Viscous liquid, at volume flow rate Q. is pumped through the central opening into the narrow gap between the parallel disks shown. The flow rate is low, so the flow is laminar, and the pressure gradient due to convective acceleration in the gap is negligible compared with the gradient caused by viscous forces (this is termed creeping flow). Obtain a general expression for the variation of average velocity in the gap between the disks. For creeping flow, the velocity profile at any cross section in the gap is the same as for fully developed flow between stationary parallel plates. Evaluate the pressure gradient, dp/dr, as a function of radius. Obtain an expression for p(r). Show that the net force required to hold the upper plate in the position shown is
Viscous liquid, at volume flow rate Q. is pumped through the central opening into the narrow gap between the parallel disks shown. The flow rate is low, so the flow is laminar, and the pressure gradient due to convective acceleration in the gap is negligible compared with the gradient caused by viscous forces (this is termed creeping flow). Obtain a general expression for the variation of average velocity in the gap between the disks. For creeping flow, the velocity profile at any cross section in the gap is the same as for fully developed flow between stationary parallel plates. Evaluate the pressure gradient, dp/dr, as a function of radius. Obtain an expression for p(r). Show that the net force required to hold the upper plate in the position shown is
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:1. Viscous liquid, at volume flow rate Q, is pumped through the central opening
into the narrow gap between the parallel disks shown. The flow rate is low,
so the flow is laminar, and the pressure gradient due to convective
acceleration in the gap is negligible compared with the gradient caused by
viscous forces (this is termed creeping flow). Obtain a general expression for
the variation of average velocity in the gap between the disks. For creeping
flow, the velocity profile at any cross section in the gap is the same as for
fully developed flow between stationary parallel plates. Evaluate the pressure
gradient, dp/dr, as a function of radius. Obtain an expression for p(r). Show
that the net force required to hold the upper plate in the position shown is
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