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How many gallons of rainwater are collected at a rate of one inch per hour on a ten foot by twenty foot roof at forty-five degree angle?
Wiki User
∙ 15y ago
Basic geomentry provides the following: The shape of the roof defines a right triangle with opposite angles being 45 degrees and therefore opposite sides must be equal in length. Knowing this and the basic Pythagorean theorem that a2 + b2 = c2 and a must equal b in our example, yields the substitution of a2 + a2 = c2 cbeing 10 feet in our example yields 2a2 = 100 feet a2 = 50 feet a = SquareRoot of 50 feet a = 7.07 feet Assuming that the horizontal dimension is the larger value (20 feet), the roof has the effective dimension of 7.07 feet by 20 feet or 141.4 square feet. Multiply by 144 (number of square inches per square foot) yields 20,361.6 square inches Mulitply by 1 inch of rainfall per hour yields 20,361.6 cubic inches of rain per hour Divide 20,361.6 by 231 (cubic inches per gallon) yeilds 88.145 gallons per hour Note: This is a theoretical maximum, the actual accumulation will be slightly less due to the amount needed make the roof surface "wet" before runoff begins. Also, rain drops splatter at this rate and there will be a modest loss around the edges of the roof that will reduce the total runoff. At this rate of rainfall, it will take about 11 hours and 21 minutes to collect 1,000 gallons of water.
Wiki User
∙ 15y ago
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