Poiseuille's Law Calculator
Calculate laminar flow rate and resistance in cylindrical pipes using Hagen-Poiseuille equation
Calculate Laminar Flow Parameters
Fluid viscosity (water ≈ 0.001 Pa⋅s at 20°C)
Internal radius of the pipe (diameter ÷ 2)
Total length of the pipe
Pressure difference between pipe ends (p₁ - p₂)
Poiseuille's Law Results
Volumetric Flow Rate (Q)
Flow Resistance (R)
Poiseuille's equation: Q = (π × Δp × r⁴) / (8 × μ × l)
Resistance equation: R = (8 × μ × l) / (π × r⁴)
Flow type: Laminar flow in cylindrical pipes
Flow Analysis
Example Calculation
Water Flow in Garden Hose
Fluid: Water at 20°C (μ = 0.001 Pa⋅s)
Hose radius: 6 mm = 0.006 m
Hose length: 15 m
Pressure difference: 2 bar = 200,000 Pa
Calculation
Q = (π × 200,000 × (0.006)⁴) / (8 × 0.001 × 15)
Q = (π × 200,000 × 1.296×10⁻⁹) / (0.12)
Q = 8.146×10⁻⁴ / 0.12
Q = 6.79×10⁻³ m³/s = 6.79 L/s
Common Fluid Viscosities
Applications
Blood flow in blood vessels and cardiovascular studies
Airflow resistance in respiratory system analysis
Pipe flow calculations in plumbing systems
Engine design and lubrication systems
Microfluidics and lab-on-chip devices
Understanding Poiseuille's Law
What is Poiseuille's Law?
Poiseuille's Law, also known as the Hagen-Poiseuille equation, describes the laminar flow of an incompressible Newtonian fluid through a long cylindrical pipe with constant cross-section. It relates the volumetric flow rate to the pressure difference, pipe geometry, and fluid properties.
Key Assumptions
- •Steady, laminar flow (Reynolds number < 2300)
- •Incompressible Newtonian fluid
- •Rigid, straight, cylindrical pipe
- •No-slip boundary condition at pipe walls
Mathematical Equations
Q = (π × Δp × r⁴) / (8 × μ × l)
R = (8 × μ × l) / (π × r⁴)
- Q: Volumetric flow rate (m³/s)
- Δp: Pressure difference (Pa)
- r: Pipe radius (m)
- μ: Dynamic viscosity (Pa⋅s)
- l: Pipe length (m)
- R: Flow resistance (Pa⋅s/m³)
Note: Flow rate is proportional to r⁴, so small changes in radius have dramatic effects on flow rate.