Viscosity (Fluid Friction)
Simple Explanation
Viscosity is a fluid's internal friction — its resistance to flowing or to layers of it sliding past each other. A highly viscous fluid (like honey) resists flow much more than a low-viscosity fluid (like water).
Why Do We Need It?
Viscosity determines how much force is needed to pump a fluid through a pipe, how fast an object sinks through a fluid, and why some fluids feel "thick" while others feel "thin."
Formula
Newton's Law of Viscosity
F = ηA(v/d)
The tangential force needed to drag one layer of fluid over another, at speed v, across a fluid layer of thickness d — proportional to how "thick" (viscous) the fluid is.
- F
- — tangential (viscous) force, in newtons (N)
- η
- — dynamic viscosity of the fluid, in pascal-seconds (Pa·s)
- A
- — area of the moving layer in contact with the fluid, in square metres (m²)
- v
- — relative speed between the two layers, in metres per second (m/s)
- d
- — perpendicular distance (thickness) between the two layers, in metres (m)
When to use it: Whenever the internal friction force within a flowing fluid, or between a fluid and a moving surface, needs to be found.
Worked Example
Find a viscous force
A layer of water (η=0.001 Pa·s) of area 0.5 m² is dragged across a fixed layer 0.002 m below it, at a relative speed of 0.3 m/s. Find the viscous force.
Why Does This Work?
Adjacent layers of fluid moving at different speeds drag on each other — the faster layer tends to speed up the slower one, and vice versa — and this drag force grows with the area in contact, the speed difference, and the fluid's own "stickiness" (η), while shrinking as the layers are spaced farther apart.
Real-Life Example
Why honey pours more slowly than water
Pouring honey from a jar takes much longer than pouring an equal amount of water.
Honey has a far higher viscosity than water, so its internal layers resist sliding past each other much more strongly — the same principle behind this formula's dependence on η.
Practice
A fluid layer (η=0.0008 Pa·s) of area 0.2 m² moves at 0.5 m/s relative to a fixed layer 0.001 m away. Find the viscous force.
MediumCommon mistake
Confusing viscosity (a fluid's own internal resistance to flow) with density (how much mass a fluid packs into a given volume) — a fluid can be dense but not very viscous (like mercury), or viscous but not dense (like a thin oil).
Quick Review
- F = ηA(v/d) — the tangential force to drag one fluid layer over another.
- Higher η means "thicker," more resistant flow.
- Different from density — the two are independent properties.