# Navier Stokes Equations - General Question

• gilgtc
In summary, the Navier-Stokes equations include both a pressure term and a gravity term. The pressure term is responsible for pressure force, which drives the fluid, while the gravity term represents the body force, which is a distinct force from pressure and cannot be lumped together with it. This is important for understanding energy balance in systems with different fluid bodies at varying altitudes. The body force can also include other forces such as centrifugal force. The momentum equation highlights the different forces that contribute to the change of momentum in a fluid.
gilgtc
(This is from the perspective of Geophysical Fluid Dynamics)

In the Navier Stokes equations I am confused as to why there is both a pressure term and a gravity term. Is this pressure resulting from differences in densities and temperature differences alone? I would think that the gravity term would be lumped into the pressure term. Can someone please clarify?

I am sorry if this makes no sense I am just trying to understand,

Thanks for your help.

g

Engineering-wise a look into energy balance is always comfortable. If in the system there are two distinct bodies of fluid, having same velocity, density, pressure and temperature, but at different altitudes, the system still has the energy potential to do something. If the gravity term would be missing from Navier-Stokes equations, then they would not show this potential.

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Chusslove Illich (Часлав Илић)

gravity is usually shown for the body force component. However this can also be centrifugal force etc.

the pressure term should be for the pressure force driving the fluid. In compressible flow this is the same pressure that change with temperature and density. The body force is of different nature. It cannot be lump into the pressure term. Perhaps because all terms on RHS are forces, and this gives you the impression that they can be lump together. In fact, they are different.

the momentum equation:

Change of momentum = pressure force + viscous force + body force

## 1. What are Navier-Stokes equations?

Navier-Stokes equations are a set of partial differential equations that describe the motion of fluid substances, such as liquids and gases.

## 2. What is the significance of Navier-Stokes equations?

Navier-Stokes equations are important because they provide a mathematical framework for understanding and predicting the behavior of fluids in various settings, such as in engineering, weather forecasting, and aerodynamics.

## 3. What is the general form of Navier-Stokes equations?

The general form of Navier-Stokes equations consists of a continuity equation, which describes the conservation of mass, and a momentum equation, which describes the conservation of momentum. These equations also take into account external forces, such as gravity and pressure, that act on the fluid.

## 4. What are the assumptions made in deriving Navier-Stokes equations?

Navier-Stokes equations are derived based on certain assumptions, including the fluid being incompressible, the flow being steady and laminar, and the fluid having constant properties such as density and viscosity. These assumptions may not always hold true in real-world situations, but they provide a good approximation in many cases.

## 5. What are some applications of Navier-Stokes equations?

Navier-Stokes equations have a wide range of applications, including predicting the behavior of fluids in pipes and channels, designing aircraft and other vehicles, simulating weather patterns, and understanding ocean currents. They are also used in fields such as turbulence research, fluid dynamics, and computational fluid dynamics.

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