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Fluid dynamics learning guide

Viscosity and Fluid Dynamics Interactive Guide

Explore viscosity, flow speed, pressure, Reynolds number, drag, and laminar-to-turbulent behaviour in an interactive fluid dynamics lab.

Open the fluid dynamics lab →

Change viscosity, density, geometry, and speed while observing flow behaviour.

Start with the model

Concept overview

Viscosity measures a fluid's resistance to shear deformation: neighbouring layers moving at different speeds exchange momentum and produce shear stress. Dynamic viscosity carries units of pascal-seconds, while kinematic viscosity divides dynamic viscosity by density. Viscosity is not simply the same as density, and it can change strongly with temperature and fluid composition.

Reynolds number compares inertial effects with viscous effects for a chosen speed and length scale. Low values often support smooth, viscosity-dominated flow; high values make instabilities and turbulence more likely. The transition is not one universal number because geometry, roughness, disturbances, and the definition of characteristic length matter. Use the lab to compare controlled cases, not to certify real pipes, aircraft, or medical flows.

Concept 1

Shear and viscosity

A velocity gradient between fluid layers produces viscous shear stress. Newtonian-fluid models use a proportionality between shear stress and velocity gradient.

Concept 2

Reynolds similarity

Flows with matching geometry and Reynolds number can share important patterns even at different size, speed, density, or viscosity. Other dimensionless groups may also matter.

Concept 3

Boundary layers and drag

No-slip at a solid surface creates a velocity gradient and boundary layer. Viscosity, separation, shape, and Reynolds number influence the total drag.

Guided investigation

Can different settings produce the same Reynolds number?

  1. 1Choose a reference fluid, speed, and length; record density, viscosity, and calculated Reynolds number.
  2. 2Double speed while holding every other input fixed and record the new value.
  3. 3Restore the original Reynolds number by changing one other parameter; explain your calculation.
  4. 4Compare the displayed flow pattern and list any model variables that Reynolds number alone does not capture.

Evidence to record

Record density, dynamic viscosity, speed, characteristic length, Reynolds number, and observed regime for four trials. Show units and one proportional comparison.

Equations and variables

Re = rho v L / mu = vL / nu

Ratio of inertial to viscous effects for the selected characteristic scales.

  • • rho: fluid density
  • • v: characteristic speed
  • • L: characteristic length
  • • mu: dynamic viscosity
  • • nu: kinematic viscosity

tau = mu du/dy

Newtonian-fluid relation between shear stress and velocity gradient.

  • • tau: shear stress
  • • mu: dynamic viscosity
  • • du/dy: velocity gradient normal to the flow

Worked example

Apply the model

Water with rho = 1000 kg/m^3 and mu = 0.001 Pa s flows at 0.20 m/s through a 0.010 m characteristic diameter. Find Re.

  1. Step 1: Multiply the numerator: rho v L = 1000 x 0.20 x 0.010 = 2.
  2. Step 2: Divide by mu: Re = 2 / 0.001.

Answer: Re = 2000 for the selected scales. Interpreting the regime still requires the relevant geometry, disturbance conditions, and transition evidence.

Misconceptions to test

Common claim

“Dense fluids are always more viscous.”

Correction: Density and viscosity are different material properties. A fluid can be relatively dense but not especially viscous, or less dense and highly viscous.

Common claim

“Reynolds number alone predicts every detail of a flow.”

Correction: It is a powerful similarity parameter, but geometry, roughness, boundary conditions, compressibility, gravity, and other dimensionless groups can matter.

Teacher-ready worksheet

Viscosity and Reynolds number sheet

  1. 1.Define dynamic and kinematic viscosity with units.
  2. 2.Calculate Reynolds number for two controlled trials.
  3. 3.Design a second trial with the same Reynolds number.
  4. 4.Explain one observed flow-regime change.
  5. 5.List two factors the classroom model does not capture.

Print or save this page as PDF to use the investigation and worksheet offline.

Knowledge check

Check your understanding

Check viscosity, units, Reynolds number, and modelling limits.

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