Under laminar pipe flow conditions, what is the ratio of centerline fluid velocity to the cross-sectional mean velocity?
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Answer: D. 2
Explanation
Laminar pipe flow features a symmetrical parabolic velocity profile across the cross-section. The maximum fluid velocity occurs directly at the central axis of the pipe. Integration proves the centerline velocity is precisely twice the cross-sectional mean velocity. No-slip boundary conditions force fluid velocity to zero at the inner pipe wall. Viscous shear forces shape the parabolic velocity distribution in laminar flow regimes. Mean velocity represents the volumetric flow rate divided by the total cross-sectional area.
Pipeline transport of heavy viscous oils often operates under laminar flow conditions. Laboratory viscometers utilize centerline velocity relationships to determine fluid properties. Fluid mechanics students calculate velocity ratios to understand internal boundary dynamics. Equal centerline and mean velocities only occur in idealized plug flow velocity profiles. Fractional ratios such as 0.5 or 0.67 contradict the parabolic integration math. Turbulent flows exhibit flatter velocity profiles with lower centerline-to-mean ratios.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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