The Correct Answer and Explanation is:
Correct Answer: 2.2 MGD
To convert 3.4 cubic feet per second (cfs) to million gallons per day (MGD), a series of unit conversions must be performed. The goal is to change the volume unit from cubic feet to gallons and the time unit from seconds to days, while also accounting for the “million” in MGD.
First, we need the conversion factor between cubic feet and gallons. One cubic foot is equivalent to approximately 7.48 U.S. gallons. We can use this to convert the volume component of the measurement.
Next, we must convert the time component from seconds to days. There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day. Multiplying these together gives the total number of seconds in one day: 60 x 60 x 24 = 86,400 seconds per day.
Now we can set up the calculation using dimensional analysis to ensure the units cancel correctly. We start with the given value of 3.4 cfs:
(3.4 ft³/sec) × (7.48 gal / 1 ft³) × (86,400 sec / 1 day)
Let’s calculate this step by step. First, convert cubic feet per second to gallons per second:
3.4 ft³/sec × 7.48 gal/ft³ = 25.432 gal/sec
Next, convert gallons per second to gallons per day (GPD):
25.432 gal/sec × 86,400 sec/day = 2,197,324.8 gal/day (GPD)
The final step is to convert gallons per day to million gallons per day (MGD). Since MGD represents millions of gallons, we divide the GPD value by 1,000,000:
2,197,324.8 GPD / 1,000,000 = 2.197 MGD
The original value of 3.4 has two significant figures, so the final answer should be rounded accordingly. Rounding 2.197 to two significant figures gives 2.2. Therefore, 3.4 cfs is equivalent to 2.2 MGD.
