Show that the Navier-Stokes equations for a three dimensional, incompressi- ble, and Newtonian fluid are: DV, = pg x %D dx? dy? ,2 dz? Dt DV, y (a?v, a?v, a?v, ƏP pg y y y + + Dt dy dx? dy? az? ӘР = pg z dx 2²v, ¸ a²v, ¸ a²v; dy? DV, + + %3D Dt dx? ,2 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
icon
Related questions
Topic Video
Question

Find the condition for this velocity vector to be the solution to the Navier-Stokes equations.

Show that the Navier-Stokes equations for a three dimensional, incompressi-
ble, and Newtonian fluid are:
DV,
= pg x
%D
dx?
dy?
,2
dz?
Dt
DV,
y
(a?v, a?v, a?v,
ƏP
pg y
y
y
+
+
Dt
dy
dx?
dy?
az?
ӘР
= pg z
dx
2²v, ¸ a²v, ¸ a²v;
dy?
DV,
+
+
%3D
Dt
dx?
,2
dz?
Transcribed Image Text:Show that the Navier-Stokes equations for a three dimensional, incompressi- ble, and Newtonian fluid are: DV, = pg x %D dx? dy? ,2 dz? Dt DV, y (a?v, a?v, a?v, ƏP pg y y y + + Dt dy dx? dy? az? ӘР = pg z dx 2²v, ¸ a²v, ¸ a²v; dy? DV, + + %3D Dt dx? ,2 dz?
Two components of a two-dimensional flow are given
:
V = x - y and V, = -2xy.
as
Transcribed Image Text:Two components of a two-dimensional flow are given : V = x - y and V, = -2xy. as
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Knowledge Booster
Fluid Statics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY