### 14.3.1. Example: Reynolds Number Dependent Viscosity

In this example it is assumed that some of the fluid properties, including the dynamic viscosity, are not known. However the Reynolds number, inlet velocity and a length scale are known. The flow is compressible and therefore the density is variable.

Given this information it is possible to calculate the fluid dynamic viscosity based on the Reynolds number. The Reynolds number is given by:

where is density, U a velocity scale, L a length scale and the dynamic viscosity. The velocity scale is taken as the inlet velocity, the length scale as the inlet width and the density is calculated as the average density over the inlet area.

The LIBRARY section of the CCL (CFX Command Language) file appears as follows:

    LIBRARY :
       CEL :
          EXPRESSIONS :
             Re = 4.29E6 [  ]
             Vel = 60 [m s^-1]
             L=1.044[m]
             Visc=areaAve(density)@in*Vel*L/Re
          END
       END
       MATERIAL : Air Ideal Gas
          Option = Pure Substance
          PROPERTIES :
             Option = Ideal Gas
             Molar Mass = 2.896E1 [kg kmol^-1]
             Dynamic Viscosity = Visc
             Specific Heat Capacity = 1.E3 [J kg^-1 K^-1]
             Thermal Conductivity = 2.52E-2 [W m^-1 K^-1]
          END
       END
    END

This shows that four CEL expressions have been created. The first three expressions define constant values that are used in the `Visc` expression. The `Visc` expression calculates the dynamic viscosity based on the equation for Reynolds number given above. Within the expression the function `areaAve(density)@in` is used to evaluate the average density at the inlet.

The `Visc` expression can now be used to replace the value of `Dynamic Viscosity` in the `MATERIAL` > `PROPERTIES` section.

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