Laminar Pipe Flow Calculator

Estimate laminar pipe flow using proven pressure-drop relations. Switch units; solve from flow or pressure. Review velocity, Reynolds, friction factor, and head loss quickly.

Calculator Inputs

Pick the input you trust most. The tool solves the remaining quantities.
Water at 20°C is about 1 mPa·s.

Example data table

Try these sample cases to validate unit choices and expectations.
Case D (mm) L (m) μ (mPa·s) ρ (kg/m³) Given
Water, small tube 20 5 1.0 998 Q = 30 L/min
Light oil 15 12 25 870 V = 0.4 m/s
Glycerin-like fluid 10 2 900 1260 ΔP = 20 kPa

Formula used

For fully developed, incompressible laminar flow in a round pipe:

  • Area: A = πD²/4
  • Flow relation: Q = V·A
  • Hagen–Poiseuille: ΔP = 32μLV/D² = 128μLQ/(πD⁴)
  • Reynolds number: Re = ρVD/μ
  • Laminar friction factor: f = 64/Re (Darcy definition)
  • Head loss: hf = ΔP/(ρg)
  • Centerline velocity: Vmax = 2V

How to use this calculator

  1. Select a calculation mode: Q, V, or ΔP.
  2. Enter pipe diameter, length, viscosity, and density.
  3. Provide the mode-specific input with your chosen unit.
  4. Click Calculate to view results above the form.
  5. Use CSV for spreadsheets or PDF for printed reports.

Laminar pipe flow overview

1) Why laminar pipe flow matters

Laminar flow appears when viscous effects keep motion orderly. It is common in small-diameter tubing, microfluidic channels, and slow-flow process lines. Because the velocity profile is stable, pressure drop can be estimated reliably for design checks and troubleshooting. It also supports pump and regulator sizing during early design and commissioning tasks.

2) Core assumptions behind the model

The calculator uses fully developed, incompressible, Newtonian flow in a straight, circular pipe. “Fully developed” means the entrance region is excluded and the profile no longer changes with distance. The method also assumes steady conditions and constant properties along the pipe.

3) Inputs that drive the result

Diameter D and length L set the geometry, while viscosity μ and density ρ describe the fluid. Unit selectors convert to SI internally. Viscosity is especially important: if μ doubles (often due to temperature change), the predicted pressure drop doubles for the same flow.

4) Hagen–Poiseuille pressure drop

For laminar pipe flow, Hagen–Poiseuille gives ΔP = 128 μ L Q /(π D⁴). In velocity form, ΔP = 32 μ L V / D². The strong D⁴ dependence explains why small tubes require much higher pressure for the same flow than larger pipes.

5) Reynolds number validity check

Reynolds number Re = ρ V D / μ indicates whether laminar assumptions are reasonable. A common guideline is laminar for Re < 2300, transitional between about 2300 and 4000, and turbulent above that. The results section flags cases where Re exceeds the laminar threshold.

6) Friction factor and head loss

For laminar flow, the Darcy friction factor is f = 64/Re. The calculator also converts pressure drop to head loss using hf = ΔP /(ρ g), which helps compare losses across fluids with different densities. Head loss is convenient in pumping and hydraulics workflows.

7) Velocity profile and wall shear

Laminar pipe flow has a parabolic profile with centerline velocity Vmax = 2V. Wall shear stress is reported as τw = (ΔP·D)/(4L), useful for estimating drag forces, coating or deposition risk, and shear-sensitive fluids. Higher shear also increases viscous heating in tight channels.

8) Practical interpretation and limits

Use the three calculation modes to work from your most trusted measurement: flow rate, average velocity, or pressure drop. If the pipe is very short, highly rough, coiled, or if the fluid is non-Newtonian, real behavior can deviate. Treat outputs as baseline engineering estimates and validate with measured data when possible.

FAQs

1) What Reynolds number is considered laminar in a pipe?

For internal flow in a round pipe, a widely used guideline is laminar when Re < 2300. Between about 2300 and 4000 the flow may transition, and above that turbulence becomes more likely.

2) Can I use kinematic viscosity instead of dynamic viscosity?

This calculator uses dynamic viscosity μ. If you have kinematic viscosity ν, convert using μ = ρν. Ensure consistent units, for example ν in m²/s and ρ in kg/m³.

3) Does pipe roughness affect laminar pressure drop?

In ideal laminar flow, roughness has a much smaller effect than in turbulence. However, significant roughness or deposits can reduce the effective diameter, which can sharply increase ΔP due to the D⁴ dependence.

4) Why is pressure drop so sensitive to diameter?

Hagen–Poiseuille contains D⁴ in the denominator. Halving diameter increases ΔP by about 16× for the same flow. Small tubing is therefore pressure-intensive, especially for viscous fluids.

5) What if the fluid is a gas?

If density changes significantly along the pipe, incompressible assumptions can fail. For low Mach number and small pressure changes, the model can still be a reasonable approximation. For larger pressure ratios, use a compressible-flow approach.

6) What does wall shear stress tell me?

Wall shear stress estimates the tangential stress at the pipe surface caused by viscosity. It helps evaluate drag on surfaces, potential erosion or coating behavior, and whether a shear-sensitive fluid may degrade in narrow passages.

7) How should I choose the best calculation mode?

Select the mode that matches your most reliable input. If you have a flow meter, use Q. If you have velocity from a sensor, use V. If you measured pressure drop across a known length, use ΔP.