Flow Rate Basics - Q = A × V
The fundamental flow rate equation says that flow (Q) equals the cross-sectional area of the channel or pipe (A) multiplied by the velocity of the water moving through it (V). This equation shows up for pipe sizing, channel capacity, and verifying whether a flow meter is reading correctly.
| Q | Flow rate | Result in cubic feet per second (CFS) when using ft² and ft/s |
| A | Cross-sectional area | Square feet - depends on shape (rectangle, circle, etc.) |
| V | Velocity | Feet per second - how fast the water moves through that area |
Once you have CFS, you can convert to the units you actually need:
- CFS × 448.8 = GPM (gallons per minute)
- CFS ÷ 1.547 = MGD (million gallons per day)
- GPM × 0.00144 = MGD
Live Q = AV Calculator
⚙ Flow Rate from Area × Velocity
Flow Unit Conversion Calculator
Flow rate conversions are everywhere on the exam. Enter any value in any unit and get all equivalents instantly.
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Three Worked Examples
Q = A × V = 6 ft² × 1.5 ft/s = 9 CFS
GPM = 9 × 448.8 = 4,039.2 GPM
MGD = 9 ÷ 1.547 = 5.818 MGD
Area = 0.785 × D² = 0.785 × (1)² = 0.785 ft²
Q = A × V = 0.785 × 2 = 1.57 CFS
GPM = 1.57 × 448.8 = 704.6 GPM
MGD = 1.57 ÷ 1.547 = 1.015 MGD
CFS = 500 GPM ÷ 448.8 = 1.114 CFS
500 GPM = 0.720 MGD = 1.114 CFS
Common Exam Questions About Flow Rate
"A rectangular channel is X ft wide with Y ft depth and Z ft/s velocity. What is the flow in MGD?" - Classic Q = AV problem. Calculate area, multiply by velocity to get CFS, then convert.
"Convert X GPM to MGD" - These are pure unit conversion questions. Memorize: GPM × 0.00144 = MGD, and CFS × 448.8 = GPM. These come up constantly.
Watch for diameter vs. radius in pipe problems. A 12-inch pipe has a 6-inch (0.5 ft) radius but a 1 ft diameter. The area formula using diameter is A = 0.785 × D². Using the wrong number here is the most common mistake.
"A plant treats X MGD. The daily pump run time is Y hours. What is the average pump rate in GPM?" - Divide by time, convert units: (X MGD × 1,000,000) ÷ (Y hours × 60 min/hr) = GPM.
Flow Rate Problems Tripping You Up? Ask Randy.
Randy can give you unlimited flow rate practice problems, explain why the conversions work, and quiz you on the specific question types that appear on your state's exam.
Unit Conversion Trap: Flow rate questions hide conversions everywhere. A problem might give you feet per second but ask for MGD. Always check: what units am I given? What units does the formula need? Write the conversion factor down before calculating.