- Boundary-Layer Theory | choisiochildhand.gq
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- Boundary Layer Theory Study Notes for Civil Engineering

On the slide we show the streamwise velocity variation from free stream to the surface. In reality, the effects are three dimensional.

## Boundary-Layer Theory | choisiochildhand.gq

From the conservation of mass in three dimensions, a change in velocity in the streamwise direction causes a change in velocity in the other directions as well. There is a small component of velocity perpendicular to the surface which displaces or moves the flow above it. One can define the thickness of the boundary layer to be the amount of this displacement. The displacement thickness depends on the Reynolds number which is the ratio of inertial resistant to change or motion forces to viscous heavy and gluey forces and is given by the equation : Reynolds number Re equals velocity V times density r times a characteristic length l divided by the viscosity coefficient mu.

Boundary layers may be either laminar layered , or turbulent disordered depending on the value of the Reynolds number. For lower Reynolds numbers, the boundary layer is laminar and the streamwise velocity changes uniformly as one moves away from the wall, as shown on the left side of the figure.

For higher Reynolds numbers, the boundary layer is turbulent and the streamwise velocity is characterized by unsteady changing with time swirling flows inside the boundary layer. The external flow reacts to the edge of the boundary layer just as it would to the physical surface of an object.

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So the boundary layer gives any object an "effective" shape which is usually slightly different from the physical shape. Skip to main content Skip to table of contents. Advertisement Hide. Boundary-Layer Theory.

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Front Matter Pages Some Features of Viscous Flows. Hermann Schlichting Deceased , Klaus Gersten.

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Pages Fundamentals of Boundary—Layer Theory. Field Equations for Flows of Newtonian Fluids. In doing so the fluid will be considered to be a continuum. Before we discuss solutions of the equations of motion in the next chapter, some general properties of these equations shall first be discussed. First we will examine which quantities enter into the solutions of the equations of motion. The task of finding exact solutions of the Navier—Stokes equations is generally extremely difficult.

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## Boundary Layer Theory Study Notes for Civil Engineering

The nonlinearity of these equations forbids the use of the principle of superposition which served so well in the case of inviscid incompressible potential flows. We now wish to treat flows with very small viscosity or very high Reynolds numbers. An important contribution to the science of fluid motion was made in by L. Prandtl Prandtl showed the manner in which the viscosity has its effect for high Reynolds number flows and how the Navier—Stokes differential equations can be simplified to yield approximate solutions for this limiting case.

We shall now derive the simplifications which arise for the Navier—Stokes equations in the case of very small friction forces in a physically illustrative manner. Before further examples of the calculation of boundary layers are treated in the next chapter, some general properties of boundary—layer equations will be discussed. We will confine ourselves to steady, two—dimensional, incompressible boundary layers. In order to calculate the flow in the boundary layer, in general partial differential equations must by solved.

Today there are many very effective and precise numerical methods available, as will be shown in Chap. Our considerations of boundary—layer flows up until now have referred only to the velocity field. These will now be correspondingly extended to include the temperature field. It will be assumed that heat is transferred to the flow field through the surrounding walls, so that a temperature field forms together with the velocity field.

In the treatment of thermal boundary layers until now, we assumed constant physical properties and so the velocity field was independent of the temperature field.

In this chapter we will investigate the effect of variable physical properties. It emerges from the previous discussions of boundary—layer flows that the boundary conditions, i.

In the previous chapters, the calculation of boundary layers was restricted to the plane case, where the two velocity components depended only on two spatial coordinates. There was no velocity component present in the direction of the third spatial coordinate.