GATE Exam > GATE Questions > In a fully developed turbulent flow through a...
Start Learning for Free
In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted. Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest to
- a)0.34
- b)0.62
- c)0.87
- d)1.00
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In a fully developed turbulent flow through a circular pipe, a head lo...
Most Upvoted Answer
In a fully developed turbulent flow through a circular pipe, a head lo...
Understanding Head Loss in Pipe Flow
In turbulent flow through a circular pipe, the head loss is influenced by the pipe diameter and flow rate. When the diameter of the pipe is increased, the flow characteristics change, affecting the head loss.
Key Concepts
- Head Loss (h): Represents the energy loss due to friction as fluid flows through the pipe.
- Friction Factor (f): A dimensionless number that characterizes the flow resistance in a pipe. For turbulent flow, it remains fairly constant for a given Reynolds number and surface roughness.
Flow Rate and Diameter Increase
1. Initial Condition: The original pipe has a diameter D and experiences a head loss of h1.
2. Increased Diameter: The diameter is increased by 10%, making the new diameter D' = 1.1D.
3. Flow Rate: The flow rate remains constant throughout this process.
Calculating Head Loss Ratio
- The head loss in a pipe can be approximated by the Darcy-Weisbach equation:
h = (f * L * v^2) / (2 * g * D)
Where:
- L = length of the pipe
- v = velocity of the fluid
- g = acceleration due to gravity
- With a 10% increase in diameter, the new diameter D' affects the velocity (v) because of the constant flow rate (Q = A * v).
- The new area A' = π * (D'/2)^2 = π * (1.1D/2)^2 = 1.21 * π * (D/2)^2, leading to a decrease in velocity v' = Q/A'.
- The ratio of head losses can be derived as follows:
h2/h1 ≈ (D/D')^5
- Substituting D' = 1.1D gives:
h2/h1 ≈ (D/(1.1D))^5 = (1/1.1)^5 ≈ 0.62
Conclusion
Thus, the ratio h2/h1 is closest to 0.62, confirming that option 'B' is indeed the correct answer.
In turbulent flow through a circular pipe, the head loss is influenced by the pipe diameter and flow rate. When the diameter of the pipe is increased, the flow characteristics change, affecting the head loss.
Key Concepts
- Head Loss (h): Represents the energy loss due to friction as fluid flows through the pipe.
- Friction Factor (f): A dimensionless number that characterizes the flow resistance in a pipe. For turbulent flow, it remains fairly constant for a given Reynolds number and surface roughness.
Flow Rate and Diameter Increase
1. Initial Condition: The original pipe has a diameter D and experiences a head loss of h1.
2. Increased Diameter: The diameter is increased by 10%, making the new diameter D' = 1.1D.
3. Flow Rate: The flow rate remains constant throughout this process.
Calculating Head Loss Ratio
- The head loss in a pipe can be approximated by the Darcy-Weisbach equation:
h = (f * L * v^2) / (2 * g * D)
Where:
- L = length of the pipe
- v = velocity of the fluid
- g = acceleration due to gravity
- With a 10% increase in diameter, the new diameter D' affects the velocity (v) because of the constant flow rate (Q = A * v).
- The new area A' = π * (D'/2)^2 = π * (1.1D/2)^2 = 1.21 * π * (D/2)^2, leading to a decrease in velocity v' = Q/A'.
- The ratio of head losses can be derived as follows:
h2/h1 ≈ (D/D')^5
- Substituting D' = 1.1D gives:
h2/h1 ≈ (D/(1.1D))^5 = (1/1.1)^5 ≈ 0.62
Conclusion
Thus, the ratio h2/h1 is closest to 0.62, confirming that option 'B' is indeed the correct answer.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer?
Question Description
In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer?.
In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer?.
Solutions for In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer?, a detailed solution for In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.Assume friction factor for both the cases of pipe flow is the same. The ratio of h2 / h1 is closest toa)0.34b)0.62c)0.87d)1.00Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup