The pressure loss 4p along a pipe is known to depend on the pipe diameter D, the length of the pipe L, the wall roughness k, the flow velocity V and the fluid density p and viscosity μ. (a) Using the Buckingham Pi theorem, show that the pressure loss is given by: Lk 4p pvz 1 = fn ( D² D² DVD) μ (b) In an experiment, water flows through a pipe with a 20 mm diameter at a velocity of 0.1 m/s. The pressure drop is measured as 8 N/m² per metre length of pipe. Determine the corresponding velocity for the flow of air in a pipe with a 10 mm diameter, under dynamically similar conditions. (c) Determine the corresponding pressure drop per metre length of pipe, for the air flow. The following values can be assumed: Water: Air: p = 1000 kg/m³ p=1.2 kg/m³ μ = 1 x 10³ kg/m s μ= 1.98 x 105 kg/m s
The pressure loss 4p along a pipe is known to depend on the pipe diameter D, the length of the pipe L, the wall roughness k, the flow velocity V and the fluid density p and viscosity μ. (a) Using the Buckingham Pi theorem, show that the pressure loss is given by: Lk 4p pvz 1 = fn ( D² D² DVD) μ (b) In an experiment, water flows through a pipe with a 20 mm diameter at a velocity of 0.1 m/s. The pressure drop is measured as 8 N/m² per metre length of pipe. Determine the corresponding velocity for the flow of air in a pipe with a 10 mm diameter, under dynamically similar conditions. (c) Determine the corresponding pressure drop per metre length of pipe, for the air flow. The following values can be assumed: Water: Air: p = 1000 kg/m³ p=1.2 kg/m³ μ = 1 x 10³ kg/m s μ= 1.98 x 105 kg/m s
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
Related questions
Question
Mechanical Engineering
Fluid
![The pressure loss 4p along a pipe is known to depend on the pipe diameter D, the length of
the pipe L, the wall roughness k, the flow velocity V and the fluid density p and viscosity μ.
(a) Using the Buckingham Pi theorem, show that the pressure loss is given by:
4p
PVZ
μ
fn ( D² D² DVD)
(b) In an experiment, water flows through a pipe with a 20 mm diameter at a velocity of
0.1 m/s. The pressure drop is measured as 8 N/m² per metre length of pipe. Determine
the corresponding velocity for the flow of air in a pipe with a 10 mm diameter, under
dynamically similar conditions.
(c) Determine the corresponding pressure drop per metre length of pipe, for the air flow.
The following values can be assumed:
Water:
Air:
p=1000 kg/m³
p=1.2 kg/m³
μ= 1 x 10³ kg/m s
μ = 1.98 x 10¹5 kg/m s
(Ans: 3.3 m/s; 10.5 N/m²)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe02bd108-b4d0-4c2f-944f-b5fec665b534%2Fafa7b674-a013-49f5-993c-56ef4f9398e8%2Fv5gm5ul_processed.png&w=3840&q=75)
Transcribed Image Text:The pressure loss 4p along a pipe is known to depend on the pipe diameter D, the length of
the pipe L, the wall roughness k, the flow velocity V and the fluid density p and viscosity μ.
(a) Using the Buckingham Pi theorem, show that the pressure loss is given by:
4p
PVZ
μ
fn ( D² D² DVD)
(b) In an experiment, water flows through a pipe with a 20 mm diameter at a velocity of
0.1 m/s. The pressure drop is measured as 8 N/m² per metre length of pipe. Determine
the corresponding velocity for the flow of air in a pipe with a 10 mm diameter, under
dynamically similar conditions.
(c) Determine the corresponding pressure drop per metre length of pipe, for the air flow.
The following values can be assumed:
Water:
Air:
p=1000 kg/m³
p=1.2 kg/m³
μ= 1 x 10³ kg/m s
μ = 1.98 x 10¹5 kg/m s
(Ans: 3.3 m/s; 10.5 N/m²)
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 4 steps
![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, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Control Systems Engineering](https://www.bartleby.com/isbn_cover_images/9781118170519/9781118170519_smallCoverImage.gif)
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
![Mechanics of Materials (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337093347/9781337093347_smallCoverImage.gif)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
![Engineering Mechanics: Statics](https://www.bartleby.com/isbn_cover_images/9781118807330/9781118807330_smallCoverImage.gif)
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY