Consider a steady laminar flow through the annular space formed by two coaxial tubes alignedwith the z-axis, as shown below. The flow is along the axis of the tubes and is maintained by theconstant pressure gradient. The symbol a is the radius of the inner tube and b is the radius of theouter tube, and assume that b = 3a.dp/dz9.a(a) Start with Navier-Stokes equation and assume that the body force does not affect the flow.Derive the axial velocity at any radius R (a < R < b) uz(R) in terms of dp/dz, R, a and µ(fluid dynamic viscosity).(b) Find the radius at which the maximum velocity is reached(c) Find the volume flow rate(d) Find the stress distribution

let us consider a small element of thickness dr at a radius r from the center of annular space which…

Consider a steady laminar flow through the annular space formed by two coaxial tubes aligned with the z-axis, as shown below. The flow is along the axis of the tubes and is maintained by the constant pressure gradient. The symbol a is the radius of the inner tube and b is the radius of the outer tube, and assume that b = 3a. dp/dz

Consider a steady laminar flow through the annular space formed by two coaxial tubes aligned with the z-axis, as shown below. The flow is along the axis of the tubes and is maintained by the constant pressure gradient. The symbol a is the radius of the inner tube and b is the radius of the outer tube, and assume that b = 3a. dp/dz

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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Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

Consider a steady laminar flow through the annular space formed by two coaxial tubes aligned
with the z-axis, as shown below. The flow is along the axis of the tubes and is maintained by the
constant pressure gradient. The symbol a is the radius of the inner tube and b is the radius of the
outer tube, and assume that b = 3a.
dp/dz
9.
a
(a) Start with Navier-Stokes equation and assume that the body force does not affect the flow.
Derive the axial velocity at any radius R (a < R < b) uz(R) in terms of dp/dz, R, a and µ
(fluid dynamic viscosity).
(b) Find the radius at which the maximum velocity is reached
(c) Find the volume flow rate
(d) Find the stress distribution

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