a) Can we use the incompressible Navier-Stokes equations: Conservation of mass: du, dv dw dx dy dz Conservation of momentum: du +u- at dp pgx PuPuu dz? du du dy du dz dv +u dt dp dy dv dv dv dy dz ax? ay dz? Pw w w ax ay dx dw + w dw + v- Əx dw dw +w- dp dz? for the flow defined by the following velocity field? (2x-y)t U = v = -(x+ 2y)t b) What other assumptions are inherent to this velocity field? Rewrite the simplified set of equations (using assumptions) for this flow. c) Find an expression for the pressure.

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
Question
a) Can we use the incompressible Navier-Stokes equations:
Conservation of mass:
du, dv, dw
ду
dz
Conservation of momentum:
du
dt
Fu u Pu
du
du
du
+ W
+ V-
az
dy
=pgx
+
dx
dx? ay?
dz?
dv
dv
+ u
dt
dv
dv
pgyay
+v-
+w-
dy
dy? az?
aw w w
ay? dz?
dw
dw
+w-
dw
dw
+w
ду
= p9z
+
dx?
for the flow defined by the following velocity field?
(2a – y)t
U =
v = -(x + 2y)t
b) What other assumptions are inherent to this velocity field? Rewrite the simplified
set of equations (using assumptions) for this flow.
c) Find an expression for the pressure.
d) What might the boundary conditions be?
e) How would you solve the set of equations numerically by finite differences?
f) Can we use the potential equations instead?
g) Sketch the flow.
Transcribed Image Text:a) Can we use the incompressible Navier-Stokes equations: Conservation of mass: du, dv, dw ду dz Conservation of momentum: du dt Fu u Pu du du du + W + V- az dy =pgx + dx dx? ay? dz? dv dv + u dt dv dv pgyay +v- +w- dy dy? az? aw w w ay? dz? dw dw +w- dw dw +w ду = p9z + dx? for the flow defined by the following velocity field? (2a – y)t U = v = -(x + 2y)t b) What other assumptions are inherent to this velocity field? Rewrite the simplified set of equations (using assumptions) for this flow. c) Find an expression for the pressure. d) What might the boundary conditions be? e) How would you solve the set of equations numerically by finite differences? f) Can we use the potential equations instead? g) Sketch the flow.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 5 images

Blurred answer
Knowledge Booster
Fluid Kinematics
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
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