Water Pressure to Flow Rate Calculator
Enter the gauge pressure at the source.
The internal diameter of the opening where water exits.
0.62 – Sharp Edged Orifice (Default)
0.80 – Short Tube
0.98 – Smooth Nozzle/Rounded
0.60 – Rough Opening
Select the type of opening. Use 0.62 for standard holes, 0.98 for smooth nozzles.
Calculation Results
Flow Rate (GPM):
–
Flow Rate (LPM):
–
Water Velocity:
–
Opening Area:
–
How to Calculate Water Flow Rate from Pressure
Understanding the relationship between water pressure and flow rate is essential for plumbing, irrigation, and fluid dynamics engineering. While pressure (PSI) and flow rate (GPM) are distinct measurements, they are physically related through the area of the pipe or opening the water flows through.
This calculator estimates the potential flow rate of water through an opening based on Torricelli's Law and Bernoulli's Principle. It assumes the water is exiting from a pressurized environment into the open atmosphere.
Note: Static pressure (when water is not moving) is different from dynamic pressure. This calculator estimates the maximum flow through an orifice given a specific pressure differential.
The Physics Formula
To calculate the flow rate ($Q$) from pressure ($P$), we typically use a derived formula involving the area of the opening ($A$) and a discharge coefficient ($C_d$):
Step 1: Calculate Velocity ($v$)
The theoretical velocity of water exiting a pressurized vessel is calculated as:
v = √(2 × P / ρ)
- P: Pressure in Pascals (Pa)
- ρ (Rho): Density of water (approx. 1000 kg/m³)
Step 2: Calculate Flow Rate ($Q$)
Once velocity is known, flow rate is determined by the size of the opening and its efficiency:
Q = C_d × A × v
- C_d: Discharge Coefficient (accounts for friction and turbulence, typically 0.60 to 0.98).
- A: Cross-sectional area of the opening.
Understanding Inputs
- Pressure (PSI): Pounds per Square Inch. Common household pressure ranges from 40 to 60 PSI.
- Diameter (Inches): The internal diameter of the pipe, nozzle, or hole. Even a small increase in diameter significantly increases flow because area increases with the square of the radius.
- Discharge Coefficient: This represents efficiency. A sharp-edged hole creates turbulence (reducing flow to ~62%), while a smooth, rounded nozzle allows nearly 98% efficiency.
Example Calculation
If you have a garden hose spigot with a pressure of 50 PSI and an opening diameter of 0.5 inches:
- 50 PSI converts to approx. 344,738 Pascals.
- Theoretical velocity ≈ 26.2 meters/second.
- A 0.5-inch diameter has an area of roughly 0.000127 square meters.
- Assuming a standard orifice coefficient of 0.62, the flow rate would be approximately 19.9 GPM.
Factors That Reduce Flow
In real-world piping systems, the flow rate calculated above is a theoretical maximum at the point of discharge. Actual flow is often lower due to:
- Friction Loss: Long pipes reduce pressure significantly over distance.
- Elevation: Pushing water uphill reduces pressure (0.433 PSI loss per foot of elevation).
- Fittings: Elbows, valves, and tees add resistance.