A small family home in Tucson, Arizona, has a rooftop area of 1967 square feet, and it is possible to capture rain falling on about 56% of the roof. A typical annual rainfall is about 14 inches. If the family wanted to install a tank to capture the rain for an entire year, without using any of it, what would be the required volume of the tank in m^3 and in gallons? How much would the water weigh when the tank was full (in N and in lbf)?
To find the required volume of the tank in m^3 and in gallons, we need to calculate the amount of rainwater that can be captured from the roof in one year.
First, let's calculate the area of the roof that can capture rain:
Area of the roof = Rooftop area * Percentage of roof capturing rain
= 1967 square feet * 0.56
= 1099.52 square feet
Next, we need to convert the area to square meters (since m^3 is the unit for volume in the metric system):
1 square foot = 0.092903 square meters
Area of the roof in square meters = Area of the roof in square feet * 0.092903
= 1099.52 square feet * 0.092903
= 102.19 square meters
Now, let's calculate the volume of rainwater that can be captured in one year:
Volume of rainwater = Area of the roof * Rainfall
= 102.19 square meters * 0.3556 meters (convert 14 inches to meters)
= 36.36 cubic meters
To convert the volume to gallons, we can use the conversion factor:
1 cubic meter = 264.172 gallons
Volume of rainwater in gallons = Volume of rainwater in cubic meters * 264.172
= 36.36 cubic meters * 264.172
= 9597.86 gallons (approximately)
To calculate the weight of the water when the tank is full, we need to know the density of water. The density of water is approximately 1000 kg/m^3.
Weight of water in newtons (N) = Volume of water in cubic meters * Density of water
= 36.36 cubic meters * 1000 kg/m^3
= 36,360 kg
To convert the weight from kilograms to newtons, we can use the conversion factor:
1 kilogram = 9.81 newtons
Weight of water in newtons = Weight of water in kg * 9.81
= 36,360 kg * 9.81
= 357,013.60 newtons (approximately)
To convert the weight of water to pounds-force (lbf), we can use the conversion factor:
1 newton = 0.224809 lbf
Weight of water in pounds-force (lbf) = Weight of water in newtons * 0.224809
= 357,013.60 newtons * 0.224809
= 80,266.40 lbf (approximately)
Therefore, the required volume of the tank would be approximately 36.36 cubic meters or 9,597.86 gallons. When the tank is full, the water would weigh approximately 357,013.60 newtons or 80,266.40 pounds-force.