Water Flow Rate Calculator
Estimate water discharge based on pressure and opening diameter.
The gauge pressure at the opening.
Internal diameter of pipe or nozzle.
0.60 – 0.62 for sharp edges, 0.95 – 0.98 for smooth nozzles.
To calculate total volume.
Calculation Results
Flow Rate (GPM):
–
Flow Rate (Liters/min):
–
Exit Velocity:
–
Total Volume (over 60 mins):
–
How to Calculate Water Flow Rate Using Pressure
Determining the flow rate of water through a pipe, nozzle, or leak based purely on pressure is a common task in plumbing, irrigation, and engineering. The relationship between pressure and flow rate is governed by fundamental fluid dynamics, specifically derived from Bernoulli's principle.
The Physics: Bernoulli and Torricelli
When water exits a pressurized system through an orifice (an opening), pressure energy is converted into kinetic energy (velocity). The theoretical velocity of the water exiting the opening can be calculated using Torricelli's Law:
v = √(2 * P / ρ)
Where:
v = Velocity of the fluid
P = Pressure (in Pascals)
ρ = Density of water (approx. 1000 kg/m³)
The Flow Rate Formula
To find the volumetric flow rate (Q), we multiply the velocity by the cross-sectional area of the opening (A), and apply a Discharge Coefficient (Cd). The Cd accounts for real-world friction and turbulence that slows the water down compared to the theoretical ideal.
Q = Cd * A * √(2 * P / ρ)
Understanding the Inputs
- Water Pressure (PSI): This is the static pressure measured by a gauge near the opening. Higher pressure forces water out faster.
- Opening Diameter: The size of the hole. Even small increases in diameter dramatically increase flow because Area is a function of the radius squared (A = πr²).
- Discharge Coefficient (Cd): This is an efficiency factor.
- Use 0.60 – 0.62 for a sharp-edged hole (like a drilled hole in a tank or a burst pipe).
- Use 0.80 – 0.85 for a short tube.
- Use 0.95 – 0.98 for a smooth, well-designed nozzle (like a fire hose nozzle).
Example Calculation
Let's calculate the flow rate for a standard garden hose spigot with a pressure of 50 PSI and an opening diameter of 0.5 inches.
- Convert Pressure: 50 PSI ≈ 344,738 Pascals.
- Convert Diameter: 0.5 inches = 0.0127 meters. Radius = 0.00635 m.
- Calculate Area: A = π * (0.00635)² ≈ 0.0001267 m².
- Ideal Velocity: √(2 * 344738 / 1000) ≈ 26.26 m/s.
- Apply Cd (0.62): Real Velocity ≈ 16.28 m/s.
- Flow Rate: 16.28 * 0.0001267 ≈ 0.00206 m³/s.
- Convert to GPM: 0.00206 m³/s ≈ 32.6 GPM.
Note: This calculation assumes free discharge into the atmosphere. If the water is flowing into another pressurized pipe, you must use the pressure difference (ΔP) between the two points.