Poiseuille's Law:
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Poiseuille's Law describes the flow rate of a fluid through a cylindrical pipe. It states that the flow rate is proportional to the pressure difference and the fourth power of the radius, and inversely proportional to the viscosity and length of the pipe.
The calculator uses Poiseuille's Law:
Where:
Explanation: The equation shows that flow rate is highly sensitive to changes in pipe radius (r⁴ relationship) and linearly dependent on pressure difference.
Details: Accurate flow rate calculation is essential for designing fluid transport systems, medical applications (blood flow), and industrial processes involving fluid dynamics.
Tips: Enter pressure values in Pascals, radius and length in meters, and viscosity in Pascal-seconds. All values must be positive, with radius, viscosity and length greater than zero.
Q1: What are the assumptions of Poiseuille's Law?
A: The fluid must be Newtonian, incompressible, and laminar flow through a straight, rigid cylindrical pipe with no-slip boundary conditions.
Q2: How does radius affect flow rate?
A: Flow rate is proportional to the fourth power of radius. Doubling the radius increases flow rate by 16 times.
Q3: What is a typical viscosity value for water?
A: At 20°C, water has a viscosity of approximately 0.001 Pa·s (1 centipoise).
Q4: Can this be used for blood flow calculations?
A: While blood is non-Newtonian, Poiseuille's Law provides reasonable approximations for blood flow in larger vessels under certain conditions.
Q5: What are the SI units for flow rate?
A: The SI unit for flow rate is cubic meters per second (m³/s), though liters per second or minute are also commonly used.