Solution Found!
Some non-Newtonian fluids behave as a Bingham plastic .
Chapter 2, Problem 110P(choose chapter or problem)
Problem 110P
Some non-Newtonian fluids behave as a Bingham plastic . For which shear stress can be expressed as τ = τy+ μ (duldr) for laminar flow of a Bingham plastic in a horizontal pipe radius R, the velocity profile is given as u(r) = (ΔP/4μL)(r2 − R2) + (τy/μ)(r − R), where ΔP/L is the constant pressure drop along the pipe per unit length, fi is the dynamic viscosity, r is the radial distance from the centerline, and τy is the yield stress of Bingham plastic. Determine (a) the shear stress at the pipe wall and (b) the drag force acting on a pipe section of length L.
Questions & Answers
QUESTION:
Problem 110P
Some non-Newtonian fluids behave as a Bingham plastic . For which shear stress can be expressed as τ = τy+ μ (duldr) for laminar flow of a Bingham plastic in a horizontal pipe radius R, the velocity profile is given as u(r) = (ΔP/4μL)(r2 − R2) + (τy/μ)(r − R), where ΔP/L is the constant pressure drop along the pipe per unit length, fi is the dynamic viscosity, r is the radial distance from the centerline, and τy is the yield stress of Bingham plastic. Determine (a) the shear stress at the pipe wall and (b) the drag force acting on a pipe section of length L.
ANSWER:
Step 1
The shear stress in this case is given by
(1)
And the velocity profile is given by
(2)
Now using this two equation we have to calculate the shear stress at the pipe wall and then we have to calculate the drag force for the length .
