What does a Lagrangian description of fluid flow provide?

What does a Lagrangian description of fluid flow provide? Correct Answer Position of a fluid particle at every time instant

Explanation:

Fluid Kinematics:

• Study of the motion of the fluid without any reference of force and moment is known as fluid Kinematics. There are two descriptions to define the fluid motion.
• Lagrangian Description.
• Eulerian Description.

​Lagrangian Description:

• The Lagrangian Description is one in which individual fluid particles are tracked, much like the tracking of billiard balls in a highschool physics experiment.
• In the Lagrangian description of fluid flow, individual fluid particles are "marked," and their positions, velocities, etc. are described as a function of time.
• The physical laws, such as Newton's laws and conservation of mass and energy, apply directly to each particle.
• If there were only a few particles to consider, as in a high school physics experiment with billiard balls, the Lagrangian description would be desirable.
• However, fluid flow is a continuum phenomenon, at least down to the molecular level. It is not possible to track each "particle" in a complex flow field.
• Thus, the Lagrangian description is rarely used in fluid mechanics.

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​Eulerian Description:

• The Eulerian Description is one in which a control volume is defined, within which fluid flow properties of interest are expressed as field
• In the Eulerian description of fluid flow, individual fluid particles are not identified. Instead, a control volume is defined.
• Pressure, velocity, acceleration, and all other flow properties are described as fields within the control volume.
• In other words, each property is expressed as a function of space and time, as shown for the velocity field in the diagram.
• In the Eulerian description of fluid flow, one is not concerned about the location or velocity of any particular particle, but rather about the velocity, acceleration, etc. of whatever particle happens to be at a particular location of interest at a particular time.
• Since fluid flow is a continuum phenomenon, at least down to the molecular level, the Eulerian description is usually preferred in fluid mechanics.
• Note, however, that the physical laws such as Newton's laws and the laws of conservation of mass and energy apply directly to particles in a Lagrangian description. Hence, some translation or reformulation of these laws is required for use with an Eulerian description.
• Either description method is valid in fluid mechanics, but the Eulerian description is usually preferred because there are simply too many particles to keep track of in a Lagrangian description.

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