In the hydrodynamic entrance region of a pipe with a steady flow of an incompressible liquid

A. The average velocity increases with distance from the entrance.
B. The average velocity stays the same with distance from the entrance.
C. The maximum velocity increases with distance from the entrance.
D. The maximum velocity decreases with distance from the entrance.
E. B and C
F. B and D

C. The maximum velocity increases with distance from the entrance

Explanation:

As the fluid particles moves into the pipe, the layer of fluid in contact with the surface of the pipe come to a complete stop. This layer also causes the fluid

particles in the adjacent layers to gradually slow down as a result of friction between fluid molecules, leaving the fluid at the center of the pipe with the maximum velocity.

Since the fluid is incompressible, to make up for this velocity reduction, the velocity of the fluid at the mid-

section of the pipe has to increase to keep the mass flow rate through the

pipe constant. As a result, a velocity gradient develops along the pipe and the maximum velocity which is at the center of the pipe increases with distance from entrance.