Final answer:
To deliver 31 acre-inches of water in 19 hours, a pumping rate of approximately 12.30 cubic feet per second (cfs) is required.
Step-by-step explanation:
To find the pumping rate required to deliver 31 acre-inches of water in 19 hours, we can use a unit conversion process involving flow rate and volume. One acre-inch is the volume of water that covers an acre of area to a depth of one inch. To find the required flow rate in cubic feet per second (cfs), we will first convert the volume in acre-inches to cubic feet and then divide by the time in seconds.
There are 27,154.2 cubic feet in one acre-inch, so for 31 acre-inches:
- Volume in cubic feet = 31 acre-inches × 27,154.2 cubic feet/acre-inch = 841,780.2 cubic feet
There are 3,600 seconds in one hour, so for 19 hours:
- Time in seconds = 19 hours × 3,600 seconds/hour = 68,400 seconds
The pumping rate (Q) in cubic feet per second can then be calculated as follows:
- Q = Volume in cubic feet / Time in seconds
- Q = 841,780.2 cubic feet / 68,400 seconds
- Q ≈ 12.30 cfs
Therefore, a pumping rate of approximately 12.30 cfs is required to deliver 31 acre-inches of water in 19 hours.