Flow Rate Calculator from Pressure
Calculate fluid flow rate based on differential pressure, pipe diameter, and fluid density.
PSI
Bar
kPa
Pa
Pressure drop across the orifice or nozzle.
mm
in
Internal diameter of the flow opening.
Water ≈ 1000, Gasoline ≈ 740, Air ≈ 1.225.
Typically 0.60 to 0.98. Use 0.61 for sharp-edged orifice.
Calculation Results
Flow Rate (Gallons/min):
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Flow Rate (Liters/min):
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Flow Rate (m³/hour):
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Flow Velocity:
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Understanding Flow Rate from Pressure
In fluid dynamics, the relationship between flow rate and pressure is fundamental to engineering tasks ranging from irrigation system design to industrial pipe sizing. Calculating the flow rate ($Q$) based on a known pressure drop ($P$) typically involves applying Bernoulli's principle or specific equations derived for orifices and nozzles.
This calculator assumes you are measuring the flow through a restriction (like an orifice plate, nozzle, or a leak in a tank) where the pressure difference drives the fluid through the opening.
The Flow Rate Formula
The calculation utilizes the standard orifice equation derived from Torricelli's law. The formula used to determine the flow rate is:
Q = Cd × A × √(2 × ΔP / ρ)
Where:
- Q = Volumetric Flow Rate (m³/s)
- Cd = Discharge Coefficient (dimensionless). This accounts for energy losses and the contraction of the jet stream. A sharp-edged orifice typically has a $C_d$ of roughly 0.60–0.62.
- A = Cross-sectional Area of the opening (m²)
- ΔP = Differential Pressure or Pressure Drop (Pascals). This is the pressure forcing the fluid through.
- ρ (rho) = Fluid Density (kg/m³). For example, water is approximately 1000 kg/m³.
Key Inputs Explained
To get an accurate result, understanding your inputs is crucial:
- Pressure (Differential): This is not necessarily the absolute pressure in the pipe, but the difference in pressure between the upstream side and the downstream side. If a tank is venting to the atmosphere, the differential pressure is the gauge pressure inside the tank.
- Fluid Density: Heavier fluids (like mercury) flow slower than lighter fluids (like gasoline) under the same pressure. Temperature changes can affect density, but standard values are sufficient for estimation.
- Discharge Coefficient ($C_d$): This is an efficiency factor. In a perfect world, $C_d$ would be 1.0. However, due to turbulence and friction, real-world flow is less.
Common values: Sharp orifice = 0.61, Venturi nozzle = ~0.98.
Example Calculation
Imagine you have a water tank with a hole near the bottom. The pressure gauge reads 50 PSI. The hole diameter is 25mm.
- Convert Units: 50 PSI ≈ 344,738 Pascals. 25mm = 0.025 meters. Density of water = 1000 kg/m³.
- Calculate Area: $A = \pi \times (0.0125)^2 \approx 0.0004909 \text{ m}^2$.
- Apply Formula: Assuming $C_d = 0.61$.
$v = \sqrt{(2 \times 344738) / 1000} \approx 26.25 \text{ m/s}$
$Q = 0.61 \times 0.0004909 \times 26.25 \approx 0.00786 \text{ m}^3/\text{s}$ - Result: Convert $0.00786 \text{ m}^3/\text{s}$ to Liters/min $\approx 471 \text{ L/min}$.