The Cox-Merz rule for the first normal stress difference is only valid for a limited range of shear rates. Laun [7] has proposed an empirical rule that is valid over a larger interval of shear rates, and is given by the following:

(9–7)

Equation 9–7 is found to be valid for polyethylenes. Similar relationships can be created for other families of polymers.

Using an elastic recoil mechanism, Tanner [11] proposed a simple expression that relates the extrudate diameter to the first normal stress difference, as follows:

(9–8)

where and are the diameters of the extrudate and of the die, respectively, and is the wall shear stress in the capillary die.