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.

Where,

x = Distance from leading edge up to which laminar
boundary layer exists

U = Free stream velocity of the fluid

v = Kinematic viscosity of the fluid

Further we will go ahead to start a new topic i.e. Turbulent boundary layer, in the subject of fluid mechanics with the help of our next
post.

Do you have any suggestions? Please write in comment
box.

### Reference:

Fluid mechanics, By R. K. Bansal

Image courtesy: Google

## No comments:

## Post a Comment