Problem 2.197 i Consider a spiral channel with the geometry given by the equation r= +ro where 7 = radius, r is the distance from the spin axis, and 0, measured in radians, is the angular position of a point in the spiral channel. If the top disk rotates with a constant angular speed o = 30,000 rpm, and assuming that the fluid particles in contact with the rotating disk are essentially stuck to it, use the polar coordinate system shown and determine the velocity and acceleration of one fluid particle when it is at r = 170 um. 12 um is called the polar slope, ro = 146 um is the starting %3D %3D
Problem 2.197 i Consider a spiral channel with the geometry given by the equation r= +ro where 7 = radius, r is the distance from the spin axis, and 0, measured in radians, is the angular position of a point in the spiral channel. If the top disk rotates with a constant angular speed o = 30,000 rpm, and assuming that the fluid particles in contact with the rotating disk are essentially stuck to it, use the polar coordinate system shown and determine the velocity and acceleration of one fluid particle when it is at r = 170 um. 12 um is called the polar slope, ro = 146 um is the starting %3D %3D
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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![Problems 2.196 and 2.197
A micro spiral pump consists of a spiral channel attached to a stationary plate. This
late bas two ports, one for fluid inlet and another for outlet, the outlet being farther from
che center of the plate than the inlet. The system is capped by a rotating disk. The fluid
anned between the rotating disk and the stationary plate is put in motion by the rotation
of the top disk, which pulls the fluid through the spiral channel.
spin axis
rotating disk-
inlet
pin joint-
outlet
spiral groove
stationary plate-
Figure P2.196 and P2.197
Problem 2.197 Consider a spiral channel with the geometry given by the equation
r= n0 +ro, where n = 12 um is called the polar slope, ro = 146 um is the starting
radius, r is the distance from the spin axis, and 6, measured in radians, is the angular
position of a point in the spiral channel. If the top disk rotates with a constant angular
speed w = 30,000 rpm, and assuming that the fluid particles in contact with the rotating
disk are essentially stuck to it, use the polar coordinate system shown and determine the
velocity and acceleration of one fluid particle when it is at r = 170 µm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6d25f93-4fe5-4c6f-9fdd-86868360ff0d%2Fd3a0bb06-d8fd-48f8-987c-8a4f65565126%2Fi50e5qm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problems 2.196 and 2.197
A micro spiral pump consists of a spiral channel attached to a stationary plate. This
late bas two ports, one for fluid inlet and another for outlet, the outlet being farther from
che center of the plate than the inlet. The system is capped by a rotating disk. The fluid
anned between the rotating disk and the stationary plate is put in motion by the rotation
of the top disk, which pulls the fluid through the spiral channel.
spin axis
rotating disk-
inlet
pin joint-
outlet
spiral groove
stationary plate-
Figure P2.196 and P2.197
Problem 2.197 Consider a spiral channel with the geometry given by the equation
r= n0 +ro, where n = 12 um is called the polar slope, ro = 146 um is the starting
radius, r is the distance from the spin axis, and 6, measured in radians, is the angular
position of a point in the spiral channel. If the top disk rotates with a constant angular
speed w = 30,000 rpm, and assuming that the fluid particles in contact with the rotating
disk are essentially stuck to it, use the polar coordinate system shown and determine the
velocity and acceleration of one fluid particle when it is at r = 170 µm.
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