Understanding the Navier-Stokes Equations: Conservation of Momentum and More

In summary, the Navier-Stokes equations are a set of partial differential equations used to describe the motion of fluids. They have various applications, such as predicting weather patterns and designing vehicles. However, they are notoriously difficult to solve and have led to the development of computational fluid dynamics methods. Some simplifications and assumptions are made in the equations, and they have greatly impacted the field of fluid dynamics, leading to advancements in transportation and our understanding of fluid behavior.
  • #1
hermano
41
0
Hi,

Stupid question: the Navier-Stokes equations, do they only consist of the equations for a statement of the conservation of momentum or do they also include the equations for conservation of mass (continuity equation), conservation of energy and an equation of state?

Thanks.
 
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  • #2
hermano said:
Hi,

Stupid question: the Navier-Stokes equations, do they only consist of the equations for a statement of the conservation of momentum or do they also include the equations for conservation of mass (continuity equation), conservation of energy and an equation of state?

Thanks.
Only conservation of momentum.
 

1. What are the Navier-Stokes equations?

The Navier-Stokes equations are a set of partial differential equations that describe the motion of a fluid. They take into account factors such as viscosity, pressure, and acceleration in order to predict the behavior of fluid flow.

2. What are the applications of Navier-Stokes equations?

The Navier-Stokes equations have many practical applications, including predicting weather patterns, designing aircraft and automobiles, and modeling ocean currents. They are also used in fields such as aerospace engineering, meteorology, and geophysics.

3. Are the Navier-Stokes equations solvable?

The Navier-Stokes equations are notoriously difficult to solve, especially for turbulent flows. In fact, solving the equations for all possible fluid flows is one of the Millennium Prize Problems, with a prize of $1 million offered by the Clay Mathematics Institute.

4. What are some simplifications or assumptions made in the Navier-Stokes equations?

The Navier-Stokes equations make several simplifications and assumptions in order to make them solvable. These include assuming that the fluid is incompressible, neglecting the effects of heat transfer, and assuming that the fluid is Newtonian (i.e. its viscosity is constant).

5. How have the Navier-Stokes equations impacted the field of fluid dynamics?

The Navier-Stokes equations have had a significant impact on the field of fluid dynamics. They have allowed for the development of computational fluid dynamics (CFD) methods, which have greatly advanced our understanding of fluid behavior. They have also been used to develop new designs for aircraft and other vehicles, leading to more efficient and safer transportation.

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