Hydraulic engineers in the United States often use, as a units of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre (where 1 acre = 43560 ft2) of land to a depth of 1 ft. A severe thunderstorm dumped 2.6 in. of rain in 30 min on a town of area 39 km2. What volume of water, in acre-feet, fell on the town? can any one help.
106984.8
To find the volume of water that fell on the town in acre-feet, we can follow these steps:
Step 1: Convert the area of the town from square kilometers to square feet.
Since 1 km^2 = 1,000,000 m^2 and 1 m^2 = 10.764 ft^2, we have:
Area of the town in square feet = 39 km^2 * 1,000,000 m^2/km^2 * 10.764 ft^2/m^2
Step 2: Convert the depth of rainfall from inches to feet.
Since 1 ft = 12 in, we have:
Depth of rainfall in feet = 2.6 in * 1 ft/12 in
Step 3: Calculate the volume of water in cubic feet.
Volume of water in cubic feet = Area of the town in square feet * Depth of rainfall in feet
Step 4: Convert the volume of water from cubic feet to acre-feet.
Since 1 acre-foot = 43,560 ft^3, we have:
Volume of water in acre-feet = Volume of water in cubic feet / 43,560 ft^3/acre-foot
Let's calculate the volume of water that fell on the town using these steps.
Step 1: Convert the area of the town from square kilometers to square feet.
Area of the town in square feet = 39 km^2 * 1,000,000 m^2/km^2 * 10.764 ft^2/m^2
Area of the town in square feet = 42,335,604 ft^2 (rounded to the nearest whole number)
Step 2: Convert the depth of rainfall from inches to feet.
Depth of rainfall in feet = 2.6 in * 1 ft/12 in
Depth of rainfall in feet = 0.21667 ft (rounded to 5 decimal places)
Step 3: Calculate the volume of water in cubic feet.
Volume of water in cubic feet = Area of the town in square feet * Depth of rainfall in feet
Volume of water in cubic feet = 42,335,604 ft^2 * 0.21667 ft
Volume of water in cubic feet = 9,170,914.77 ft^3 (rounded to 2 decimal places)
Step 4: Convert the volume of water from cubic feet to acre-feet.
Volume of water in acre-feet = Volume of water in cubic feet / 43,560 ft^3/acre-foot
Volume of water in acre-feet = 9,170,914.77 ft^3 / 43,560 ft^3/acre-foot
Volume of water in acre-feet = 210.41 acre-feet (rounded to 2 decimal places)
Therefore, approximately 210.41 acre-feet of water fell on the town during the severe thunderstorm.