Viscosity and Coefficient of Viscosity Explained Simply

Viscosity is the internal friction of a fluid. When a liquid or gas flows, its layers slide past each other, and each layer drags on its neighbours. That resistance to sliding is what we call viscosity. Honey has high viscosity, so it pours slowly, while water has low viscosity and flows easily.

Viscosity matters everywhere fluids move. Engine oil must be viscous enough to keep metal parts apart but thin enough to flow in cold weather. Blood viscosity affects how hard the heart must work. Paint viscosity decides whether paint spreads smoothly or drips off the wall.

Key Concepts

• Viscosity: the property of a fluid that opposes the relative motion of its layers. It is a kind of internal friction.
• Velocity gradient (dv/dx): how fast the flow speed changes as you move from one layer to the next, measured in s^-1 (per second).
• Shear stress: the tangential force per unit area between sliding layers, measured in pascals (Pa), where Pa = N/m^2.
• Coefficient of viscosity (eta): the constant of proportionality in Newton's law of viscosity. SI unit: pascal-second (Pa.s), also written N.s/m^2. A common smaller unit is the poise, where 1 Pa.s = 10 poise.
• Newtonian fluid: a fluid whose coefficient of viscosity stays constant whatever the flow speed, for example water and light oils.

Formulas

• Newton's law of viscosity: shear stress = eta x velocity gradient, or F/A = eta x (dv/dx). Assumptions: steady, laminar flow; the fluid is Newtonian; temperature is constant.
• Coefficient of viscosity: eta = (F/A) / (dv/dx). Units: Pa.s. One poise = 0.1 Pa.s.
• Limits: the linear law breaks down in turbulent flow and for non-Newtonian fluids like paint, toothpaste or blood, whose apparent viscosity changes with shear rate.

Worked Example

A flat plate of area 0.05 m^2 sits on a 2 mm thick layer of oil. It takes a horizontal force of 2.5 N to pull the plate at a steady speed of 0.5 m/s relative to the fixed surface below. Find the coefficient of viscosity of the oil.

1. Shear stress = F / A = 2.5 / 0.05 = 50 Pa.
2. Velocity gradient = change in speed / layer thickness = 0.5 / 0.002 = 250 s^-1.
3. eta = shear stress / velocity gradient = 50 / 250 = 0.2 Pa.s.
4. In poise: 0.2 x 10 = 2 poise.

So eta = 0.2 Pa.s, about 200 times water's.

Common Misconceptions

• Viscosity is not the same as density. Mercury is very dense yet flows almost as freely as water, while honey is light but very viscous. Density measures mass per volume; viscosity measures resistance to flow.
• Temperature affects liquids and gases oppositely. Heating a liquid usually makes it thinner (lower viscosity), but heating a gas makes it more viscous, because faster molecules collide more often.
• A thicker fluid does not always slow everything equally. How a body falls through a fluid also depends on buoyancy and the body's size and density, so viscosity alone does not set the falling speed.

Real-World Applications

• Engine and gearbox oils are graded by viscosity so they protect parts in both winter cold and engine heat.
• Doctors track blood viscosity, since thicker blood forces the heart to work harder and raises the risk of clots.
• Paints and inks are formulated with just the right viscosity to spread evenly and stay put without dripping.

Viscosity is the internal friction that resists flow, and its coefficient eta (in Pa.s) links shear stress to the velocity gradient between layers. From engine oil to blood, knowing eta lets engineers predict exactly how a fluid will behave.