Consider the simple power-law model for a non-Newtonian fluid given by Eq. 2.16. Extend the analysis of

Question:

Consider the simple power-law model for a non-Newtonian fluid given by Eq. 2.16. Extend the analysis of Section 8.2 to show that the velocity profile for fully developed laminar flow of a powerlaw fluid between stationary parallel plates separated by distance $2 h$ may be written

\[u=\left(\frac{h}{k} \frac{\Delta p}{L}\right)^{1 / n} \frac{n h}{n+1}\left[1-\left(\frac{y}{h}\right)^{(n+1) / n}\right]\]

where $y$ is the coordinate measured from the channel centerline. Plot the profiles $u / U_{\max }$ versus $y / h$ for $n=0.7,1.0$, and 1.3.

Data From Equation 2.16

image text in transcribed