---
title: "Viscosity, Poiseuille Flow and the Reynolds Number"
description: "A real fluid drags on itself and on the pipe wall, which gives a parabolic speed profile and a flow rate that falls with the fourth power of the radius. Comparing inertial to viscous effects gives one"
canonical: https://lightmysky.com/learn/science/viscosity-poiseuille-flow-and-the-reynolds-number-mt_-1sWgkRtMs
source: https://lightmysky.com/learn/science/viscosity-poiseuille-flow-and-the-reynolds-number-mt_-1sWgkRtMs.md
retrieved: 2026-09-12
---

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# Viscosity, Poiseuille Flow and the Reynolds Number

A real fluid drags on itself and on the pipe wall, which gives a parabolic speed profile and a flow rate that falls with the fourth power of the radius. Comparing inertial to viscous effects gives one dimensionless number that says whether the flow will stay smooth or break into turbulence.

Subject: Science · Area: Forces & Motion · Ages 20 to 21
Page: https://lightmysky.com/learn/science/viscosity-poiseuille-flow-and-the-reynolds-number-mt_-1sWgkRtMs

## Ready when they can

- Explains why halving a pipe's radius cuts the flow rate by a factor of sixteen at fixed pressure difference
- Builds the Reynolds number from the quantities in the problem and uses it to predict laminar or turbulent flow
- Says which of two situations Bernoulli's equation may be applied to, and why viscosity rules the other one out

## Lesson: Sticky flow, narrow pipes, rough flow

Viscosity is the internal stickiness of a fluid that resists layers sliding past each other. In a pipe it drags the flow into a parabolic profile: fastest in the middle and still at the walls. Steady pushing is needed just to keep it moving. Objects in a viscous fluid feel drag that grows with speed, which sets a terminal speed where drag exactly balances the push.

Poiseuille law says the flow rate grows with the fourth power of the radius at fixed pressure difference. Halving the radius therefore cuts the flow sixteenfold. Narrowing punishes hard, which is why clogged arteries and thin straws dominate the effort. Double the driving push and the flow doubles too, but shrink the pipe and everything collapses.

The Reynolds number weighs inertia against viscosity in one pure number. Build it from density, speed, a characteristic length, and viscosity: multiply the first three and divide by the last. Past a threshold of a few thousand in pipes, eddies take over and drag climbs steeply. Below the threshold expect smooth laminar flow; above it expect mixing, extra loss, and noise.

**Tip.** Apply Bernoulli only where viscosity is negligible and the flow stays laminar along a streamline. Rule it out wherever sticky shear losses dominate, such as thin long pipes or turbulent zones. When drag must be counted, energy arguments alone will not work. Check the Reynolds number first, then choose your tool.

**Recap.** Viscosity drags pipes into a parabolic profile, the fourth power punishes narrow pipes sixteenfold, and the Reynolds number tells you whether Bernoulli may apply.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Drag and Terminal Speed from the Equation of Motion](https://lightmysky.com/learn/science/drag-and-terminal-speed-from-the-equation-of-motion-mt_In6VeoADzZ)
- [Continuity and Bernoulli's Equation for Ideal Flow](https://lightmysky.com/learn/science/continuity-and-bernoullis-equation-for-ideal-flow-mt_pKxlVYTy0Y)