A fluid trapped between two plates, the lower one fixed and the upper one dragged sideways. Set the viscosity, the plate speed, the gap and the plate area, and the lab reports the shear rate, the shear stress, the force on the plate and the power going into the fluid as heat — every one of them recomputed as you drag.
Viscosity & Shear Stress
A Couette shear cell: the lower plate is fixed, the upper plate is dragged sideways, and the fluid between them is sheared. Move the sliders to watch τ = μ × (du/dy) respond — the arrows are the fluid's own speed at each height.
What Is the Viscosity Simulator?
The viscosity simulator is a free interactive physics lab that runs in your browser — nothing to install and no sign-up. Drag the plate, change the gap and the fluid, and watch shear stress equal viscosity times shear rate in real time. It reports shear rate du/dy, shear stress τ, Viscous force, power dissipated and Kinematic viscosity ν as you drag the sliders.
| Control | Range | Step |
|---|---|---|
| Dynamic viscosity in pascal seconds | 0.001 – 2 Pa·s | 0.001 |
| Speed of the upper plate | 0 – 5 m/s | 0.05 |
| Gap between the plates | 0.5 – 20 mm | 0.1 |
| Area of the moving plate | 0.01 – 1 m² | 0.01 |
How to Use the Viscosity Simulator
Four sliders feed one equation. Dynamic viscosity chooses the fluid, with buttons for water, olive oil and glycerine — three orders of magnitude in a click — and if your figure came off a datasheet in centistokes, the viscosity converter turns it into the Pa·s this slider wants. Plate speed sets how fast the top plate is hauled along and Gap how far apart the plates sit, while Plate area is the odd one out: it scales the force and the power and deliberately leaves the stress alone, because a stress is already a force spread over an area.
The arrows between the plates are the fluid's own speed at each height, drawn to the printed key beneath them, and their tips land on a straight line for a reason worth pausing on. The bottom plate holds the fluid touching it at a standstill while the top plate carries its layer along at the full plate speed, so both ends are pinned. Between them no layer is pushed harder than its neighbour, and the only way to climb from nought to the plate speed with no preference for any height is to rise at a steady rate — so drag the speed slider and watch the line pivot rather than bend.
The gap slider is where the lesson bites. Leave the plate speed alone and halve the gap: the same total change in speed now has half the distance to happen in, so the shear rate doubles, and because the stress is the viscosity multiplied by that rate, the stress doubles with it — force and power follow. That is why thin films are punishing; a bearing on a film a few microns thick shears its oil at tens of thousands per second, and the units behind those numbers are laid out in viscosity: definition, units and examples.
One habit is worth breaking, and the lab is built to break it: the idea that a thick fluid always demands more force. Select glycerine, note the force, then wind the plate speed down towards zero and watch that force collapse while the viscosity readout never moves. Stress needs both factors — the fluid's viscosity and the rate you shear it at — and either one at zero gives you nothing, the same bargain struck by an object moving through a fluid in the drag force discussion.
Frequently asked questions
What does the shear-rate readout mean?
It is du/dy, the velocity gradient: how quickly the fluid's speed changes as you move up through the gap, measured in reciprocal seconds. The simulator computes it as the plate speed divided by the gap, so 1 m/s across a 2 mm gap gives 500 per second. Read it as the steepness of the arrow staircase on the left. A steeper climb means neighbouring layers are sliding past each other faster, and it is that sliding, not the plate's speed on its own, that the fluid resists.
Why does power rise faster than speed?
Because the plate speed enters twice. Doubling it doubles the shear rate, which doubles the stress and therefore the force; then that doubled force is dragged at twice the speed. Two doublings multiply, so the power quadruples. Try it: set the speed to 1 m/s and note the power, then set it to 2 m/s. The force reading doubles while the power reading goes up four times. This is why stirring something thick twice as fast costs four times the effort, and why high-speed bearings shed so much heat.
What happens if I set the gap very small?
The shear rate climbs steeply, because the same change in speed is being squeezed into a shorter distance. The gap slider stops at 0.5 mm, which is a deliberate floor: the shear rate is the plate speed divided by the gap, and a gap of zero would be a division by zero. At the 0.5 mm end with glycerine at full speed the stress reaches roughly 14 kPa, which is the sort of figure a journal bearing really does see. Note also that the picture draws the gap on a compressed scale so the thinnest films stay visible; the figure printed beside it is the true one.
Does the simulator model non-Newtonian fluids?
No. It assumes a Newtonian fluid, meaning the viscosity is a fixed property that does not change with how hard you shear it, which is why the arrow tips always fall on a straight line. Real ketchup, blood, paint and cornflour paste are not like that: their effective viscosity rises or falls with the shear rate, and their velocity profiles curve. Water, air, glycerine and most oils are Newtonian to a good approximation over ordinary conditions, so the three presets here are all honest cases.
How do I convert the result to centipoise?
Multiply the dynamic viscosity in Pa·s by 1000. One centipoise is a thousandth of a pascal second, so the 0.001 Pa·s water preset is 1 cP and the 1.412 Pa·s glycerine preset is 1412 cP. For the kinematic viscosity the simulator already prints centistokes beside the value, since 1 cSt is exactly 1e-6 m²/s. One caveat on the presets: the viscosity slider steps in thousandths of a Pa·s, so water is set at a round 0.001 rather than its measured 1.002 mPa·s at 20 °C.
References & formula source
- Halliday, Resnick & Walker — Fundamentals of Physics, Chapter 14 (Fluids), viscous flow and Newton's law of viscosity.
- Young & Freedman — University Physics with Modern Physics, §12.6 (Viscosity and Turbulence).
- F. M. White — Fluid Mechanics, §1.7 (Viscosity and Other Secondary Properties) on Couette flow between parallel plates.
- CRC Handbook of Chemistry and Physics — dynamic viscosity of water, olive oil and glycerine at 20 °C.
- Further reading: Viscosity — Wikipedia