How Is the Boundary Layer Analyzed as Incompressible in Viscous Flow?

In summary, incompressible viscous flow is a type of fluid flow characterized by constant density and viscosity. The governing equations for this type of flow are the Navier-Stokes equations, which are derived from the laws of fluid mechanics. Real-world examples include water flow in pipes, air movement around objects, and blood flow in the human body. Incompressible viscous flow differs from compressible flow in that the density remains constant and the effects of compressibility must be taken into account. Common methods for solving incompressible viscous flow problems include analytical and numerical methods, as well as computational fluid dynamics (CFD).
  • #1
Stonescar
2
0
Hello,
I'm looking at this problem which states:

"A parallel air flow along a semi infinite flat plate has undisturbed parameters as follows: "

Then they list the speed, temprature, viscousity and pressure.

"Demonstrate that the boundary layer can treated by means of incompressible analysis. "

The solution says:

Incompressible if M[itex]^{2}_{\infty}[/itex]>>4

Where M[itex]^{2}_{\infty}[/itex]=[itex]\frac{U^{2}}{\gamma R T}[/itex]

I'm just wondering what formula this is? I've never seen it before.
What is M ?
 
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  • #2
M is the Mach Number.
 

Related to How Is the Boundary Layer Analyzed as Incompressible in Viscous Flow?

1. What is incompressible viscous flow?

Incompressible viscous flow is a type of fluid flow in which the fluid is assumed to have a constant density and does not change in volume as it flows. The flow is also characterized by its viscosity, which is a measure of the internal friction of the fluid.

2. What are the governing equations for incompressible viscous flow?

The governing equations for incompressible viscous flow are the Navier-Stokes equations. These equations describe the conservation of momentum and mass for the fluid, and are derived from the laws of fluid mechanics.

3. What are some real-world examples of incompressible viscous flow?

Incompressible viscous flow can be observed in many common situations, such as the flow of water in pipes, the movement of air around objects, and blood flow in the human body. It is also important in engineering applications, such as in the design of hydraulic systems and aerodynamics of airplanes.

4. How is incompressible viscous flow different from compressible flow?

The main difference between incompressible viscous flow and compressible flow is that in incompressible flow, the density of the fluid remains constant, while in compressible flow, the density can change. Additionally, in compressible flow, the effects of compressibility and changes in fluid density must be taken into account in the governing equations.

5. What are some common methods for solving incompressible viscous flow problems?

Some common methods for solving incompressible viscous flow problems include analytical methods, such as the method of separation of variables, and numerical methods, such as finite difference and finite volume methods. Computational fluid dynamics (CFD) is also commonly used to simulate and analyze incompressible viscous flow in complex geometries and situations.

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