Average filtration rate Windex of an area is given by _______ where P = Total precipitation, Q=Total runoff, tr = duration of rainfall in hours
- A(P-Q) / trCorrect
- B(P+Q) / tr
- CP/ tr
- DQ/ tr
Solution
Concept
The W-index is the average infiltration rate during the entire period of a storm. It represents the water that enters the soil instead of flowing over the surface.
Formula
W-index = (P - Q) / tr
Step-by-step solution
1. Identify the given symbols: P is the total precipitation (rainfall), Q is the total runoff (water that flows into rivers), and tr is the total duration of rainfall in hours. 2. Understand that the difference (P - Q) represents the total amount of water that soaked into the ground (infiltration) plus any initial losses. 3. To find the average rate, divide this total loss (P - Q) by the total time (tr). 4. The formula becomes: W-index = (P - Q) / tr. Answer: (A) (P-Q) / tr
Explanation
The W-index calculates the average infiltration by subtracting the runoff from the total rainfall and dividing it by the storm duration. It includes initial losses like interception and depression storage. This index is used to estimate how much water will reach the ground surface during a storm.
Why the other options are wrong
B: Adding P and Q is physically incorrect as runoff comes out of precipitation. C: This gives the average rainfall intensity, not the infiltration rate. D: This gives the average runoff rate, not the infiltration rate.
Shortcut
W for 'Whole' duration. It uses the total time 'tr', unlike the Phi-index which only uses the time of excess rainfall.
Common mistake
Students often confuse W-index with Phi-index (φ-index), which only considers the period when rainfall intensity is greater than the infiltration rate.
Correct answer: A) (P-Q) / tr