Discussion
For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the following statements about the average velocity in the developing region is TRUE?
Answer: B
The average velocity is constant and equal to the average velocity in the fully developed region.
For incompressible flow the volume flow rate is the same at every cross-section, and the pipe area is constant, so the average velocity Q/A cannot change anywhere along the pipe.
What changes in the entrance region is the velocity profile: the boundary layer grows, the fluid near the wall slows down and the core speeds up, until the parabolic profile of fully developed laminar flow is reached. The centreline velocity rises, but the average stays fixed. So the options saying the average increases, decreases or is lower all contradict continuity.
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