Hydraulic Library User Manual - NUPET

Hydraulic Library 4.2User ManualHowever the absolute viscosity is not very often used in fundamental equations.For example the dynamics of the elementary volume between the two layers isexpressed as:A-----dydτ = ρAdy--------------dU( y)dydtand thus using the shear stress calculation:dU--------------( y)--1-----dτ --µ d2 Uy= = -----------------( )dt ρdyρ dy 2In other formulas (e.g. Navier Stokes) the ratio between the absolute viscosity andthe density occurs so often that a new parameter called the kinematic viscosity ν isintroducedµν = --ρof dimension [L 2 T -1 ] and so the SI unit is the m 2 /s. The older unit of kinematicviscosity is the Stoke, St, which is 10 -4 m 2 /s. However, even this is a very smallunit and hence the centistoke cSt is the common unit with 1 cSt = 10 -6 m 2 /s. Thisparameter is easily measured with viscometers.Note that the viscosity varies significantly with the fluid temperature.Figure 2.50: Viscosity against temperatureNormally in absence of air release and cavitation the variation with pressure is notgreat unless the pressure is very extreme.47