relationship.

Therefore, the correct answer is that SDR varies inversely with \(A^{0.2}\). This implies that as the drainage area becomes larger, the capacity of sediment to reach the outlet decreases due to factors such as sediment deposition along the way and variance in flow paths.