The Viscosity of Gasses

Equations describing the effect of gas viscosity flow forces although still involving a fluid will differ from those of a liquid due to the compressibility of the gas.

The Poiseuille’s Equation Gas Flow Through an Open Tube

A liquid is considered incompressible and thus the equation,

can be integrated directly.

As the gas is compressible, however, the density will decrease along the tube and so if () is the density a (Q) the volume of gas passing any cross-section per unit time (Q) will be constant and as () is proportional to the pressure (P) then (PQ) will be constant for any cross section of the tube. Thus, if (P₁) is the pressure at the inlet,

Where (P₂) is the pressure at the outlet.

       Thus, integrating,                 

                   Hence,                           

                                  That is,           

The practical equation for the viscosity that includes the major correction factors, including the slipping correction derived by Erk and the Hagenbach correction is,

where () is termed the slipping constant.