Pipe Flow for Power-Law and Carreau Fluids
Pipe Flow for Power-Law and Carreau Fluids
The velocity profile versus radial position is obtained for the steady-state laminar flow of power-law and Carreau fluids in a pipe. The pipe radius is and the applied pressure gradient is =1. For both the power-law and Carreau fluids, the green dots represent the solutions obtained using the Chebyshev collocation technique. The velocity profile for a power-law fluid (the blue curve) is obtained from the analytical solution given by [1, 2]. The velocity profile for a Carreau fluid (the red curve) is obtained using the shooting technique and the built-in Mathematica function NDSolve. For both fluids, you can vary the exponent (see Details section).
R=1
ΔP
L
v(r)=(-)/(1+1/n)
1/n
ΔP
2Lκ
1+1/n
R
1+1/n
r