Viscosity

Key Concept: Viscosity is a measure of the resistance of a fluid to shear rate. "Thicker" fluids

have a higher shear rate.

In a Nut Shell: Clearly water flows more freely than molasses. The fluid property exhibited in

this case is viscosity. For Newtonian fluids the shear stress, τ, is directly proportional to the time

rate of shearing strain, du/dy, developed in the fluid. The proportionality constant, μ, is called the “dynamic” or “absolute”, viscosity.

The governing relation relating shear stress to time rate of shear strain for a Newtonian fluid takes

the following form:

τ = μ du/dy

An important characteristic of viscous fluids is the so-called, “no-slip” condition at solid boundaries.

For viscous fluids the fluid velocity increases from zero, at the boundary, to some value at the edge

of the “boundary layer” beyond which the velocity can be approximated as uniform.

Kinematic viscosity, ν, is the ratio of the dynamic viscosity to the density of the fluid as given

below.

ν = μ / ρ

The table below list dimensions and common units related to viscosity.

Quantity Dimensions Common Units

τ shear stress	F/L^2	lb/in^2, lb/ft^2, N/m^2
μ dynamic viscosity	FT/L^2	lb sec/ft^2 , N sec/m^2
ν kinematic viscosity	L^2/T	ft^2/sec, m^2/sec
du/dy rate of shearing strain	1/T	1/sec
ρ fluid density	FT^2/L^4 or M/L^3	slugs/ft^3, kg/m^3

Dynamic (or kinematic) viscosity may be temperature dependent, such as exhibited in

multi-grade oil (10W30 as an example). See appendices in text. Click here for examples.

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