# Fluid Viscosity Properties

## Fluid Viscosity

Fluid Viscosity, sometimes referred to as dynamic viscosity or absolute viscosity, is the fluid's resistance to flow, which is caused by a shearing stress within a flowing fluid and between a flowing fluid and its container.

Viscosity is usually denoted by the Greek symbol μ (mu) and is defined as the ratio of shearing stress τ (Greek letter tau) to the rate of change of velocity, v, which in mathematical terms can be expressed as dv/dy (where this is the derivative of the of the velocity with respect to the distance y).

The derivative dv/dy is called the velocity gradient.

This results in the important equation for fluid shear for viscous or laminar flow:

τ = μ•dv/dy

However, the above equation is not applicable for turbulent flow where a large amount of the shear stress is due to the exchange of momentum between adjacent layers of the fluid. To determine whether the flow is laminar or turbulent requires that you calculate the Reynold's number of the flowing fluid. Laminar flow will occur where the Reynold's number is less than 2300.

From the above equation it can be determined that the dimensions of viscosity are force multiplied by time divided by length squared or FT/L² The units of viscosity in the English system and the SI system are:

lb•sec/ft² or Slug/ft•sec and N•s/m² or kg/m•s

### Dynamic Viscosity / Absolute Viscosity

The Pascal unit (Pa) is specifies pressure, or stress = force per area

Pascals can be combined with time (seconds) to define dynamic viscosity.

μ = Pa•s

1.00 Pa•s = 10 Poise = 1000 Centipoise

Centipoise (cP) is commonly used to describe dynamic viscosity because water at a
temperature of 20°C has a viscosity of 1.002 Centipoise.

This value must be converted back to 1.002 x 10^-3 Pa•s for use in calculations.

### Kinematic Viscosity

Viscosity can be measured by timing the flow of a known volume of fluid from a
viscosity measuring cup. The timings can be used in a formula to estimate the
kinematic viscosity value of the fluid in Centistokes (cSt).

The motive force driving the fluid out of the cup is the head of fluid, which is also contained within the equation that makes up the volume of the fluid. When the equations are rationalized the fluid head term is eliminated leaving the units of Kinematic viscosity as area / time.

v = m²/s

1.0 m²/s = 10000 Stokes = 1000000 Centistokes

Water at a temperature of 20°C has a viscosity of 1.004 x 10^-6 m²/s

This evaluates to 1.004000 Centistokes.

This value must be converted back to 1.004 x 10^-6 m²/s for use in calculations.

The kinematic viscosity can also be determined by dividing the dynamic viscosity by the fluid density.

### Kinematic Viscosity and Dynamic Viscosity Relationship

Kinematic Viscosity = Dynamic Viscosity / Density

v = μ/ρ