WOLFRAM|DEMONSTRATIONS PROJECT

Pipe Flow for Power-Law and Carreau Fluids

​
power-law exponent
1
Carreau exponent
0.5
power-law
Carreau
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
R=1
and the applied pressure gradient is
ΔP
L
=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
v(r)=
1/n
ΔP
2Lκ
(
1+1/n
R
-
1+1/n
r
)/(1+1/n)
[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).