Question

Why boundary layer thickness of turbulent is higher than laminar flow?

Answer 1

Consider flow over a flat plate

As the fluid flows over the plate, a velocity profile is set up across the direction perpendicular to flow predominantly. Velocity of the fluid near the plate is the velocity of the plate with which it is moving. If the plate is at rest (stationary), the velocity of the plate is zero. While the free stream away from the plate surface will have the maximum velocity.

This region, where there is a velocity profile in the flow due to the shear stress at the wall, we call the boundary layer.

We define the thickness of this boundary layer as the distance from the wall to the point where the velocity is 99% of the "free stream" velocity, the velocity in the middle of the pipe or river.

boundary layer thickness, d = distance from wall to point where u = 0.99 U(freestream)

The value of d will increase with distance from the point where the fluid first starts to pass over the boundary - the flat plate in our example. It increases to a maximum in fully developed flow.

Laminar flow is characterised by the systematic movement of fluid in the form of layers moving adjacent to each layer.

we could calculate whether a particular flow in a pipe is laminar or turbulent using the Reynolds number.

Re = (dur)/m

(r = density u = velocity m = viscosity d = pipe diameter)

Laminar flow: Re < 2000

Transitional flow: 2000 < Re < 4000

Turbulent flow: Re > 4000

Once the boundary layer has reached the centre of the pipe the flow is said to be fully developed. (Note that at this point the whole of the fluid is now affected by the boundary friction.)

the rate at which the boundary layer thickness of a laminar boundary layer is small.

For a flat plate it is given by

For a turbulent flow it is given by

So for laminar flow,

Boundary layer thickness is proportional to x^.5

For turbulent flow,

Boundary layer thickness is proportional to x^.8

Hope so it will help you ^-^