Final answer:
For a steady uniform flow of an incompressible fluid entering a pipe, the maximum velocity decreases with distance from the entrance as the flow profile becomes fully developed, in accordance with the continuity equation.
Step-by-step explanation:
When considering the flow of an incompressible fluid in a pipe, the continuity equation applies, which states that the product of the cross-sectional area (A) and the velocity (v) at any point along the flow must be constant. This is because the flow rate (Q = Av) must be maintained; hence, if the cross-sectional area of a pipe decreases, the velocity must increase to compensate, ensuring the flow rate remains the same.
In the context of the entrance region of a pipe for a steady uniform flow, as the fluid transitions from the entrance to the fully developed flow, the velocity profile develops. Initially, the flow will have a high velocity at the center and slower near the edges due to viscosity.
As the fluid moves further into the pipe, this profile becomes more uniform and the maximum velocity, which is usually at the center, will generally decrease until it reaches a fully developed profile where it remains constant.
Therefore, the correct statement about the entrance region is that the maximum velocity decreases with distance from the entrance as the flow becomes fully developed.