{"id":785,"date":"2026-08-12T00:32:13","date_gmt":"2026-08-12T00:32:13","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=785"},"modified":"2026-08-24T13:03:43","modified_gmt":"2026-08-24T13:03:43","slug":"viscosity-units-examples","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/fluids\/viscosity-units-examples\/","title":{"rendered":"Viscosity: Definition, Units and Examples"},"content":{"rendered":"\n
Definition<\/div>

\n\nViscosity is a fluid’s resistance to flow, caused by internal friction as layers of the fluid slide past one another. It equals the shear stress divided by the velocity gradient, and its SI unit is the pascal second (Pa\u00b7s). Honey has high viscosity; water and air have low viscosity.\n\n<\/p><\/div>\n\n

Tip a jar of honey and a glass of water over at the same moment. The water is gone in a second; the honey is still deciding. Same gravity, same tilt \u2014 utterly different behaviour.<\/p>\n\n

That difference has a name, a formula and a unit, and it governs far more than breakfast. It sets how thick your engine oil needs to be in January, why blood struggles through narrowed arteries, and why a spoonful of custard turns solid when you stir it fast.<\/p>\n\n

What Is Viscosity?<\/h2>\n\n

Viscosity is a measure of how strongly a fluid resists being sheared \u2014 that is, how hard it is to make one layer of the fluid slide over the layer beneath it. High viscosity means the fluid fights the motion; low viscosity means it gives way easily.<\/p>\n\n

Think of a deck of cards lying flat. Push the top card sideways and the cards below drag along a little, held back by friction between the surfaces<\/a>. A fluid does the same thing \u2014 except the “cards” are molecular layers, and the resistance between them is viscosity.<\/p>\n\n

Two details make this work. First, fluid touching a solid surface sticks to it and moves with it \u2014 the no-slip condition<\/strong>. Second, because the wall holds one edge still and something else drags the other edge along, the speed must change gradually across the gap.<\/p>\n\n

That change in speed with distance is the velocity gradient<\/strong>. Viscosity is simply the constant that links it to the force required.<\/p>\n\n

The Viscosity Formula<\/h2>\n\n

The viscosity formula states that shear stress equals dynamic viscosity multiplied by the velocity gradient. This is Newton’s law of viscosity, and it is the definition from which every viscosity unit follows.<\/p>\n\n

\u03c4 = \u03bc(du\/dy)<\/div>\n\n

Each symbol carries a specific SI unit:<\/p>\n\n

    \n
  • \u03c4<\/strong> (tau) \u2014 shear stress: the tangential force per unit area on a fluid layer, in pascals (Pa), equal to N\/m2<\/sup>.<\/li>\n
  • \u03bc<\/strong> (mu) \u2014 dynamic viscosity, the fluid property itself, in pascal seconds (Pa\u00b7s).<\/li>\n
  • du\/dy<\/strong> \u2014 velocity gradient or shear rate: how quickly flow speed changes across the gap, in reciprocal seconds (s\u22121<\/sup>).<\/li>\n
  • u<\/strong> \u2014 local flow speed, in metres per second (m\/s).<\/li>\n
  • y<\/strong> \u2014 distance measured perpendicular to the flow, in metres (m).<\/li>\n<\/ul>\n\n

    Rearranged, \u03bc = \u03c4 \u00f7 (du\/dy). So dynamic viscosity is the shear stress needed per unit of shear rate \u2014 and that is exactly what a Pa\u00b7s means: one pascal of stress producing a shear rate of one per second.<\/p>\n\n

    \n
    \"Viscosity<\/figure>\n<\/div>\n\n

    Fluid sheared between two plates. The no-slip condition pins the fluid to each plate, producing a steady velocity gradient across the gap.<\/p>\n\n

    <\/span>Viscosity Lab<\/span><\/div>