a. Given the velocity field u=(u,v,w) in Cartesian coordinates with u=2x+y, v=2zt, w=0. . i. Find the equations of the corresponding streamlines (Eulerian concept) ii. Find the equations of the corresponding particle paths, i.e., the pathlines (Lagrangian concept). b. Show that the Vu=0 everywhere implies that volumes are conserved, i.e., the volume of red particles at t=0 is the same as at t=t. Hint: Write out what you must prove and use the theorems to get there.

a. Given the velocity field u=(u,v,w) in Cartesian coordinates with u=2x+y, v=2zt, w=0. . i. Find the equations of the corresponding streamlines (Eulerian concept) ii. Find the equations of the corresponding particle paths, i.e., the pathlines (Lagrangian concept). b. Show that the Vu=0 everywhere implies that volumes are conserved, i.e., the volume of red particles at t=0 is the same as at t=t. Hint: Write out what you must prove and use the theorems to get there.

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

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

a. Given the velocity field u=(u,v,w) in Cartesian coordinates with u=2x+y, v=2zt,
w=0.
i. Find the equations of the corresponding streamlines (Eulerian concept)
ii. Find the equations of the corresponding particle paths, i.e., the pathlines
(Lagrangian concept).
b. Show that the Vu=0 everywhere implies that volumes are conserved, i.e., the
volume of red particles at t-0 is the same as at t=t. Hint: Write out what you must
prove and use the theorems to get there.

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