WHAT IS LAMINAR BOUNDARY LAYER ?

We were discussing the basic concept of streamline and equipotential line, dimensional homogeneity, Buckingham pi theorem, difference between model and prototype, basic principle of similitude i.e. types of similarity, various forces acting on moving fluid and Boundary layer theory in the subject of fluid mechanics, in our recent posts.

Now we will go ahead to start a new topic i.e. Laminar boundary layer, in the subject of fluid mechanics with the help of this post.

Laminar boundary layer

We will try to understand here the basic principle and meaning of laminar boundary layer and turbulent boundary layer. First, we will see here laminar boundary layer.

Let us consider the flow of a fluid over a smooth thin and flat plate. Let us assume that this thin and flat plate is located parallel to the direction of fluid flow as displayed here in following figure.

Let us consider that fluid is flowing with free stream velocity U and with zero pressure gradient on one side of the stationary plate.

As we have already discussed that when a real fluid will flow over a solid body or a solid wall, the particles of fluid will adhere to the boundary and there will be condition of no-slip. We can also conclude that the velocity of the fluid particles, close to the boundary, will have equal velocity as of the velocity of boundary.

As we have assumed that plate is stationary and therefore the velocity of fluid flow over the surface of plate will be zero.

If we move away from the plate, the velocity of fluid particles will also be increasing. Velocity of fluid particles will be changing from zero at the surface of stationary boundary to the free stream velocity (U) of the fluid in a direction normal to the plate.

Therefore, there will be presence of velocity gradient, due to variation of velocity of fluid particles, near the surface of the fluid.

This velocity gradient will develop shear resistance and this shear resistance will retard the fluid. Therefore, fluid with free stream velocity (U) is retarded in the surrounding area of the solid surface of the plate and boundary layer region will be started at the sharp leading edge.

Once we will go away from the sharp leading edge, retardation of the fluid will be increased and therefore boundary layer region increases with increase in the retardation of the fluid. The increase in the region of boundary layer with increase in the retardation of the fluid will also be termed as growth of boundary layer.

Near the leading edge of the surface of the plate, where thickness will be small, the flow in the boundary layer will be laminar and this layer of the fluid will be termed as laminar boundary layer.

Let us see the above figure. AE indicates the laminar boundary layer.

Laminar zone

Length of the plate from the leading edge up to which laminar boundary layer exists will be termed as laminar zone. AB indicates the laminar zone in above figure.

Length of the plate from the leading edge up to which laminar boundary layer exists i.e. laminar zone will be determined with the help of following formula as mentioned here.