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In fully-developed turbulent pipe flow, assuming 1/7th power law, the ratio of time mean velocity at the centre of the pipe to that averagev elocity of the flow is:
- a)2.0
- b)1.5
- c)1.22
- d)0.817
Correct answer is option 'D'. Can you explain this answer?
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In fully-developed turbulent pipe flow, assuming 1/7th power law, the ...
Ans. (d) =
or without calculating this we may say that it must be less than one and option (d) is only choice.
or without calculating this we may say that it must be less than one and option (d) is only choice.
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In fully-developed turbulent pipe flow, assuming 1/7th power law, the ...
Ans. (d) =
or without calculating this we may say that it must be less than one and option (d) is only choice.
or without calculating this we may say that it must be less than one and option (d) is only choice.
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In fully-developed turbulent pipe flow, assuming 1/7th power law, the ...
Ratio of Time Mean Velocity at the Centre of the Pipe to Average Velocity in Turbulent Pipe Flow
To calculate the ratio of the time mean velocity at the center of the pipe to the average velocity of the flow in fully-developed turbulent pipe flow, we can use the 1/7th power law. The 1/7th power law states that the velocity profile in fully-developed turbulent pipe flow can be described by the equation:
V(r) = V_avg * [1 - (r/R)^7]^(1/7)
where V(r) is the velocity at a radial distance r from the center of the pipe, V_avg is the average velocity of the flow, and R is the radius of the pipe.
Step 1: Calculate the time mean velocity at the center of the pipe
To find the time mean velocity at the center of the pipe, we need to integrate the velocity profile equation over the entire cross-section of the pipe and divide by the pipe cross-sectional area. However, since the velocity profile is symmetrical about the centerline of the pipe, the time mean velocity at the center of the pipe will be equal to the average velocity of the flow.
Step 2: Calculate the average velocity of the flow
The average velocity of the flow can be calculated by integrating the velocity profile equation over the entire cross-section of the pipe and dividing by the pipe cross-sectional area:
V_avg = (1/A) * ∫[0 to R] V(r) * 2πr dr
where A is the cross-sectional area of the pipe.
Step 3: Calculate the ratio of the time mean velocity at the center of the pipe to the average velocity of the flow
Since the time mean velocity at the center of the pipe is equal to the average velocity of the flow, the ratio will be 1.
Therefore, the correct answer is option D) 0.817, which is an incorrect answer. It seems that there might be an error in the given options or the question itself.
To calculate the ratio of the time mean velocity at the center of the pipe to the average velocity of the flow in fully-developed turbulent pipe flow, we can use the 1/7th power law. The 1/7th power law states that the velocity profile in fully-developed turbulent pipe flow can be described by the equation:
V(r) = V_avg * [1 - (r/R)^7]^(1/7)
where V(r) is the velocity at a radial distance r from the center of the pipe, V_avg is the average velocity of the flow, and R is the radius of the pipe.
Step 1: Calculate the time mean velocity at the center of the pipe
To find the time mean velocity at the center of the pipe, we need to integrate the velocity profile equation over the entire cross-section of the pipe and divide by the pipe cross-sectional area. However, since the velocity profile is symmetrical about the centerline of the pipe, the time mean velocity at the center of the pipe will be equal to the average velocity of the flow.
Step 2: Calculate the average velocity of the flow
The average velocity of the flow can be calculated by integrating the velocity profile equation over the entire cross-section of the pipe and dividing by the pipe cross-sectional area:
V_avg = (1/A) * ∫[0 to R] V(r) * 2πr dr
where A is the cross-sectional area of the pipe.
Step 3: Calculate the ratio of the time mean velocity at the center of the pipe to the average velocity of the flow
Since the time mean velocity at the center of the pipe is equal to the average velocity of the flow, the ratio will be 1.
Therefore, the correct answer is option D) 0.817, which is an incorrect answer. It seems that there might be an error in the given options or the question itself.
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In fully-developed turbulent pipe flow, assuming 1/7th power law, the ratio of time mean velocity at the centre of the pipe to that averagev elocity of the flow is:a)2.0b)1.5c)1.22d)0.817Correct answer is option 'D'. Can you explain this answer?
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In fully-developed turbulent pipe flow, assuming 1/7th power law, the ratio of time mean velocity at the centre of the pipe to that averagev elocity of the flow is:a)2.0b)1.5c)1.22d)0.817Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In fully-developed turbulent pipe flow, assuming 1/7th power law, the ratio of time mean velocity at the centre of the pipe to that averagev elocity of the flow is:a)2.0b)1.5c)1.22d)0.817Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In fully-developed turbulent pipe flow, assuming 1/7th power law, the ratio of time mean velocity at the centre of the pipe to that averagev elocity of the flow is:a)2.0b)1.5c)1.22d)0.817Correct answer is option 'D'. Can you explain this answer?.
In fully-developed turbulent pipe flow, assuming 1/7th power law, the ratio of time mean velocity at the centre of the pipe to that averagev elocity of the flow is:a)2.0b)1.5c)1.22d)0.817Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In fully-developed turbulent pipe flow, assuming 1/7th power law, the ratio of time mean velocity at the centre of the pipe to that averagev elocity of the flow is:a)2.0b)1.5c)1.22d)0.817Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In fully-developed turbulent pipe flow, assuming 1/7th power law, the ratio of time mean velocity at the centre of the pipe to that averagev elocity of the flow is:a)2.0b)1.5c)1.22d)0.817Correct answer is option 'D'. Can you explain this answer?.
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In fully-developed turbulent pipe flow, assuming 1/7th power law, the ratio of time mean velocity at the centre of the pipe to that averagev elocity of the flow is:a)2.0b)1.5c)1.22d)0.817Correct answer is option 'D'. Can you explain this answer?, a detailed solution for In fully-developed turbulent pipe flow, assuming 1/7th power law, the ratio of time mean velocity at the centre of the pipe to that averagev elocity of the flow is:a)2.0b)1.5c)1.22d)0.817Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of In fully-developed turbulent pipe flow, assuming 1/7th power law, the ratio of time mean velocity at the centre of the pipe to that averagev elocity of the flow is:a)2.0b)1.5c)1.22d)0.817Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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