2] Consider the following stedy, incompressible, two-dimensional velocity field: V=(u,v)=(0.5+1.2x) i+ (-2,0-1.2y) j Senerate an analytical expression for the flow streamlines and draw several streamlin he upper-right quadrant from x=0 to 5 and y=0 to 6. (Here use the relation: dy/dx=v

2] Consider the following stedy, incompressible, two-dimensional velocity field: V=(u,v)=(0.5+1.2x) i+ (-2,0-1.2y) j Senerate an analytical expression for the flow streamlines and draw several streamlin he upper-right quadrant from x=0 to 5 and y=0 to 6. (Here use the relation: dy/dx=v

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

[2] Consider the following stedy, incompressible, two-dimensional velocity field:
V=(u,v)=(0.5+1.2x) 7+ (-2.0-1.2y)
Generate an analytical expression for the flow streamlines and draw several streamlines in
the upper-right quadrant from x=0 to 5 and y=0 to 6. (Here use the relation: dy/dx=v/u in
the streamlines.)

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(2) Consider the following fluid velocity fields: F(x,y) = (x,y), F(x,y)=(-x, y), F(x,y) = (y, 0). (a) Plot the three fields as glyphs. Which of these vector fields represent an expansion, a compression and a shear flow? (b) Calculate the divergence of the three fields V F. Can you relate the value of the divergence with the nature (compression, expansion or shear of the flow)? (c) Calculate the circulation V x F and relate it with the nature of the flow.