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Answer :
Final answer:
A) The volume of runoff from the shed after a rainstorm of 2 inches of rain is approximately 33.34 cubic feet or 4.46 gallons.
B) The velocity of water flowing out of a 6-inch pipe with a flow rate of 5 ft3/s is approximately 25.47 ft/s. If you double the diameter of the pipe, the velocity decreases to approximately 6.37 ft/s.
Explanation:
A) Volume of Runoff
To calculate the volume of runoff from the shed, we need to multiply the area of the shed by the depth of the rain. The area of the shed is given as 10 feet by 20 feet, which gives us a total area of 200 square feet. The depth of the rain is given as 2 inches, which is equivalent to 2/12 = 0.1667 feet.
Using the formula for the volume of a rectangular prism (length x width x height), we can calculate the volume of the runoff:
Volume = 10 feet x 20 feet x 0.1667 feet = 33.34 cubic feet
To convert the volume from cubic feet to gallons, we can multiply by the conversion factor 0.1337:
Volume in gallons = 33.34 cubic feet x 0.1337 = 4.46 gallons
B) Velocity of Water Flow
To calculate the velocity of water flowing out of the pipe, we can use the equation Q = A x V, where Q is the flow rate, A is the cross-sectional area of the pipe, and V is the velocity.
For the given flow rate of 5 ft3/s, we can rearrange the equation to solve for the velocity:
V = Q / A
The cross-sectional area of a pipe can be calculated using the formula A = πr^2, where r is the radius of the pipe. Since the diameter of the pipe is given as 6 inches, the radius is half of that, or 3 inches. Converting the radius to feet, we get 3/12 = 0.25 feet.
Using the formula for the cross-sectional area of a pipe, we can calculate the area:
A = π(0.25 feet)^2 = 0.1963 square feet
Substituting the values into the equation for velocity, we get:
V = 5 ft3/s / 0.1963 square feet = 25.47 ft/s
If we double the diameter of the pipe, the radius will also double, resulting in a new radius of 6 inches or 0.5 feet. Using the formula for the cross-sectional area of a pipe, we can calculate the new area:
A = π(0.5 feet)^2 = 0.7854 square feet
Substituting the new area into the equation for velocity, we get:
V = 5 ft3/s / 0.7854 square feet = 6.37 ft/s
Therefore, doubling the diameter of the pipe decreases the velocity of the water flow by a factor of four.
Learn more about calculating volume of runoff and velocity of water flow here:
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