Question

1. Some non-Newtonian fluids behave as a Bingham plastic for which shear stress can be expressed as + For laminar flow of a Bingham plastic in a horizontal pipe of radius R, the velocity profile is given as 4wr -R)+ (r-R), where AP/L is the constant pressure drop along the pipe per unit length, is the dynamic viscosity,r is the radial distance from the centerline, and is the yield stress of Bingham plastic. Develop a relation for (a) the shear stress at the pipe wall and (b) the drag force acting on a pipe section of length L. MP). AP

Answer 1

As per HOMEWORKLIB POLICY, one (first) question is answered. See solution below:

u) - Al (x2-R²) & YHL (R) - Text s du y Differentiating wits: duty) AP (2-0) + ry (1) dy - Apr dr 246 + y substitute, dy in equation ③ Taty + ( ) APY 1244

= Ty T APY & Tu 2 L a = 274 + Opr 2 L a) At pipe wall, var - 2Ty & APR e answer 6) Drag force F=T. As As surface area of pipe As = IT (2R). I - 2TIRL ..F=(2Ty + OP. 2) 25RL 21 F = 4TRL Ty & TAL AP tanswer.