Poiseuille Flow Calculator: Laminar Flow in a Tube, Pressure Drop, Flow Rate and Viscosity

Laminar flow of a viscous fluid in a narrow tube.

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

Choose flow, pressure or viscosity, and pick the fluid.

Enter the diameter, the length and the pressure or flow rate.

The calculator gives the answer, the velocities, the wall shear stress and the Reynolds number.

Formulas used

  • Q = \frac{\pi D^4\Delta P}{128\mu L}
  • \tau_w = \frac{D\Delta P}{4L}
  • Re = \frac{\rho VD}{\mu}

Worked example

With the default numbers in the calculator above:

  1. Flow rate by the Hagen-Poiseuille equation: 1.5677 mL/s (94.06 mL/min, 0.09406 L/min)
  2. Mean velocity of the fluid: 0.499 m/s
  3. Velocity at the centre of the tube (the profile is a parabola, twice the mean): 0.998 m/s
  4. Shear stress at the wall: 2 Pa
  5. Reynolds number: 994.02 (laminar: the equation applies)
  6. Hydraulic power used to push the fluid through: 0.0031353 W

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

A second worked example

A different case, with these numbers: What do you want? The pressure difference for a flow rate.

  1. Pressure difference needed for that flow: 1.9137 kPa (1913.7 Pa)
  2. Mean velocity of the fluid: 0.47746 m/s
  3. Velocity at the centre of the tube (the profile is a parabola, twice the mean): 0.95493 m/s
  4. Shear stress at the wall: 1.9137 Pa
  5. Reynolds number: 951.12 (laminar: the equation applies)
  6. Hydraulic power used to push the fluid through: 0.0028705 W

Common questions

What is the Hagen-Poiseuille equation?

It gives the flow of a viscous fluid in a long round tube. The flow is proportional to the pressure difference and to the fourth power of the diameter.

When does it apply?

For laminar flow, where the Reynolds number is below about 2300.

Why does a narrow tube restrict flow so much?

The flow depends on the fourth power of the diameter, so halving the diameter cuts the flow to one sixteenth.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any fluid mechanics text (laminar pipe flow).

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