Laminar and Turbulent Flow
Observation shows that two entirely different types of fluid flow exist. This was demon- strated by Osborne Reynolds in 1883 through an experiment in which water was discharged from a tank through a glass tube. The rate of flow could be controlled by a valve at the outlet, and a fine filament of dye injected at the entrance to the tube. At low velocities, it was found that the dye filament remained intact throughout the length of the tube, showing that the particles of water moved in parallel lines. This type of flow is known as laminar, viscous or streamline, the particles of fluid moving in an orderly manner and retaining the same relative positions in successive cross- sections.
As the velocity in the tube was increased by opening the outlet valve, a point was eventually reached at which the dye filament at first began to oscillate and then broke up so that the colour was diffused over the whole cross-section, showing that the particles of fluid no longer moved in an orderly manner but occupied different relative position in successive cross-sections. This type of flow is known as turbulent and is characterized by continuous small fluctuations in the magnitude and direction of the velocity of the fluid particles, which are accompanied by corresponding small fluctuations of pressure.
When the motion of a fluid particle in a stream is disturbed, its inertia
will tend to carry it on in the new direction, but the viscous forces due to the surrounding fluid will tend to make it conform to the motion of the rest of the stream. In viscous flow, the viscous shear stresses are sufficient to eliminate the effects of any deviation, but in turbulent flow they are inadequate. The criterion which determines whether flow will be viscous of turbulent is therefore the ratio of the inertial force to the viscous force acting on the particle. The ratio
μ
ρvl const force Viscous force Inertial ⨯= Thus, the criterion which determines whether flow is viscous or turbulent is the quantity ρvl /μ, known as the Reynolds number. It is a ratio of forces and, therefore, a pure number and may also be written as ul /v where is the kinematic viscosity (v=μ/ρ).
Experiments carried out with a number of different fluids in straight pipes of different diameters have established that if the Reynolds number is calculated by making 1 equal to the pipe diameter and using the mean velocity v , then, below a critical value of ρvd /μ = 2000, flow will normally be laminar (viscous), any tendency to turbulence being damped out by viscous friction. This value of the Reynolds number applies only to flow in pipes, but critical values of the Reynolds number can be established for other types of flow, choosing a suitable characteristic length such as the chord of an aerofoil in place of the pipe diameter. For a
