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An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________
Correct answer is '2'. Can you explain this answer?
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An incompressible fluid is flowing at a steady rate in a horizontal pi...
Understanding Fluid Flow in Parallel Pipes
When an incompressible fluid flows through a pipe that branches into two parallel sections, the behavior of the flow can be analyzed using the principles of fluid mechanics, particularly the conservation of mass and the concept of velocity in relation to pipe diameter.
Key Concepts
- Continuity Equation: For an incompressible fluid, the flow rate must remain constant throughout the system. This can be expressed as:
Q = A1 * V1 = A2 * V2
where Q is the flow rate, A is the cross-sectional area, and V is the velocity.
- Cross-Sectional Area: The area of a circular pipe can be calculated as A = π * (d/2)². Therefore, if:
d1 = 4d2,
Then A1 = π * (d1/2)² = π * (4d2/2)² = 4π * (d2/2)² = 4A2.
Velocity Relationship
- Considering the conservation of mass at the junction where the pipe splits:
Q_total = Q1 + Q2
- Since A1 = 4A2, we can express the velocities as V1 and V2 for the larger and smaller pipes respectively:
Q1 = A1 * V1 and Q2 = A2 * V2
- Substituting the areas gives us:
Q = 4A2 * V1 + A2 * V2
- Rearranging leads to:
Q = A2 * (4V1 + V2)
- Because the total flow rate (Q) entering and exiting must balance, we can derive that:
4V1 + V2 = constant (which indicates that as V1 increases, V2 must adjust).
Final Velocity Ratio
- By setting Q1 = Q2 in terms of velocities and areas, we can find:
V1 = 2V2
This shows that the velocity in the larger pipe is twice that of the smaller pipe, leading to the conclusion that:
The Velocity Ratio
- The velocity ratio between the bigger and the smaller branched pipes is indeed 2.
When an incompressible fluid flows through a pipe that branches into two parallel sections, the behavior of the flow can be analyzed using the principles of fluid mechanics, particularly the conservation of mass and the concept of velocity in relation to pipe diameter.
Key Concepts
- Continuity Equation: For an incompressible fluid, the flow rate must remain constant throughout the system. This can be expressed as:
Q = A1 * V1 = A2 * V2
where Q is the flow rate, A is the cross-sectional area, and V is the velocity.
- Cross-Sectional Area: The area of a circular pipe can be calculated as A = π * (d/2)². Therefore, if:
d1 = 4d2,
Then A1 = π * (d1/2)² = π * (4d2/2)² = 4π * (d2/2)² = 4A2.
Velocity Relationship
- Considering the conservation of mass at the junction where the pipe splits:
Q_total = Q1 + Q2
- Since A1 = 4A2, we can express the velocities as V1 and V2 for the larger and smaller pipes respectively:
Q1 = A1 * V1 and Q2 = A2 * V2
- Substituting the areas gives us:
Q = 4A2 * V1 + A2 * V2
- Rearranging leads to:
Q = A2 * (4V1 + V2)
- Because the total flow rate (Q) entering and exiting must balance, we can derive that:
4V1 + V2 = constant (which indicates that as V1 increases, V2 must adjust).
Final Velocity Ratio
- By setting Q1 = Q2 in terms of velocities and areas, we can find:
V1 = 2V2
This shows that the velocity in the larger pipe is twice that of the smaller pipe, leading to the conclusion that:
The Velocity Ratio
- The velocity ratio between the bigger and the smaller branched pipes is indeed 2.
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An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________Correct answer is '2'. Can you explain this answer?
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An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________Correct answer is '2'. 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 An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________Correct answer is '2'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________Correct answer is '2'. Can you explain this answer?.
An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________Correct answer is '2'. 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 An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________Correct answer is '2'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________Correct answer is '2'. Can you explain this answer?.
Solutions for An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________Correct answer is '2'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________Correct answer is '2'. Can you explain this answer?, a detailed solution for An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________Correct answer is '2'. Can you explain this answer? has been provided alongside types of An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________Correct answer is '2'. Can you explain this answer? theory, EduRev gives you an
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