Viscosity

Viscosity of a fluid can be thought of as how resistant a fluid is to flow. Fluids with high viscosity, like honey, don’t flow as easily compared to low viscosity fluids, like water. It can be compared to friction in solids.

Definition §

More technically, viscosity is the internal frictional force between layers of fluid. In liquids, this is due to the cohesive electric force between molecules, while in gases it is due to scattering events (#tosee ).

Formula §

Viscosity of a Fluid

$$F=\eta A\frac{v}{l}⟺\eta =\frac{Fl}{Av}$$

Terms §

• $F$ = Force required to overcome viscosity (in $\text{N}$)
• $A$ = Area of the fluid ‘layer’ (in ${\text{m}}^2$)
• $\frac{v}{l}$ = Velocity gradient
  • $v$ = Speed of the top ‘layer’ of fluid (in $\text{m/s}$)
  • $l$ = Width of the fluid (in $\text{m}$)
• $\eta$ = Coefficient of viscosity, determines how viscous a fluid is. (in ${\text{Ns/m}}^2\text{ or Pa}\cdot \text{s}$)

Picture a static ideal fluid between two plates, one moving and one static. Then each ‘layer’ of fluid slowly beings to move, due to the adhesiveness (#tosee ) of the fluid. Then

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