Laminar Flow Resistance Calculator

For fully developed laminar flow in a circular pipe (Hagen–Poiseuille law):

• Hydraulic resistance: R = 8 μ L / (π r⁴)
• Pressure drop: ΔP = R · Q (equivalently ΔP = 8 μ L Q / (π r⁴))
• Mean velocity: v = Q / A, where A = π r²
• Reynolds number: Re = ρ v D / μ
• Head loss: h = ΔP / (ρ g)

This model assumes a smooth pipe, steady incompressible flow, and laminar regime.

1. Enter viscosity μ and density ρ using the unit menus.
2. Provide the pipe length L and inner diameter D.
3. Enter the volumetric flow rate Q for your case.
4. Select the desired pressure unit for display.
5. Press Calculate to see results above the form.
6. Use the download buttons to export CSV or PDF.
7. If Re is high, consider a turbulent-loss model.

Example results are approximate and depend strongly on diameter.

• Valid for steady, incompressible, fully developed laminar pipe flow.
• Entrance effects and fittings can add extra losses.
• For microfluidics, ensure diameter and viscosity units are consistent.
• A common laminar guideline is Re < 2000.

1) Why laminar resistance matters

Laminar flow resistance links pump effort to a chosen flow rate. In the laminar regime, ΔP scales linearly with Q, so control is predictable. Resistance R (Pa·s/m³) helps compare segments, size small pumps, and allocate allowable pressure drop in instruments, tubing, and microfluidic chips. It is especially helpful for low-flow laboratory lines where turbulence is absent and repeatability is critical.

2) The Hagen–Poiseuille relationship

For smooth circular pipes, Hagen–Poiseuille gives ΔP = 8 μ L Q / (π r⁴). The r⁴ term dominates: doubling D cuts ΔP by 16× at the same Q. A 10% diameter underestimate increases predicted ΔP by about 46%.

3) Typical viscosity values and temperature effects

Water at 20°C is ~1 mPa·s; light oils are often ~10–100 mPa·s; glycerin can exceed 1 Pa·s. Because R ∝ μ, temperature-driven viscosity changes map directly to ΔP. If μ drops 20%, ΔP drops 20% for fixed L, D, and Q.

4) Reynolds number as a validity gate

The model targets fully developed laminar flow, often associated with Re < 2000. With Re = ρ v D / μ, higher Q or larger D quickly raises Re. Use the displayed Re to flag transitional flow and justify switching to turbulent-loss correlations.

5) Resistance, conductance, and networks

Laminar hydraulics behaves like circuits. Series segments add resistance: R_total = ΣR. Parallel branches add conductance: (1/R_total) = Σ(1/R). Reporting both R and 1/R helps combine capillaries, manifold channels, and bundled tubes without repeated algebra.

6) Units and interpretation of results

R has units Pa·s/m³, converting Q (m³/s) into ΔP (Pa). Choose Pa, kPa, or bar for display while exports keep SI values. Head loss in meters uses h = ΔP/(ρg), useful for pump curves, elevation budgets, and quick system comparisons.

7) A quick design intuition example

With water (μ ≈ 0.001 Pa·s) in a 1 m, 10 mm tube at Q = 1×10⁻⁵ m³/s, ΔP is on the order of tens of pascals and Re is about 10³. Keeping Q constant but reducing D to 6 mm raises ΔP by (10/6)⁴ ≈ 7.7×.

8) Practical limits and best practices

Real systems include entrance effects and fittings. Entrance length can matter for short tubes, and valves or bends add minor losses not included here. Use this tool for straight, smooth segments, add handbook K-values for components, and validate with measurements when tight pressure tolerances exist.

1) What does “resistance” mean in this calculator?

It is the proportionality between pressure drop and flow for laminar pipe flow: ΔP = R·Q. Larger R means more pressure is required to push the same flow through the pipe.

2) Why does diameter affect results so strongly?

Poiseuille flow depends on r⁴. A small reduction in diameter sharply increases ΔP at fixed Q, which is why narrow tubing and microchannels can require large driving pressures.

3) When should I avoid using Poiseuille’s law?

If Reynolds number is high (often above 2000), if the flow is not fully developed, or if the pipe is very rough, the laminar linear model can underpredict losses. Use a turbulent or transitional model instead.

4) Does this include losses from elbows, valves, or fittings?

No. The calculation covers straight-pipe viscous losses only. Add minor losses separately using K-values or equivalent length methods, then sum those with the straight-pipe ΔP for a total budget.

5) Can I use this for non-Newtonian fluids?

Only as an approximation. Non-Newtonian fluids have viscosity that changes with shear rate, so a single μ may not represent the flow. Use a rheology-based model or an effective viscosity measured at relevant shear conditions.

6) Why do I need density if the formula uses viscosity?

Density is used to compute Reynolds number and head loss. Reynolds helps validate laminar assumptions, and head loss converts ΔP into meters of fluid for pump and system comparisons.

7) What’s the benefit of CSV and PDF export?

Exports let you document design cases, share assumptions, and build quick comparison tables across multiple diameters, lengths, or fluids. The PDF is convenient for reports, and the CSV is ideal for spreadsheets.