Pressure vs Flow Rate Calculator
Orifice and Pipe Flow Fluid Dynamics
Understanding the Relationship Between Pressure and Flow
In fluid dynamics, the relationship between pressure and flow rate is fundamental to engineering tasks ranging from plumbing to industrial chemical processing. This calculator utilizes Bernoulli's Principle and the orifice flow equation to determine how fluid behaves as it passes through a restriction.
The Mathematics: Orifice Flow Equation
The flow of a fluid through an orifice is not linear; it is a square-root relationship. The standard formula used by this calculator is:
Q = Cd × A × √(2 × ΔP / ρ)
- Q: Volumetric flow rate
- Cd: Discharge coefficient (accounts for friction and turbulence)
- A: Cross-sectional area of the opening
- ΔP: Pressure difference (Differential Pressure)
- ρ (rho): Fluid density
Key Factors Influencing Results
1. The Square Root Law: Because flow is proportional to the square root of pressure, doubling your pressure does not double your flow. To double the flow rate, you actually need to quadruple the pressure (assuming the orifice size remains constant).
2. Discharge Coefficient (Cd): This is a dimensionless number that characterizes the efficiency of the flow. A sharp-edged orifice typically has a Cd of around 0.61, whereas a smooth, tapered nozzle can reach up to 0.98.
3. Fluid Density: Heavier fluids (higher density) require more pressure to achieve the same flow rate as lighter fluids.
Practical Example
If you have a water pipe with a 10mm opening and a pressure of 3 Bar, what is the flow? Using a standard Cd of 0.61 for water (1000 kg/m³):
- Pressure in Pascals: 300,000 Pa
- Area: ~0.0000785 m²
- Result: Approx 1.17 Liters per second (~70 L/min).
If you wanted to increase that flow to 140 L/min (double), you would need to increase the pressure to 12 Bar (four times the original pressure).