Reynolds Number Calculator: Laminar or Turbulent Flow

Find the Reynolds number for flow in a pipe, a duct, an annulus or along a flat plate, see whether it is laminar or turbulent, and get the friction loss.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

The Reynolds number is the density times the speed times the size of the passage, divided by the viscosity. A low number means the viscosity wins and the fluid moves in smooth layers (laminar flow). A high number means the inertia wins and the flow mixes and swirls (turbulent flow).

In a round pipe the flow is laminar below about 2300 and turbulent above about 4000, with an unstable range in between. For a duct or an annulus the hydraulic diameter is used for the size. Along a flat plate the layer turns turbulent at about half a million.

The friction factor is 64 over the Reynolds number for laminar flow, and comes from the Haaland equation with the wall roughness for turbulent flow. It gives the pressure drop and the head loss for each metre of run.

Formulas used

  • Re = \dfrac{\rho V D}{\mu} = \dfrac{V D}{\nu}
  • f = \dfrac{64}{Re}\ \text{(laminar)}
  • \dfrac{\Delta p}{L} = f\,\dfrac{\rho V^2}{2 D}
  • D_h = \dfrac{4A}{P_w}

Worked example

With the default numbers in the calculator above:

  1. Speed and flow rate: 1.50 m/s and 10.60 m³/h
  2. Kinematic viscosity: 1.0040e-6 m²/s
  3. Reynolds number: 74700.60
  4. Flow regime: turbulent
  5. Speed where the flow stops being laminar (Re = 2300): 0.0462 m/s
  6. Speed where it is fully turbulent (Re = 4000): 0.0803 m/s
  7. Friction factor (Darcy): 0.0223
  8. Pressure drop per metre of run: 500.34 Pa/m
  9. Head loss per metre of run: 0.0511 m per m

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What Reynolds number is laminar?

In a round pipe, below about 2300. Above about 4000 it is turbulent. Between the two it is unstable and hard to predict.

Why does warm water have a higher Reynolds number?

Warm water is thinner, so its viscosity is lower and the Reynolds number is higher for the same speed.

What is the hydraulic diameter?

It stands in for the diameter of a passage that is not round. It is four times the flow area divided by the wetted perimeter.

Related calculators

Further reading: Standard fluid mechanics texts (Reynolds number, pipe friction and the Haaland equation).

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