Created By : Naaz Fatima

Reviewed By : Phani Ponnapalli

Last Updated : May 18, 2023

The Hagen-law Poiseuille's Calculator is a multi-tasking instrument for calculating not just laminar flow rate in a long, cylindrical pipe with the constant cross-sectional area, but also fluid/airway resistance and pressure change.

Choose a Calculation
Dynamic viscosity (μ):
Radius of the pipe (r):
Length of the pipe (l):
Pressure change (Δp):

What is Poiseuille's Equation?

Poiseuille's equation is also called as the Hagen-Poiseuille Law. In fluid dynamics computations, the Hagen-Poiseuille law is a simple formula. This equation represents the laminar flow in a cylindrical container, or, to put it another way, imagine a straight pipe with water flowing through it.

The Hagen-Poiseuille equation (Poiseuille's law) defines how much water flows through the pipe in one second, based on

  • The viscosity of the fluid (its thickness and ability to travel against the friction of the pipe walls);
  • The length of the pipe.
  • The radius (or diameter) of the pipe.
  • The differential in pressure between the pipe's beginning and end.

Poiseuille Flow Equation

The equation for Poiseuille Flow is given by the formula Q = (π * Δp * r4) / ( 8 * μ * l)

  • Where, Q - Flow rate (m³/s);
  • π - Our famous and beloved constant pi, equals to 3.14159
  • μ - Dynamic viscosity (Pa * s)
  • r - Radius of the pipe
  • l - Length of the pipe and
  • Δp - Pressure change (Pa).

Hagen-Poiseuille equation for flow resistance is given by R = (8 * μ * l)/ (π * r4)

  • Where:
  • R - Resistance (Pa * s/ m³);
  • π - Our famous and beloved constant pi, equals to 3.14159...;
  • μ - Dynamic viscosity (Pa * s);
  • r - Radius of the pipe; and
  • l - Length of the pipe.


For more concepts check out to get quick answers by using this free tool.

Applications of the Poiseuille Flow Equation

Now that we know what Poiseuille's equation is, we need to find out when we'll need to utilise it.

  • This equation can be used to estimate blood flow in blood vessels and to describe many fluid-related processes in the human body (in which case Poiseuille's law works as a blood flow equation).
  • It can be used to calculate the resistance to airflow in human airways. This is extremely significant in asthma and COPD studies.
  • The work of the kidney and the pressure in tubules and glomeruli are also described using Poiseuille's flow equation.
  • The equation of Poiseulle's law proved crucial in the development of artificial kidneys and hemodialysis devices.
  • The Hagen-Poiseuille equation can also be applied to engine design.

How to use Poiseuille's Law Calculator?

Only four simple steps are required to use our Poiseuille's equation calculator (or three if you want to calculate flow resistance)

  • Step 1: Enter the dynamic viscosity (μ, /mi/)
  • Step 2: Pa * s is its fundamental unit. Check the pressure converter for different pressures.
  • Step 3: Enter the pipe's radius, which is equal to half of its diameter.
  • Step 4: Fill in the pipe's length.

Find the pressure difference (only required for the flow rate). If you don't know the pressure change, use the advanced mode button to enter your initial and final pressures, or use the formula below to subtract the final pressure from the start pressure

Change in pressure (Δp) = pressure 1 - pressure 2

Both the flow rate and the resistance will be included in Poiseuille's law calculator's output.

FAQs on Poiseuille Law Calculator

1. What is the formula for Poiseuille's Law?

Q=(P2−P1)πr48ηl is Poiseuille's law for flow in a tube. P2-P1=RQ is the pressure drop induced by flow and resistance.

2. What is the blood flow law of Poiseuille?

The volume flow rate is exactly proportional to the pressure gradient (difference in pressure per length of pipe section that we are studying) and the radius raised to the fourth power, according to Poiseuille's equation. This can lead to problems such as high blood pressure and complications.

3. Where is Poiseuille's law used?

The pressure drop of a constant viscosity fluid flowing laminarly through a rigid pipe can be calculated using Poiseuille's equation.

4. What is the significance of the Hagen Poiseuille law?

Using varying diameters of peripheral and central cannulas, the Hagen–Poiseuille equation can be used to calculate vascular resistance and, as a result, the flow rate of intravenous (IV) fluids.