Flow Rate Viscosity Calculator
Calculate dynamic viscosity using the Hagen-Poiseuille equation for laminar flow.
Calculated Dynamic Viscosity:
0 Pa·s
How to Calculate Viscosity from Flow Rate
In fluid mechanics, the relationship between the flow rate of a liquid and its viscosity is governed by the Hagen-Poiseuille Law. This principle specifically applies to Newtonian fluids undergoing laminar (smooth) flow through a cylindrical pipe with a constant cross-section.
The Hagen-Poiseuille Equation
To find the viscosity, we rearrange the standard flow rate formula. The resulting equation for dynamic viscosity (η) is:
Where:
- η (Eta): Dynamic Viscosity (measured in Pascal-seconds, Pa·s)
- ΔP (Delta P): Pressure difference between the two ends of the pipe (Pascals)
- r: Internal radius of the pipe (meters)
- Q: Volumetric flow rate (cubic meters per second, m³/s)
- L: Total length of the pipe (meters)
Step-by-Step Calculation Example
Imagine you have a fluid flowing through a 2-meter long pipe with a radius of 0.01 meters. If the measured pressure drop is 1000 Pa and the flow rate is 0.0001 m³/s, the calculation would look like this:
- Square the radius to the 4th power: 0.01⁴ = 0.00000001
- Multiply by π (3.14159) and Pressure Drop (1000): 0.00000001 × 3.14159 × 1000 = 0.0000314159
- Calculate the denominator (8 × Q × L): 8 × 0.0001 × 2 = 0.0016
- Divide the results: 0.0000314159 / 0.0016 = 0.0196 Pa·s
Important Considerations
This calculation assumes laminar flow. Laminar flow typically occurs when the Reynolds Number is below 2100. If the flow becomes turbulent (high velocity or low viscosity), this formula will no longer be accurate. Additionally, ensure all units are converted to the International System of Units (SI) before performing the calculation to avoid errors.
Common Viscosity Units
While the standard SI unit is Pa·s, many industries use Centipoise (cP). Note that 1 Pa·s = 1000 cP. Water at room temperature, for instance, has a viscosity of approximately 1 cP (0.001 Pa·s).