Explain Development of boundary layer within circular pipe.

Development of boundary layer within the  circular pipe:

The development of boundary layer within a circular pipe is shown in the figure below for two cases:

• When the final flow is laminar

• When the final flow is turbulent

In case of pipe,all particles will start to flow with the same velocity except for the very thin film in contact with the wall as shown in the figure. As the fluid progresses along the pipe, the streamlines in the vicinity of the wall are slowed down by friction emanating  from the wall, but since for steady flow the mass flow rate at the different section must be the same, the velocity in the centre must be accelerated , until the final velocity is a parabola.

Theoretically an infinite distance is required for this , but it has been established by both observation and theory that the maximum velocity in the centre of the pipe will reach 99% of its ultimate value in the distance `L....Show More

Development of boundary layer within the  circular pipe:

The development of boundary layer within a circular pipe is shown in the figure below for two cases:

• When the final flow is laminar

• When the final flow is turbulent

In case of pipe,all particles will start to flow with the same velocity except for the very thin film in contact with the wall as shown in the figure. As the fluid progresses along the pipe, the streamlines in the vicinity of the wall are slowed down by friction emanating  from the wall, but since for steady flow the mass flow rate at the different section must be the same, the velocity in the centre must be accelerated , until the final velocity is a parabola.

Theoretically an infinite distance is required for this , but it has been established by both observation and theory that the maximum velocity in the centre of the pipe will reach 99% of its ultimate value in the distance `L_e` would be,

`L_e=0.058 R_e*D`.....(i)

In the entry region of the length `L_e`, the flow is unestablished.i.e, the velocity profile is changing.The outer zone increases in thickness as it moves along the wall , and is known as Boundary layer.

At section AB as shown in figure, the boundary layer has grown until it progresses to the entire section of the pipe. At this  point, for laminar flow, the velocity profile is a perfect parabola. Beyond section AB, the velocity profile does not change, and the flow is known as established flow.

After the flow is established in laminar flow, the velocity profile is parabolic as shown in figure.

If the Reynold number is above the critical value, so that the developed flow is turbulent , the initial condition is much like that in above figure. But as the laminar boundary layer increases in thickness, a point is soon reached where a transition occurs and the boundary layer becomes turbulent,. In other words, the development starts with a laminar profile, undergoes a transition and change over to turbulent profile and stays turbulent thereafter as shown in figure. The turbulent boundary layer thickness increases much more rapidly and soon the two layers from opposite sides meet at the pipe axis and there is then fully developed turbulent flow.

The boundary layer can grow only upto the centerline of the pipe and the boundary layer thickness cannot exceed the thickness of the radius of the pipe. Since the velocity must be zero at the surface of the wall, a laminar sublayer occurs immediately next to the wall.

The rate of the growth of the boundary layer depends upon the Reynolds number as:

For laminar layer,

`delta/X=5/root()(R_e)`

And for turbulent layer,

`delta/X=0.37/R_e^0.2`

Note:Two figures are to be included here����.i.e for laminar flow and turbulent flow..they will be uploaded soon...