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For an irrigational flow, the velocity potential lines, and the streamlines are always-
- a)parallel to each other
- b)coplanar
- c)orthogonal to each other
- d)inclined to horizontal
Correct answer is option 'C'. Can you explain this answer?
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For an irrigational flow, the velocity potential lines and the streamlines are always orthogonal to each other.
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Irrigational Flow: Velocity Potential Lines and Streamlines
Definition of Velocity Potential Lines and Streamlines
- Velocity potential lines are imaginary lines that indicate the constant values of velocity potential in a fluid flow field.
- Streamlines are imaginary lines that indicate the direction of fluid flow at any point in the field.
Relationship between Velocity Potential Lines and Streamlines
- In an irrigational flow, the velocity potential lines and streamlines are always orthogonal to each other.
- This means that they intersect each other at right angles.
- This relationship is due to the fact that the velocity potential is a scalar quantity, while the fluid velocity is a vector quantity.
- Mathematically, this relationship can be expressed as: ∇Φ ⋅ V = 0, where ∇Φ is the gradient of the velocity potential and V is the fluid velocity vector.
Implications of the Relationship
- The orthogonal relationship between velocity potential lines and streamlines has important implications for fluid flow analysis and design.
- It allows us to determine the velocity vector at any point in the field by simply finding the gradient of the velocity potential and taking its orthogonal complement.
- It also allows us to predict the behavior of fluids in complex flow fields, such as those found in irrigation systems.
- Finally, it can be used to optimize the design of irrigation systems by minimizing energy losses due to friction and other factors.
Definition of Velocity Potential Lines and Streamlines
- Velocity potential lines are imaginary lines that indicate the constant values of velocity potential in a fluid flow field.
- Streamlines are imaginary lines that indicate the direction of fluid flow at any point in the field.
Relationship between Velocity Potential Lines and Streamlines
- In an irrigational flow, the velocity potential lines and streamlines are always orthogonal to each other.
- This means that they intersect each other at right angles.
- This relationship is due to the fact that the velocity potential is a scalar quantity, while the fluid velocity is a vector quantity.
- Mathematically, this relationship can be expressed as: ∇Φ ⋅ V = 0, where ∇Φ is the gradient of the velocity potential and V is the fluid velocity vector.
Implications of the Relationship
- The orthogonal relationship between velocity potential lines and streamlines has important implications for fluid flow analysis and design.
- It allows us to determine the velocity vector at any point in the field by simply finding the gradient of the velocity potential and taking its orthogonal complement.
- It also allows us to predict the behavior of fluids in complex flow fields, such as those found in irrigation systems.
- Finally, it can be used to optimize the design of irrigation systems by minimizing energy losses due to friction and other factors.
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For an irrigational flow, the velocity potential lines, and the streamlines are always-a)parallel to each otherb)coplanarc)orthogonal to each otherd)inclined to horizontalCorrect answer is option 'C'. Can you explain this answer?
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For an irrigational flow, the velocity potential lines, and the streamlines are always-a)parallel to each otherb)coplanarc)orthogonal to each otherd)inclined to horizontalCorrect answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about For an irrigational flow, the velocity potential lines, and the streamlines are always-a)parallel to each otherb)coplanarc)orthogonal to each otherd)inclined to horizontalCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For an irrigational flow, the velocity potential lines, and the streamlines are always-a)parallel to each otherb)coplanarc)orthogonal to each otherd)inclined to horizontalCorrect answer is option 'C'. Can you explain this answer?.
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