Rainwater Harvesting Model?

📌 CONCEPT: The rainwater harvesting model involves determining the total volume of rainwater collected in a tank over a year, considering the rooftop area, rainfall, and the initial water level in the tank.

📐 RULE / FORMULA: To calculate the volume of rainwater collected, we can use the formula V = ∫[0, t] (r x A x η) dt, where V is the volume of rainwater collected, r is the average annual rainfall, A is the area of the rooftop contributing to rainwater collection, η is the efficiency of rainwater collection (25% in this case), and t is the time period (1 year).

💡 WORKED EXAMPLE: Given r = 1,000 mm = 1 m, A = 500,000 sq. m x 0.25 = 125,000 sq. m, and initial water level h = 5 m, we want to find the volume of rainwater collected over 1 year. We can rewrite the formula as V = ∫[0, 365] 1 x 125,000 x 1 dt, which simplifies to V = 125,000 x 365 = 45,625,000 cubic meters.

⚠️ COMMON MISTAKE: Students may forget to consider the initial water level in the tank when calculating the total volume of rainwater collected, or they may not account for the efficiency of rainwater collection.