Turbulence in Viscoelastic Fluids 



f ^ Purely viscous friction factor (17) 



F Friction factor ratio, Fig. 4 



I Unit tensor 



n' Flow behavior index (17) 



^Deb Deborah number, Eq. (4) 



N^g Generalized Reynolds number (17) 



Ny^ Viscoelastic ratio number, Eq. (3b) 



Nyj^ Weissenberg number, Eq. (3a) or (3c) 



p Isotropic pressure 



u Local velocity in pipe 



u* Friction velocity /\/p 



V Tube velocity, Eq. (3a); stretching velocity, Eq. (6) 



X Length (or Cartesian coordinate direction in Eq. (8)) 



y Distance from pipe wall 



S/St Convected time derivative (42) 



D/Dt Material time derivative 



II Second invariant of rate of strain tensor 



Fluid relaxation time, Eq. (1) 



/u Variable viscosity coefficient, Eq. (1) 



jl Fluid viscosity coefficient, Eq. (2) 



u Kinematic viscosity 



^ Fluid stretch rate, defined by Eq. (6) 



P Fluid density 



0)^,0)2 Fluid material properties, Eq. (2) 



r' Stress tensor, components r'^i, relative to arbitrary hydrostatic 

 pressure a (61): t = - ai + t' 



33 



