Poiseuille's Equation Calculator

Poiseuille's Equation describes the flow rate of a viscous fluid through a pipe. It is used to calculate the volumetric flow rate (Q) in laminar flow through a cylindrical tube. It’s particularly useful in fluid dynamics, especially for understanding flow in small arteries, veins, or pipe systems where the flow is steady and laminar.

Poiseuille’s Law (Equation):

Where:

• Q = Volumetric flow rate (m³/s or L/s)
• ΔP = Pressure difference between the two ends of the tube (Pa or N/m²)
• r = Radius of the tube (m)
• η = Dynamic viscosity of the fluid (Pa·s or N·s/m²)
• L = Length of the pipe or tube (m)

Explanation of the Terms:

• ΔP (Pressure Difference): This is the difference in pressure between the two ends of the tube. It drives the fluid through the tube.
• r (Radius): The radius of the tube has a significant effect on the flow rate. The flow rate is proportional to the fourth power of the radius, meaning small changes in the radius have a large effect on the flow.
• η (Dynamic Viscosity): Viscosity is a measure of the fluid's resistance to flow. Higher viscosity means the fluid flows more slowly.
• L (Length of the Pipe): The longer the pipe, the greater the resistance to flow, so the flow rate decreases with an increase in the length of the tube.

Units:

• Q (Flow Rate): Typically in m³/s or L/s.
• ΔP (Pressure Difference): In Pa (Pascal), which is equivalent to N/m².
• r (Radius): In meters (m).
• η (Viscosity): In Pa·s (Pascal-seconds) or N·s/m².
• L (Length): In meters (m).

Example Calculation:

Let’s say we have the following parameters for a pipe:

• Pressure difference (ΔP) = 2000 Pa
• Radius (r) = 0.01 m (1 cm)
• Viscosity (η) = 0.001 Pa·s (water at room temperature)
• Length (L) = 1 meter

Using Poiseuille's equation:

Thus, the flow rate is 1.57 L/s.

Additional Notes:

• Laminar Flow: Poiseuille’s law applies to laminar flow, which is smooth and orderly. If the flow becomes turbulent (which typically happens at higher flow rates or larger pipe diameters), Poiseuille's equation doesn't hold.
• Applications: Poiseuille’s Law is commonly used in blood flow calculations, fluid dynamics in pipes, and viscosity measurement.