LAMINAR AND TURBULENT FLOW

We can observe the nature of the flow of a fluid by injecting a fine filament of dye into the stream of flow and taking note of what happens to this filament. It was found in experiments that at low velocities the dye filament remained intact and that the filaments made parallel lines in the stream of flow. This is known as Laminar flow (or viscous or streamline).

If the velocity of flow is gradually increased, the dye filament is eventually broken up and spread over the cross section of the pipe. This is turbulent flow, in which the particles of fluid are not moving in parallel lines but are moving across the general direction of flow.

If a fluid particle in a stream is disturbed, its inertia will tend to move it in a new direction, however the viscous forces from the surrounding fluid will tend to move it in the general direction of flow. If the shear forces are large enough to overcome any deviation, then we have viscous or laminar flow. However, if the shear forces are relatively weaker, and not sufficient to overcome the inertia of the particles, then we have turbulent flow.

[pic]

Therefore it is the ratio of the inertia to the viscous forces which determines whether flow will be laminar or turbulent.

The ratio of the inertia forces to the viscour forces is given by:

[pic] c l (Reynolds Number) μ

Therefore, it is the Reynolds number which determines whether a flow will be laminar or turbulent.

As Kinematic Viscosity (ν) = μ, [pic]

Reynolds number can also be expressed as c l ν

l is the characteristic dimension in the system e.g. the diameter of the pipe in which the fluid is flowing.

Experiments have shown that if the Reynolds number is less than 2000, then the flow will be laminar. If it is above 2000 it is likely to be turbulent, however turbulent flow can exist at much higher Reynolds numbers.

Example Water flows through a pipe 30mm diameter at a velocity of 10 m/s. If the dynamic viscosity of water is taken as 1.30 x 10-3 kg/ms and its density as 1000 kg/m3, determine whether the flow will be laminar or turbulent.

Reynolds number = [pic] c l μ

= 1000 x 10 x 0.03 1.3 x 10-3

= 230769

This is significantly larger than 2000 and therefore the flow will be turbulent.

Problem If oil of specific gravity 0.85 and dynamic viscosity 14 x 10-2 kg/ms is pumped through the pipe at the same viscocity, what type of flow will occur.
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TURBULANT FLOW

LAMINAR FLOW

MOTION OF PARTICLES

DYE FILAMENT

FLOW

FLOW