Why thin tubes resist flow so strongly
When a viscous liquid flows slowly through a tube, the layer touching the wall stays still and each inner layer slides past the next. The velocity profile is a parabola, fastest at the center. Adding up all these layers gives Poiseuille’s law:
Q = π r⁴ ΔP ÷ (8 μ L)
- Q is the volume flow rate.
- r is the inside radius of the tube (half the diameter).
- ΔP is the pressure difference between the two ends.
- μ is the dynamic viscosity of the fluid.
- L is the length of the tube.
The striking part is the fourth power of the radius. Halving the diameter divides the flow by 16 at the same pressure.
How to use the calculator
- Enter the inside diameter, in millimeters or inches.
- Enter the tube length and the pressure difference that drives the flow, in psi, kPa, mmHg or bar.
- Choose a fluid, or select “Other” to enter its viscosity in mPa·s (equal to centipoise) and its density.
Worked example
Water at 68 °F flows through 3 ft of tubing with a 1 mm bore under a pressure difference of 1.5 psi (10.3 kPa). Poiseuille’s law gives:
- Flow: 0.277 mL/s, or about 16.6 mL per minute.
- Mean velocity: 0.353 m/s, and twice that, 0.71 m/s, at the center.
- Reynolds number: 351, well below 2,300, so the flow is laminar and the law applies.
- With a 2 mm bore, the same setup would carry 16 times more: 4.43 mL/s.
Where it is used
- Medicine: IV catheters are sized by gauge. A 14-gauge catheter carries several times more fluid than a 20-gauge one, mostly because of its radius. The same principle explains why narrowed arteries reduce blood flow so sharply.
- Laboratories: capillary viscometers measure viscosity by timing flow through a fine glass tube.
- Microfluidics and dispensing: sizing needles, nozzles and drip lines.
Limits
The law assumes laminar flow, a Newtonian fluid, a rigid, straight tube, and a length much longer than the diameter so the entrance effects are small. When the Reynolds number climbs above about 2,300, turbulence sets in and the real flow is lower than predicted. For larger pipes and water systems, use a friction loss calculator based on the Darcy–Weisbach or Hazen–Williams equations instead.