Poiseuille Flow Calculator

Formula used

For laminar flow in a circular tube: Q = (π r⁴ ΔP) / (8 μ L).

• v̄ = Q / (π r²) = r² ΔP / (8 μ L)
• vmax = 2 v̄
• τw = (ΔP r) / (2 L)
• Rh = 8 μ L / (π r⁴)
• P = ΔP · Q
• Re = ρ v̄ (2r) / μ (needs ρ)

How to use this calculator

1. Select the variable you want to solve for.
2. Enter the remaining required inputs with units.
3. Optionally add density to compute Reynolds and mass flow.
4. Press Calculate; results appear above the form.
5. Download CSV or PDF using the export buttons.

Professional article

1) What Poiseuille flow describes

Poiseuille flow models steady, fully developed, laminar motion of a Newtonian fluid in a straight circular tube. It links pressure drop, geometry, and viscosity to volumetric flow. Assumptions include no-slip at the wall and negligible entrance effects. Common uses include lab tubing, microfluidics, lubrication passages, and gentle process lines.

2) The key scaling: radius to the fourth power

Radius is the dominant lever. Because flow scales with r⁴, doubling radius increases flow sixteenfold for the same ΔP, L, and μ. Small deposits that reduce radius can therefore demand much higher pressure, especially in microchannels. Even minor diameter tolerances change results significantly today.

3) Viscosity and temperature sensitivity

Dynamic viscosity μ reflects internal friction and varies strongly with temperature. Water near room temperature is about 1 mPa·s, while many oils are 10–100 mPa·s. Since Q is inversely proportional to μ, warming a viscous fluid often lowers required pressure.

4) Interpreting pressure drop and head

Pressure drop ΔP is the driving pressure across the developed length L. If density is provided, the tool reports head h = ΔP/(ρg). As a quick check, 20 kPa in water is roughly 2.0 m of head, helpful for pump comparisons.

5) Velocity profile, shear stress, and shear rate

Laminar tube flow has a parabolic profile: centerline velocity is twice the mean (v_max = 2v̄). Wall shear stress τ_w = (ΔP r)/(2L) and wall shear rate γ̇_w = 4v̄/r matter for coatings and shear-sensitive liquids.

6) Hydraulic resistance as a circuit element

Hydraulic resistance R_h = ΔP/Q behaves like an electrical resistor at low Reynolds number. Straight segments add in series, and parallel branches share flow by conductance. Using R_h helps predict splits in manifolds and microfluidic networks.

7) Reynolds number and laminar validity

Poiseuille relations assume laminar conditions. With density ρ, the calculator estimates Re = ρv̄(2r)/μ. A common guideline is Re below about 2100 in smooth pipes, but roughness, pulsation, and entrances can trigger transition earlier. Treat Re as a screening check, not a guarantee.

8) Practical workflow and power budgeting

Select the unknown, enter remaining positive inputs with units, and review velocity, τ_w, and power P = ΔP·Q for sizing a pump or syringe. Export CSV for logs and PDF for reports, then iterate radius and length until targets are met. Keep units consistent when copying values into design sheets.

FAQs

1) When should I use this model?

Use it for steady, incompressible, Newtonian fluids in straight circular tubes with laminar, fully developed flow. It works well for small tubing, microchannels, and low-speed lines where turbulence is unlikely.

2) What if the tube is not circular?

The classic equation is for circular tubes. For noncircular ducts, use a laminar relation with hydraulic diameter or a published shape factor. Treat this calculator as a scaling guide, not an exact predictor.

3) Why do I get a very different result after changing radius?

Flow rate depends on r⁴. A 10% increase in radius raises flow by about 46% for the same ΔP, L, and μ. Small fouling or tight tolerances can therefore dominate performance.

4) How do I check if laminar assumptions hold?

Enter density to compute Reynolds number. Values well below 2100 are commonly laminar in smooth pipes, while higher values may transition. Entrances, vibration, roughness, and pulsation can shift the threshold.

5) Does this include entrance and fitting losses?

No. The model assumes a fully developed profile along the stated length. Short tubes, sharp inlets, bends, valves, and fittings add extra losses. Add those separately when sizing pumps or comparing layouts.

6) Can I estimate viscosity from measurements?

Yes. Choose viscosity as the solve target, then provide measured Q, ΔP, r, and L. Maintain stable temperature and confirm laminar flow for better accuracy. This is useful for quick checks and comparisons.

7) What does power P = ΔP·Q represent?

It is the hydraulic power dissipated by viscous losses in the tube. A pump must supply at least this amount, plus additional losses elsewhere. It helps compare tubing choices and energy requirements.