Podcast
Questions and Answers
What is the gravitational attraction exerted by Earth on a unit mass with position vector r called?
What is the gravitational attraction exerted by Earth on a unit mass with position vector r called?
The work done by a conservative force field around a closed path is zero.
The work done by a conservative force field around a closed path is zero.
True
In a barotropic atmosphere, the density ρ is a function of which variable?
In a barotropic atmosphere, the density ρ is a function of which variable?
pressure
For a frictionless barotropic flow, the expression rac{d aCa}{dt} = 0 is a direct corollary to _____ theorem.
For a frictionless barotropic flow, the expression rac{d aCa}{dt} = 0 is a direct corollary to _____ theorem.
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Match the following expressions with their significance.
Match the following expressions with their significance.
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What does the circulation theorem state regarding the time rate of change of circulation?
What does the circulation theorem state regarding the time rate of change of circulation?
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Kelvin's Circulation Theorem can only be applied to the relative velocity vector.
Kelvin's Circulation Theorem can only be applied to the relative velocity vector.
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What is the acceleration of circulation known as in the context of the circulation theorem?
What is the acceleration of circulation known as in the context of the circulation theorem?
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According to the circulation theorem, the acceleration of circulation is equal to the circulation of __________.
According to the circulation theorem, the acceleration of circulation is equal to the circulation of __________.
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Match the following concepts with their descriptions:
Match the following concepts with their descriptions:
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Study Notes
Circulation
- Circulation: A macro-scale measure of fluid rotation.
- Mathematical definition: Line integral of the velocity vector around a closed path.
- Scalar quantity
- Sign convention: Positive for anticlockwise rotation in the Northern Hemisphere, negative for clockwise; opposite in Southern Hemisphere.
- Absolute Circulation (C): Defined for absolute velocities.
- Relative Circulation (C): Defined for relative velocities.
Vorticity
- Vorticity: A micro-scale measure of rotation.
- Vector quantity
- Direction: Determined by the fluid's rotation direction relative to the plane of rotation.
- Mathematical expression : ∇ × V = î ζ + ĵ η + k ζ
- In meteorology: Vorticity is usually only the k component.
Circulation Theorems
- Circulation Theorems: Explain changes in circulation and causes.
- Kelvin's Circulation Theorem: Applied to the absolute velocity vector (V) of fluid motion.
- d/dt(Circulation) = Circulation of rate of change of the vector field (B).
- Stocked Theorem: Line integral of any vector field B around a closed path is equal to the surface integral.
Barotropic and Baroclinic Atmosphere
- Barotropic atmosphere: Horizontal temperature gradient is zero; isobars and isotherms are parallel.
- Baroclinic atmosphere: Horizontal temperature gradient exists; isobars and isotherms are not parallel.
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Description
Test your knowledge on the principles of fluid dynamics, particularly focusing on gravitational attraction, barotropic flow, and the circulation theorem. This quiz challenges you with questions that explore the definitions, significance, and applications of these concepts in a frictionless medium.
