What are the Napier-Stokes Equations and how are they related to heart pulse?

  • Thread starter PrudensOptimus
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In summary, the Navier-Stokes Equations are a set of mathematical equations developed in the 19th century by Claude-Louis Navier and George Gabriel Stokes to describe the motion of fluids. They are significant in providing a fundamental understanding of fluid behavior and are widely used in various fields. However, they make several assumptions and have limitations, such as only being applicable to certain types of fluids and not considering factors like turbulence and heat transfer. The equations can be solved using numerical methods, but the solutions may not always be accurate.
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PrudensOptimus
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Anyone know them? I heard is related to heart pulse or something.
 
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  • #2
Perhaps you mean Navier-Stokes? They are non-linear, and generally unpleasant. The set of equations form a dynamical theory, and are the core of fluid mechanics.

Check out http://astron.berkeley.edu/~jrg/ay202/node50.html [Broken]. It saves me repeating a perfectly good source.
 
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  • #3
Hmm, it seems they also have the name "Napier-Stokes" as you suggested. Never came across that before.
 

1. What are the Navier-Stokes Equations?

The Navier-Stokes Equations are a set of mathematical equations that describe the motion of fluids, such as air and water. They were developed by Claude-Louis Navier and George Gabriel Stokes in the 19th century and are used to model and predict the behavior of fluids in various situations.

2. What is the significance of the Navier-Stokes Equations?

The Navier-Stokes Equations are important because they provide a fundamental understanding of how fluids behave. They are widely used in many fields, including engineering, physics, and meteorology, to study and solve problems related to fluid dynamics.

3. What are the assumptions made in the Navier-Stokes Equations?

The Navier-Stokes Equations make several assumptions, including the assumption of continuity (the fluid is continuous and has no gaps), the assumption of incompressibility (the fluid has a constant density), and the assumption of Newton's second law (the force acting on a fluid is equal to its mass times its acceleration).

4. What are the limitations of the Navier-Stokes Equations?

The Navier-Stokes Equations have several limitations, including the fact that they are only applicable to fluids that are incompressible, have no external forces acting on them, and have a constant viscosity. They also do not take into account factors such as turbulence, heat transfer, and chemical reactions.

5. How are the Navier-Stokes Equations solved?

The Navier-Stokes Equations can be solved using various numerical methods, such as finite difference, finite volume, and finite element methods. These methods discretize the equations into a set of algebraic equations, which can then be solved using computers. However, due to the complexity of the equations, the solutions may not always be accurate and may require further simplifications or assumptions.

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