Poiseuille's Law Calculator

Calculate the volumetric flow rate of a Newtonian fluid through a long cylindrical pipe.

Last updated: March 2026 | By ForgeCalc Engineering

Pressure Difference (ΔP in Pa)

Pipe Radius (r in m)

Dynamic Viscosity (μ in Pa·s)

Pipe Length (L in m)

Volumetric Flow Rate

3.9270e-4

m³/s

What is Poiseuille's Law?

Poiseuille's Law (or the Hagen-Poiseuille equation) describes the relationship between the pressure drop in a fluid flowing through a long cylindrical pipe and the flow rate. It assumes the flow is laminar, the fluid is Newtonian(constant viscosity), and the pipe is much longer than its diameter.

The most striking feature of this law is the fourth-power relationship with the radius. This means that doubling the radius of a pipe increases the flow rate by 16 times, assuming all other factors remain constant. This is why small changes in artery diameter have such a massive impact on blood flow.

How to Calculate Flow Rate

The Hagen-Poiseuille Formula

Q = (π · ΔP · r⁴) / (8 · μ · L)

Q = Volumetric flow rate (m³/s)
ΔP = Pressure difference (Pa)
r = Internal radius of the pipe (m)

μ = Dynamic viscosity (Pa·s)
L = Length of the pipe (m)

Step-by-Step Method

Measure the internal radius of the pipe and the total length.
Determine the pressure difference between the two ends of the pipe.
Find the dynamic viscosity of the fluid at the operating temperature.
Raise the radius to the fourth power (r⁴).
Multiply π, ΔP, and r⁴.
Divide the result by the product of 8, μ, and L.

Example Calculation

Water flowing through a small tube:

Given:

Values:

Radius

0.005 m (5 mm)

Length

2 m

Pressure Diff

500 Pa

Viscosity

0.001 Pa·s

Calculation: Q = (π · 500 · 0.005⁴) / (8 · 0.001 · 2)

Final Answer: The flow rate is 6.1359e-5 m³/s.

Frequently Asked Questions

Does this law apply to gases?

Yes, but only if the gas is flowing at low speeds where it can be considered incompressible and the flow is laminar.

What happens if the flow becomes turbulent?

Poiseuille's Law no longer applies. Turbulent flow has much higher resistance, and the relationship between pressure and flow becomes non-linear.

Why is radius so important?

Because it's raised to the 4th power. A small increase in radius significantly reduces the resistance to flow, allowing much more volume to pass through.