1. 29. Non-Newtonian Flow 2
CH EN 374: Fluid Mechanics

3. Quiz 14 (1 pt) Is toothpaste viscoelastic or viscoplastic?
(1 pt) Is cornstarch and water shear thinning or shear thickening?
(1 pt) Are the velocity profiles of laminar and turbulent flow the same or different?
(2 pts) Natural gas enters a nozzle (below) at Ma = 0.8. Will this flow ever become choked?

4. 𝜏=− 𝜇 0 𝑑𝑣 𝑑𝑦 𝑛 Power Law Fluid FLOW INDEX APPARENT VISCOSITY
𝜏=− 𝜇 0 𝑑𝑣 𝑑𝑦 𝑛
APPARENT VISCOSITY
What equations will change compared to a Newtonian fluid?

5. Velocity Profile Laminar flow, circular pipe:
𝑣 𝑟 = 𝑛 𝑛 Δ𝑃 𝐿 1 2 𝜇 /𝑛 𝑅 𝑛+1 𝑛 − 𝑟 𝑛+1 𝑛
Laminar flow, circular pipe:

6. Reynold’s Number 𝑅 𝑒 𝑃𝐿 = 2 3−𝑛 𝑛 3𝑛+1 𝑛 𝑣 2−𝑛 𝐷 𝑛 𝜌 𝜇 0
𝑅 𝑒 𝑃𝐿 = 2 3−𝑛 𝑛 3𝑛+1 𝑛 𝑣 2−𝑛 𝐷 𝑛 𝜌 𝜇 0
Critical Reynold’s Number (laminar-turbulent transition):
𝑅 𝑒 𝑃𝐿,𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 =2100 (4𝑛+2)(5𝑛+3) 3 3𝑛+1 2

7. Friction Factor
Laminar flow, circular pipe:
𝑓= 16 𝑅𝑒
Yay!

8. Friction Factor
Turbulent flow, circular pipe:

9. ℎ 𝐿 =2𝑓 𝐿 𝐷 𝑣 2 𝑔 Head Loss Head loss equation stays the same!
ℎ 𝐿 =2𝑓 𝐿 𝐷 𝑣 2 𝑔
Always true for laminar, turbulent, rough, smooth, Newtonian, Non-Newtonian…

10. Kinetic Energy Correction Factor
𝛼= 3 3𝑛 (2𝑛+1)(5𝑛+3)

11. Problem
A coal slurry is to be transported by horizontal pipeline. It has been determined that the slurry may be described by the power law model with a flow index of 0.4, an apparent viscosity of 50 cP at a shear rate of 100 /s, and a density of 90 lb/ft3. What horsepower would be required to pump the slurry at a rate of 900 GPM through an 8 in. pipe that is 50 miles long ?
P = 1atm
P = 1atm
L = 50 miles