2. If an incompressible laminar flow (through pipe area A₁) is forced through a narrow orifice, it will be focused into a smaller area, known as the vena contracta (with cross-sectional area A₂), as shown below: Orifice area Ao A₁ P₁ Flanges Pipe wall P2 Vena con- tracta area A₂ Eddies Intense turbulence and loss of energy Pressure tappings Reestablished flow pattern Figure 3: Flow through an orifice. The orifice focuses the laminar flow to a vena contracta, increasing its velocity. Beyond the orifice, the flow becomes turbulent for some distance until a laminar flow pattern is re-established. By measuring pres- sures upstream (p₁) and downstream (p2) from the orifice, the vol- umetric flow rate (Q) can be determined. (a) If the velocity of the fluid entering the pipe is u₁, what is the velocity u₂ at the end of the vena contracta? (b) What is the velocity of the fluid after the flow pattern has been reestablised? (c) What is the relationship between pressure drop (p₁ - p2) and volumetric flow rate Q?
2. If an incompressible laminar flow (through pipe area A₁) is forced through a narrow orifice, it will be focused into a smaller area, known as the vena contracta (with cross-sectional area A₂), as shown below: Orifice area Ao A₁ P₁ Flanges Pipe wall P2 Vena con- tracta area A₂ Eddies Intense turbulence and loss of energy Pressure tappings Reestablished flow pattern Figure 3: Flow through an orifice. The orifice focuses the laminar flow to a vena contracta, increasing its velocity. Beyond the orifice, the flow becomes turbulent for some distance until a laminar flow pattern is re-established. By measuring pres- sures upstream (p₁) and downstream (p2) from the orifice, the vol- umetric flow rate (Q) can be determined. (a) If the velocity of the fluid entering the pipe is u₁, what is the velocity u₂ at the end of the vena contracta? (b) What is the velocity of the fluid after the flow pattern has been reestablised? (c) What is the relationship between pressure drop (p₁ - p2) and volumetric flow rate Q?
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
Need the solution by the end of the day! Thank you!
**Figure 3: Flow through an orifice.** The orifice focuses the laminar flow to a *vena contracta*, increasing its velocity.
Beyond the orifice, the flow becomes turbulent for some distance until a laminar flow pattern is re-established. By measuring pressures upstream (\(p_1\)) and downstream (\(p_2\)) from the orifice, the volumetric flow rate (\(Q\)) can be determined.
(a) If the velocity of the fluid entering the pipe is \(u_1\), what is the velocity \(u_2\) at the end of the *vena contracta*?
(b) What is the velocity of the fluid after the flow pattern has been reestablished?
(c) What is the relationship between pressure drop (\(p_1 - p_2\)) and volumetric flow rate \(Q\)?
---
**Explanation of Diagram:**
The diagram illustrates an orifice in a pipe with different sections labeled:
- **Orifice area \(A_0\)**: The initial area of the pipe before the orifice.
- **Flanges**: Segments around the orifice.
- **Vena contracta area \(A_2\)**: The smaller area where the flow converges, resulting in increased velocity.
- **Intense turbulence and loss of energy**: Turbulent flow occurs immediately after the *vena contracta*.
- **Reestablished flow pattern**: The flow returns to a laminar state further downstream.
- **Pressure tappings**: Areas where pressures \(p_1\) and \(p_2\) are measured.
- **Eddies**: Circular flow patterns indicating turbulence.
The flow is initially laminar, becomes turbulent through the orifice, and eventually returns to a laminar state.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c4faf35-dd34-476b-91f6-0d1ab44e593d%2Fda5b8900-e135-4143-ab45-0f764c041b24%2Fsjgimmkk_processed.png&w=3840&q=75)
Transcribed Image Text:2. If an incompressible laminar flow (through pipe area \(A_1\)) is forced through a narrow orifice, it will be focused into a smaller area, known as the *vena contracta* (with cross-sectional area \(A_2\)), as shown below:
**Figure 3: Flow through an orifice.** The orifice focuses the laminar flow to a *vena contracta*, increasing its velocity.
Beyond the orifice, the flow becomes turbulent for some distance until a laminar flow pattern is re-established. By measuring pressures upstream (\(p_1\)) and downstream (\(p_2\)) from the orifice, the volumetric flow rate (\(Q\)) can be determined.
(a) If the velocity of the fluid entering the pipe is \(u_1\), what is the velocity \(u_2\) at the end of the *vena contracta*?
(b) What is the velocity of the fluid after the flow pattern has been reestablished?
(c) What is the relationship between pressure drop (\(p_1 - p_2\)) and volumetric flow rate \(Q\)?
---
**Explanation of Diagram:**
The diagram illustrates an orifice in a pipe with different sections labeled:
- **Orifice area \(A_0\)**: The initial area of the pipe before the orifice.
- **Flanges**: Segments around the orifice.
- **Vena contracta area \(A_2\)**: The smaller area where the flow converges, resulting in increased velocity.
- **Intense turbulence and loss of energy**: Turbulent flow occurs immediately after the *vena contracta*.
- **Reestablished flow pattern**: The flow returns to a laminar state further downstream.
- **Pressure tappings**: Areas where pressures \(p_1\) and \(p_2\) are measured.
- **Eddies**: Circular flow patterns indicating turbulence.
The flow is initially laminar, becomes turbulent through the orifice, and eventually returns to a laminar state.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
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
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY