Final answer:
A parabolic velocity profile in a pipe flow indicates the flow is laminar, developed, steady, and symmetric, which corresponds to all four given characteristics (I, II, III, IV).
Step-by-step explanation:
The student's question is concerned with a parabolic velocity profile observed in a pipe flow and the categorization of this flow. A parabolic velocity profile, where the velocity is greatest at the center and decreases towards the walls due to friction, is indicative of a laminar flow. According to the principles of fluid mechanics, such a flow is generally smooth and orderly, with layers of fluid sliding past each other. This profile also implies that the flow is fully developed, meaning the velocity profile does not change with further movement along the pipe's length. Steady flow indicates that the fluid's velocity at any given point does not change over time, and symmetric flow suggests the velocity profile is mirrored across the pipe's central axis. Therefore, given that a parabolic profile typically signifies each of these characteristics, the flow is: I. Laminar, II. Developed, III. Steady, IV. Symmetric. Answer: D. I, II, III, and IV.