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Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
Correct answer is '0.5'. Can you explain this answer?
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Water flows through two different pipes A and B of the same circular c...
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Water flows through two different pipes A and B of the same circular c...
Given:
- Length of pipe A (LA) = 1.0 m
- Length of pipe B (LB) = 2.0 m
- Flow in both pipes is laminar and fully developed
- Frictional head loss across the length of the pipes is the same
To find:
The ratio of volume flow rates QB/QA
Solution:
1. Introduction:
In fluid mechanics, the volume flow rate is defined as the volume of fluid passing through a given cross-section per unit of time. It is given by the equation Q = A⋅v, where Q is the volume flow rate, A is the cross-sectional area, and v is the velocity of fluid.
2. Understanding the problem:
We have two pipes, A and B, with different lengths but the same cross-sectional area. The frictional head loss across the lengths of both pipes is the same. We need to find the ratio of the volume flow rates QB/QA.
3. Relationship between frictional head loss and flow rate:
In laminar flow, the frictional head loss across a pipe is given by the Darcy-Weisbach equation:
Δh = f⋅(L/D)⋅(v^2/2g)
where Δh is the head loss, f is the Darcy friction factor, L is the length of the pipe, D is the diameter of the pipe, v is the velocity of fluid, and g is the acceleration due to gravity.
Since the frictional head loss is the same for both pipes A and B, we can write:
fA⋅(LA/DA)⋅(vA^2/2g) = fB⋅(LB/DB)⋅(vB^2/2g)
4. Relationship between velocity and flow rate:
The cross-sectional area of both pipes A and B is the same. Therefore, we can write:
QA = A⋅vA
and
QB = A⋅vB
5. Relationship between lengths and velocities:
Since the flow in both pipes is fully developed, we can assume that the velocity profiles are fully developed across the cross-sections of the pipes. In fully developed flow, the velocity profile is parabolic, and the maximum velocity occurs at the center of the pipe.
In a fully developed laminar flow, the velocity is inversely proportional to the length of the pipe. Therefore, we can write:
vA/vB = LB/LA = 2/1 = 2
6. Finding the ratio of volume flow rates:
Substituting the values of vA/vB = 2 in the equation QB = A⋅vB, we get:
QB = 2⋅QA
Therefore, the ratio of volume flow rates QB/QA = 2/1 = 0.5.
- Length of pipe A (LA) = 1.0 m
- Length of pipe B (LB) = 2.0 m
- Flow in both pipes is laminar and fully developed
- Frictional head loss across the length of the pipes is the same
To find:
The ratio of volume flow rates QB/QA
Solution:
1. Introduction:
In fluid mechanics, the volume flow rate is defined as the volume of fluid passing through a given cross-section per unit of time. It is given by the equation Q = A⋅v, where Q is the volume flow rate, A is the cross-sectional area, and v is the velocity of fluid.
2. Understanding the problem:
We have two pipes, A and B, with different lengths but the same cross-sectional area. The frictional head loss across the lengths of both pipes is the same. We need to find the ratio of the volume flow rates QB/QA.
3. Relationship between frictional head loss and flow rate:
In laminar flow, the frictional head loss across a pipe is given by the Darcy-Weisbach equation:
Δh = f⋅(L/D)⋅(v^2/2g)
where Δh is the head loss, f is the Darcy friction factor, L is the length of the pipe, D is the diameter of the pipe, v is the velocity of fluid, and g is the acceleration due to gravity.
Since the frictional head loss is the same for both pipes A and B, we can write:
fA⋅(LA/DA)⋅(vA^2/2g) = fB⋅(LB/DB)⋅(vB^2/2g)
4. Relationship between velocity and flow rate:
The cross-sectional area of both pipes A and B is the same. Therefore, we can write:
QA = A⋅vA
and
QB = A⋅vB
5. Relationship between lengths and velocities:
Since the flow in both pipes is fully developed, we can assume that the velocity profiles are fully developed across the cross-sections of the pipes. In fully developed flow, the velocity profile is parabolic, and the maximum velocity occurs at the center of the pipe.
In a fully developed laminar flow, the velocity is inversely proportional to the length of the pipe. Therefore, we can write:
vA/vB = LB/LA = 2/1 = 2
6. Finding the ratio of volume flow rates:
Substituting the values of vA/vB = 2 in the equation QB = A⋅vB, we get:
QB = 2⋅QA
Therefore, the ratio of volume flow rates QB/QA = 2/1 = 0.5.
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Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).Correct answer is '0.5'. Can you explain this answer?
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Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).Correct answer is '0.5'. 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 Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).Correct answer is '0.5'. 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 Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).Correct answer is '0.5'. Can you explain this answer?.
Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).Correct answer is '0.5'. 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 Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).Correct answer is '0.5'. 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 Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).Correct answer is '0.5'. Can you explain this answer?.
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Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).Correct answer is '0.5'. Can you explain this answer?, a detailed solution for Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).Correct answer is '0.5'. Can you explain this answer? has been provided alongside types of Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).Correct answer is '0.5'. Can you explain this answer? theory, EduRev gives you an
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