Kinematic Viscosity From Terminal Velocity Calculator

Calculator Inputs

Terminal velocity

Velocity unit

Sphere size

Size type

Size unit

Sphere density

Sphere density unit

Fluid density

Fluid density unit

Gravity, g

Correction factor

Temperature note, °C

Radius uncertainty, %

Velocity uncertainty, %

Density contrast uncertainty, %

Fluid density uncertainty, %

Formula Used

For a small sphere moving at terminal velocity under Stokes flow, the calculator uses:

ν = 2r²g|ρ_s - ρ_f|C / 9ρ_fv_t

Here, ν is kinematic viscosity, r is sphere radius, g is gravity, ρ_s is sphere density, ρ_f is fluid density, C is correction factor, and v_t is terminal velocity.

The dynamic viscosity is found from μ = ρ_fν. The Reynolds check is Re = 2rv_t / ν.

How To Use This Calculator

Measure terminal velocity after the sphere reaches steady motion.
Enter the sphere diameter or radius with the correct unit.
Enter sphere density and fluid density.
Keep gravity at 9.80665 m/s², unless your lab requires another value.
Use correction factor 1 for no correction.
Add uncertainty values if you want an error estimate.
Press Calculate to view results above the form.
Use CSV or PDF buttons to save the result.

Example Data Table

Case	Terminal Velocity	Diameter	Sphere Density	Fluid Density	Kinematic Viscosity	Reynolds Number
Steel sphere in dense liquid	0.045 m/s	2.5 mm	7800 kg/m³	1260 kg/m³	392.756 cSt	0.286
Glass sphere in oil	0.022 m/s	1.5 mm	2500 kg/m³	900 kg/m³	99.057 cSt	0.333
Lead sphere in water-like fluid	0.010 m/s	1.0 mm	11300 kg/m³	1000 kg/m³	561.158 cSt	0.018

Why terminal velocity helps

A small sphere falling through a viscous liquid reaches a steady speed when weight, buoyancy, and drag balance. That steady speed is terminal velocity. Under creeping flow, Stokes law links that speed to viscosity. This calculator turns measured terminal velocity into dynamic and kinematic viscosity. Kinematic viscosity is useful because it divides dynamic resistance by fluid density. It describes how quickly momentum diffuses through a fluid.

What the result means

The main result is ν, shown in square meters per second and centistokes. A lower value means the fluid lets motion spread more easily. A higher value means the fluid resists shear more strongly for its density. The tool also reports dynamic viscosity, density contrast, and Reynolds number. Reynolds number is important. Stokes law is best when it is below one. Larger values mean inertia may affect drag, so the result should be treated as an estimate.

Good measurement practice

Use a smooth, round sphere. Measure its diameter carefully, because radius is squared in the formula. Small size errors can strongly change the final value. Record terminal velocity only after the sphere is moving steadily. Use marks that are far from the release point and container bottom. Keep the fluid temperature stable. Viscosity can change quickly with temperature. Enter density values in consistent units, or use the unit selectors. For narrow tubes, enter a correction factor if you have one from your method.

When to use this calculator

This page is designed for teaching labs, quick checks, and early engineering estimates. It is suitable for dilute, Newtonian liquids with small spheres and slow motion. It is not ideal for turbulent flow, irregular particles, strong wall effects, or non Newtonian fluids. Use the exported report to attach assumptions, inputs, and results to lab notes. Always compare the Reynolds check with your course or project limits before accepting the viscosity value.

Interpreting uncertainty

The uncertainty estimate is a guide. It uses percentage errors entered for velocity, radius, density contrast, and fluid density. Because radius is squared, radius uncertainty counts twice. This helps show which measurement deserves more care. It does not replace a full experimental error analysis. Use repeated trials when high accuracy is required, and report averages.

FAQs

What is kinematic viscosity?

Kinematic viscosity is dynamic viscosity divided by fluid density. It shows how fast momentum spreads through a fluid. Its SI unit is square meter per second.

Why is terminal velocity used?

At terminal velocity, net force becomes zero. For slow sphere motion, Stokes law can connect this steady speed with fluid viscosity.

What does the correction factor do?

The correction factor adjusts the result for known experimental effects. Use 1 when no correction is required. Use your lab method value when available.

When is Stokes law valid?

Stokes law works best for small, smooth spheres moving slowly in a Newtonian fluid. A Reynolds number below one is usually preferred.

Can I use diameter instead of radius?

Yes. Select diameter in the size type field. The calculator converts it to radius internally before applying the formula.

Why is radius important?

Radius is squared in the formula. A small radius measurement error can create a larger viscosity error, so measure it carefully.

What is centistokes?

Centistokes is a common kinematic viscosity unit. One square meter per second equals one million centistokes.

Can this handle rising particles?

Yes, it uses the absolute density contrast. If the sphere is less dense than the fluid, read the warning and verify your setup.