Flow Rate Formula (Hagen-Poiseuille Equation):
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Definition: This calculator estimates the volumetric flow rate of water through a pipe using the Hagen-Poiseuille equation.
Purpose: It helps engineers, plumbers, and fluid dynamics researchers determine water flow in cylindrical pipes under laminar flow conditions.
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 prediction ensures proper pipe sizing, efficient system design, and meets water supply requirements.
Tips: Enter pipe radius (in meters), pressure difference (in Pascals), dynamic viscosity (default 0.001002 Pa·s for water at 20°C), and pipe length (in meters). All values must be > 0.
Q1: What flow regime does this equation apply to?
A: The Hagen-Poiseuille equation applies only to laminar (smooth) flow (Re < 2000).
Q2: What's the typical viscosity of water?
A: At 20°C, water has a viscosity of about 0.001002 Pa·s. This decreases with temperature.
Q3: Why is radius to the fourth power?
A: Flow rate is extremely sensitive to pipe diameter because of the parabolic velocity profile in laminar flow.
Q4: Can I use this for turbulent flow?
A: No, for turbulent flow you would need to use the Darcy-Weisbach equation instead.
Q5: How do I convert the result to liters/second?
A: Multiply the result by 1000 (1 m³/s = 1000 L/s).