Flow Rate from PSI Calculator
Estimate water flow rate through an orifice based on pressure and diameter.
Understanding the Relationship Between Flow Rate and PSI
In fluid dynamics, calculating the flow rate from a known pressure (PSI) and orifice size is a fundamental task for engineers, plumbers, and irrigation specialists. This calculator utilizes the orifice flow equation to estimate how much water will pass through a nozzle or opening based on the system pressure.
Pressure acts as the driving force that pushes fluid through an opening. As pressure increases, the velocity of the fluid increases, resulting in a higher flow rate. However, the relationship is not linear; flow rate increases with the square root of the pressure.
The Flow Rate Formula
The standard formula used to calculate water flow rate in Gallons Per Minute (GPM) through an orifice is:
Q = 29.84 × Cd × d² × √P
- Q: Flow Rate in GPM (Gallons Per Minute).
- Cd: Discharge Coefficient (Efficiency of the opening).
- d: Diameter of the orifice in inches.
- P: Pressure in PSI (Pounds per Square Inch).
- 29.84: A constant value combining gravity and unit conversions for water.
What is the Discharge Coefficient (Cd)?
Theoretical flow calculations assume a frictionless environment. In the real world, friction and turbulence reduce the actual flow. The Discharge Coefficient ($C_d$) corrects for these losses.
- 0.95 - 0.98: Smooth, well-rounded nozzles (high efficiency).
- 0.90: Standard spray nozzles.
- 0.80 - 0.82: Short tube orifices.
- 0.60 - 0.61: Sharp-edged orifices (drilled holes in thin plates).
If you are unsure of your specific equipment's efficiency, 0.90 is a safe average for commercial nozzles, while 0.61 is standard for a simple hole drilled in a pipe.
Practical Applications
Irrigation Systems: Determining if a pump provides enough pressure to drive a specific number of sprinkler heads.
Pressure Washing: Calculating the water usage of a pressure washer nozzle based on the machine's PSI rating.
Firefighting: Estimating flow rates from hydrants and hoses to ensure adequate suppression capability.
Example Calculation
Imagine you have a pressure washer running at 2000 PSI with a nozzle tip diameter of 0.05 inches. Assuming a standard nozzle efficiency ($C_d$ = 0.95).
Using the formula:
- Square the diameter: $0.05 \times 0.05 = 0.0025$.
- Square root the pressure: $\sqrt{2000} \approx 44.72$.
- Calculate: $29.84 \times 0.95 \times 0.0025 \times 44.72$.
- Result: Approximately 3.17 GPM.