A thin layer of spherical particles rests on the bottom of a horizontal tube as shown in the figurebelow. When an incompressible fluid flows through the tube, it is observed that at some criticalvelocity the particles will rise and be transported along the tube. A model is to be used todetermine this critical velocity. Assume the critical velocity, V, to be a function of the pipediameter, D, particle diameter, d, the fluid density, p, and viscosity, μ, the density of the particles,Pp, and the acceleration of gravity, g. For a length scale of Dm/D=1/2 and a fluid density scale ofPm/p=1/0.9, what will be the critical velocity scale V/V (assuming all similarity requirements aresatisfied)?Vm/V=i

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A thin layer of spherical particles rests on the bottom of a horizontal tube as shown in the figure below. When an incompressible fluid flows through the tube, it is observed that at some critical velocity the particles will rise and be transported along the tube. A model is to be used to determine this critical velocity. Assume the critical velocity, V₁, to be a function of the pipe diameter, D, particle diameter, d, the fluid density, p, and viscosity, μ, the density of the particles, Pp, and the acceleration of gravity, g. For a length scale of Dm/D=1/2 and a fluid density scale of Pm/p=1/0.9, what will be the critical velocity scale V/V (assuming all similarity requirements are satisfied)? Vm/V= Mi

A thin layer of spherical particles rests on the bottom of a horizontal tube as shown in the figure below. When an incompressible fluid flows through the tube, it is observed that at some critical velocity the particles will rise and be transported along the tube. A model is to be used to determine this critical velocity. Assume the critical velocity, V₁, to be a function of the pipe diameter, D, particle diameter, d, the fluid density, p, and viscosity, μ, the density of the particles, Pp, and the acceleration of gravity, g. For a length scale of Dm/D=1/2 and a fluid density scale of Pm/p=1/0.9, what will be the critical velocity scale V/V (assuming all similarity requirements are satisfied)? Vm/V= Mi

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Concept explainers

Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.

Question

A thin layer of spherical particles rests on the bottom of a horizontal tube as shown in the figure
below. When an incompressible fluid flows through the tube, it is observed that at some critical
velocity the particles will rise and be transported along the tube. A model is to be used to
determine this critical velocity. Assume the critical velocity, V, to be a function of the pipe
diameter, D, particle diameter, d, the fluid density, p, and viscosity, μ, the density of the particles,
Pp, and the acceleration of gravity, g. For a length scale of Dm/D=1/2 and a fluid density scale of
Pm/p=1/0.9, what will be the critical velocity scale V/V (assuming all similarity requirements are
satisfied)?
Vm/V=
i

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