The rotating disk viscometer is a precise device for measuring the viscosity of fluids. In this type of viscometer, the flow develops in the gap (H) between the two parallel horizontal circular plates (disks) that have each a radius (R). The upper disk is rotated at a constant angular velocity (0) while the lower one is fixed. This results in a flow where only the angular component of the velocity vector (ve) is nonzero. It is possible to show that the flow velocity is: Ve(r,z)= 0.r.z/H. (a) Check that this velocity does indeed satisfy the continuity equation and the Navier-Stokes equation in the 0-direction, for steady, incompressible flow. Check that it also satisfies the boundary conditions at the lower and upper disks.
The rotating disk viscometer is a precise device for measuring the viscosity of fluids. In this type of viscometer, the flow develops in the gap (H) between the two parallel horizontal circular plates (disks) that have each a radius (R). The upper disk is rotated at a constant angular velocity (0) while the lower one is fixed. This results in a flow where only the angular component of the velocity vector (ve) is nonzero. It is possible to show that the flow velocity is: Ve(r,z)= 0.r.z/H. (a) Check that this velocity does indeed satisfy the continuity equation and the Navier-Stokes equation in the 0-direction, for steady, incompressible flow. Check that it also satisfies the boundary conditions at the lower and upper disks.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The rotating disk viscometer is a precise device for measuring the viscosity of fluids. In this type of viscometer, the flow develops in the gap (H) between the two parallel horizontal circular plates (disks) that have each a radius (R). The upper disk is rotated at a constant angular velocity (0) while the lower one is fixed. This results in a flow where only the angular component of the velocity
Transcribed Image Text:The rotating disk viscometer is a precise device for measuring the viscosity of fluids. In this type of
viscometer, the flow develops in the gap (H) between the two parallel horizontal circular plates (disks)
that have each a radius (R). The upper disk is rotated at a constant angular velocity (0) while the lower
one is fixed. This results in a flow where only the angular component of the velocity vector (ve) is
nonzero. It is possible to show that the flow velocity is:
Ve(r,z)= 0.r.z/H.
(a) Check that this velocity does indeed satisfy the continuity equation and the Navier-Stokes
equation in the 0-direction, for steady, incompressible flow. Check that it also satisfies the
boundary conditions at the lower and upper disks.
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Transcribed Image Text:(b) Use the above expression of the velocity to determine the expression of the torque (I) required
to rotate the upper disk a constant angular velocity (o) when the gap is filled with a fluid of
viscosity (μ).
(c) An experiment found that a torque of 0.01 Nm is needed to rotate the disk at 500rpm. What is
the viscosity of the fluid if the viscometer's radius and gap are 5cm and 2mm, respectively?
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