Flow Rate Formula:
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Definition: This calculator computes the volumetric flow rate of a fluid through a pipe using the Hagen-Poiseuille equation.
Purpose: It helps engineers and scientists determine fluid flow rates in pipes under pressure differences, useful in hydraulic systems, medical applications, and industrial processes.
The calculator uses the Hagen-Poiseuille equation:
Where:
Explanation: The flow rate is directly proportional to the pressure difference and the fourth power of the radius, and inversely proportional to viscosity and pipe length.
Details: Accurate flow rate calculations are essential for designing efficient fluid transport systems, predicting flow behavior, and ensuring proper system operation.
Tips: Enter the pipe radius (in meters), pressure difference (in Pascals), fluid viscosity (default 0.001 Pa·s for water at 20°C), and pipe length (default 1 meter). All values must be > 0.
Q1: What fluids does this equation apply to?
A: The Hagen-Poiseuille equation applies to Newtonian fluids in laminar flow through cylindrical pipes.
Q2: Why does radius have such a large effect (r⁴)?
A: The r⁴ relationship means small changes in pipe diameter dramatically affect flow rate due to reduced friction near the pipe walls.
Q3: What's a typical viscosity value for water?
A: Water at 20°C has a viscosity of about 0.001 Pa·s. Viscosity decreases with temperature.
Q4: What are the limitations of this equation?
A: It assumes steady, laminar flow of incompressible Newtonian fluids in straight, rigid pipes with no slip at walls.
Q5: How do I convert the result to other units?
A: 1 m³/s = 1000 L/s = 15850 gpm (gallons per minute). For different units, use appropriate conversion factors.