1. Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. a) Is the flow field incompressible at all times? b) Compute the convective derivative of each velocity component: Du/Dt and Dv/Dt. c) By considering the velocity gradients, determine whether the fluid elements experience any deformation. What type(s) of deformation do they experience? d) Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational. e) Given that the density of the fluid does not vary spatially and changes only with time, what differential equation for the density, p(t), must be satisfied for this scenario to represent a physical, compressible flow field? f) At time t=0, the density everywhere is p = po. Determine how the density changes with time, given the situation does represent a physical, compressible flow field.

1. Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. a) Is the flow field incompressible at all times? b) Compute the convective derivative of each velocity component: Du/Dt and Dv/Dt. c) By considering the velocity gradients, determine whether the fluid elements experience any deformation. What type(s) of deformation do they experience? d) Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational. e) Given that the density of the fluid does not vary spatially and changes only with time, what differential equation for the density, p(t), must be satisfied for this scenario to represent a physical, compressible flow field? f) At time t=0, the density everywhere is p = po. Determine how the density changes with time, given the situation does represent a physical, compressible flow field.

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

1.
Consider a two-dimensional flow which varies in time and is defined by
the velocity field, u = 1 and v = 2yt.
a) Is the flow field incompressible at all times?
b) Compute the convective derivative of each velocity component: Du/Dt
and Dv/Dt.
c) By considering the velocity gradients, determine whether the fluid
elements experience any deformation. What type(s) of deformation do
they experience?
d) Do the fluid elements experience angular rotation? Thus, state whether
the flow field is rotational or irrotational.
e) Given that the density of the fluid does not vary spatially and changes
only with time, what differential equation for the density, p(t), must be
satisfied for this scenario to represent a physical, compressible flow
field?
f) At time t = 0, the density everywhere is p = Po. Determine how the
density changes with time, given the situation does represent a
physical, compressible flow field.

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