Final answer:
The velocity profile for a Bingham fluid flowing under laminar conditions in a pipe is flat near the wall and parabolic in the middle, due to the yield stress characteristic of Bingham fluids.
Step-by-step explanation:
The velocity profile for a Bingham fluid flowing under laminar conditions in a pipe is different from that of Newtonian fluids. Bingham fluids require a certain amount of stress, known as yield stress, before they begin to flow like a fluid. Once the yield stress is exceeded, the fluid flows with a characteristic profile: flat near the wall and parabolic in the middle. This is because the fluid behaves like a rigid body at the pipe wall (where the stress is less than the yield stress), and as the stress increases away from the wall, the fluid starts to flow, developing a parabolic profile towards the center where the shear rate is higher.