Problems 2.196 and 2.197A micro spiral pump consists of a spiral channel attached to a stationary plate. Thislate bas two ports, one for fluid inlet and another for outlet, the outlet being farther fromche center of the plate than the inlet. The system is capped by a rotating disk. The fluidanned between the rotating disk and the stationary plate is put in motion by the rotationof the top disk, which pulls the fluid through the spiral channel.spin axisrotating disk-inletpin joint-outletspiral groovestationary plate-Figure P2.196 and P2.197Problem 2.197 Consider a spiral channel with the geometry given by the equationr= n0 +ro, where n = 12 um is called the polar slope, ro = 146 um is the startingradius, r is the distance from the spin axis, and 6, measured in radians, is the angularposition of a point in the spiral channel. If the top disk rotates with a constant angularspeed w = 30,000 rpm, and assuming that the fluid particles in contact with the rotatingdisk are essentially stuck to it, use the polar coordinate system shown and determine thevelocity and acceleration of one fluid particle when it is at r = 170 µm.

Answered: Image /qna-images/answer/d3a0bb06-d8fd-48f8-987c-8a4f65565126.jpg

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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Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

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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.

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