To find the flow rate in gallons per minute (gpm) that the drainage system must achieve, we need to convert the given specifications into a consistent unit and then calculate the flow rate.
First, let's convert the 40-acre field area into square feet, as most drainage systems are designed in terms of square footage:
1 acre = 43,560 square feet
So, 40 acres = 40 * 43,560 = 1,742,400 square feet.
Next, we need to convert the depth of standing water to the same unit. Since 1 inch is equivalent to 0.0833 feet, the standing water depth of 3/8 inch is:
(3/8) * 0.0833 = 0.03125 feet.
Now, we can calculate the volume of water that needs to be removed from the field:
Volume = Area * Depth
= 1,742,400 square feet * 0.03125 feet
= 54,450 cubic feet.
To convert cubic feet to gallons, we need to know that 1 cubic foot is equal to 7.48052 gallons. So, the volume in gallons is:
54,450 cubic feet * 7.48052 gallons/cubic foot = 406,581.366 gallons.
Since we want to remove this volume of water in 24 hours (1 day), the flow rate required would be:
Flow rate = Volume / Time
= 406,581.366 gallons / 24 hours
= 16,941.724 gallons per hour.
To convert the flow rate to gallons per minute, divide this by 60:
Flow rate = 16,941.724 gallons per hour / 60
= 282.362 gpm (rounded to three decimal places).
Therefore, the drainage system must achieve a flow rate of approximately 282.362 gpm to meet the design specification.