04. a. A control volume is an arbitrary volume of space through which fluid can flow. Let the control volume of a spherical shaped blob in a flowing fluid is V. Suppose the fluid has density p(r, t) and velocity field u. Then applying mass conservation to the blob, Rate of change of mass in-Mass out flow. The total mass of fluid entering to the blob in a control volume V is m= --fff₂ The mass out flow is given by. p dv. (pu) ds where, S is the surface bounded by the control volume V. Apply the Gauss Divergence Theorem to show that, ap +V.(pu) = 0.
04. a. A control volume is an arbitrary volume of space through which fluid can flow. Let the control volume of a spherical shaped blob in a flowing fluid is V. Suppose the fluid has density p(r, t) and velocity field u. Then applying mass conservation to the blob, Rate of change of mass in-Mass out flow. The total mass of fluid entering to the blob in a control volume V is m= --fff₂ The mass out flow is given by. p dv. (pu) ds where, S is the surface bounded by the control volume V. Apply the Gauss Divergence Theorem to show that, ap +V.(pu) = 0.
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter14: Fluid Mechanics
Section: Chapter Questions
Problem 88P: (a) Using Bernoulli's equation, show that be measured fluid speed v for a pitot tube, like the one...
Related questions
Question
![04. a.
A control volume is an arbitrary volume of space through which fluid can flow.
Let the control volume of a spherical shaped blob in a flowing fluid is V.
Suppose the fluid has density p(r, t) and velocity field u. Then applying mass
conservation to the blob,
Rate of change of mass in=- Mass out flow.
The total mass of fluid entering to the blob in a control volume V is
We a
The mass out flow is given by,
m =
p dv.
ff (PL)
(pu) ds
where, S is the surface bounded by the control volume V. Apply the Gauss
Divergence Theorem to show that,
др
at
-+V. (pu) = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65afa8bc-e5b6-45e3-873b-2d32c71e5965%2F8ff6bd3a-ea79-40a0-a10c-9ae14c294d9a%2Fyftxkbj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:04. a.
A control volume is an arbitrary volume of space through which fluid can flow.
Let the control volume of a spherical shaped blob in a flowing fluid is V.
Suppose the fluid has density p(r, t) and velocity field u. Then applying mass
conservation to the blob,
Rate of change of mass in=- Mass out flow.
The total mass of fluid entering to the blob in a control volume V is
We a
The mass out flow is given by,
m =
p dv.
ff (PL)
(pu) ds
where, S is the surface bounded by the control volume V. Apply the Gauss
Divergence Theorem to show that,
др
at
-+V. (pu) = 0.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![University Physics Volume 1](https://www.bartleby.com/isbn_cover_images/9781938168277/9781938168277_smallCoverImage.gif)
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University
![Physics for Scientists and Engineers with Modern …](https://www.bartleby.com/isbn_cover_images/9781337553292/9781337553292_smallCoverImage.gif)
Physics for Scientists and Engineers with Modern …
Physics
ISBN:
9781337553292
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
![Physics for Scientists and Engineers: Foundations…](https://www.bartleby.com/isbn_cover_images/9781133939146/9781133939146_smallCoverImage.gif)
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
![University Physics Volume 1](https://www.bartleby.com/isbn_cover_images/9781938168277/9781938168277_smallCoverImage.gif)
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University
![Physics for Scientists and Engineers with Modern …](https://www.bartleby.com/isbn_cover_images/9781337553292/9781337553292_smallCoverImage.gif)
Physics for Scientists and Engineers with Modern …
Physics
ISBN:
9781337553292
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
![Physics for Scientists and Engineers: Foundations…](https://www.bartleby.com/isbn_cover_images/9781133939146/9781133939146_smallCoverImage.gif)
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
![College Physics](https://www.bartleby.com/isbn_cover_images/9781938168000/9781938168000_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781938168000
Author:
Paul Peter Urone, Roger Hinrichs
Publisher:
OpenStax College
![Principles of Physics: A Calculus-Based Text](https://www.bartleby.com/isbn_cover_images/9781133104261/9781133104261_smallCoverImage.gif)
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning