Differential equation for gas flow motion?

In summary, the conversation discusses the use of the Navier-Stokes equation in computation fluid dynamics, specifically in relation to the motion of gas and liquid. The equation applies to both forms of fluid due to the similar behavior of attraction and repulsion forces. However, the equation does not directly account for the shape pressure of the fluid, which is a key factor in gas motion. Instead, the three terms in the equation represent the change in pressure, change in speed due to viscosity, and external force. Further discussion is needed to understand how these terms can account for gas motion in the Navier-Stokes equation.
  • #1
muffinman123
19
0
I am having some confusion in computation fluid dynamics. navier-stokes equation is the differential equation for fluid motion, but does this equation apply to gas as well? to my understanding gas qualifies as a fluid but I am having trouble seeing how the same equation applies to both liquid and gas motion.

liquid has attraction force between each element while gas attempts to occupy the entire shape of container and therefore only has repelling force rather than attraction force, but how is this reflected in the navier-stokes equation?

because I am using the introductory form of navier-stokes, assuming the fluid to be incompressible, there are only 3 terms contributing to the acceleration, change in pressure, change in speed for viscosity, and external force.

just reading the equation itself, I am guessing if fluid pressure pushes each element apart, then the viscosity acts as damper so the motion reaches stops once the shape pressure force is below the damping force. therefore gas motion would have very low viscosity so the motion keeps expanding until the gas occupies the entire space.
 
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  • #2
but how does this work in the equation? there are 3 terms and they all contribute to the acceleration. so if none of these terms represent the shape pressure of the fluid, then how does gas motion work in navier-stokes?
 

Related to Differential equation for gas flow motion?

1. What is a differential equation for gas flow motion?

A differential equation for gas flow motion is a mathematical equation that describes the behavior of gas flow in a system, taking into account factors such as pressure, temperature, and velocity. It is a fundamental tool used in fluid mechanics to understand and predict the motion of gases.

2. How is a differential equation for gas flow motion derived?

A differential equation for gas flow motion is typically derived by applying the principles of conservation of mass, momentum, and energy to a control volume in the system. This results in a set of equations that can be simplified and solved to obtain the differential equation.

3. What are the variables in a differential equation for gas flow motion?

The variables in a differential equation for gas flow motion include the gas properties (such as density, viscosity, and specific heat), the system geometry and dimensions, and the external forces acting on the gas (such as gravity or pressure differentials).

4. How is a differential equation for gas flow motion used in practical applications?

A differential equation for gas flow motion is used to analyze and design various systems involving gas flow, such as pipelines, ventilation systems, and combustion engines. It can also be used to study the effects of different parameters on gas flow, helping engineers optimize system performance.

5. Are there different types of differential equations for gas flow motion?

Yes, there are different types of differential equations for gas flow motion depending on the specific system and conditions being studied. Some common types include the Navier-Stokes equations, the Euler equations, and the Bernoulli equation. Each type has its own assumptions and limitations, and the appropriate equation to use depends on the specific application.

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