Reynolds number - Wikipedia
The Reynolds (Re) number is a quantity which engineers use to estimate if a fluid flow is laminar or turbulent. This is important, because increased mixing and . That is a remarkable demonstration. After the crank has been turned through three revolutions, you would swear that the fluid was well-mixed. This becomes a very important classification of flows and is brought out vividly It is also found that a flow in a pipe is laminar if the Reynolds Number (based on.
The Mach number also doubles as a unit. An airplane flying through the air with a speed equal to the speed of sound in air at that location has a Mach number of 1. It could also be described as flying at Mach 1. The odd reversal of the usual number-unit sequence to unit-number is unique to the Mach number. The Mach number is meaningful because it is a comparison of the inertial resistance to the compressional resistance experienced by an object moving through a fluid.
When a solid object and a fluid are in relative motion — like a bird flying through the air or the wind blowing around a mountain — it is usually the fluid that yields to the solid. Solids are held together by intermolecular forces and atomic bonds. If the cohesive forces between the particles in a solid are considered significant and long lasting, then the cohesive forces in a liquid are weak and short lived.
In a gas they are virtually nonexistent. You might think that fluids are a pushover for a moving solid, but this is not always the case.
The molecules that make up even the most tenuous of gases won't be able to get out of the way of a solid body moving at a considerable speed. Meteors quite commonly break up on entering the Earth's atmosphere from space. They also burn up, but that is as much an result of frictional heating as it is of trying to push the air out of the way. Aircraft are known to have broken up during flight from the buffeting effects of moving air on a weakened or damaged part.
Classification of Flows, Laminar and Turbulent Flows
Where the viscosity is naturally high, such as polymer solutions and polymer melts, flow is normally laminar. The Reynolds number is very small and Stokes' Law can be used to measure the viscosity of the fluid. Spheres are allowed to fall through the fluid and they reach the terminal velocity quickly, from which the viscosity can be determined.
The laminar flow of polymer solutions is exploited by animals such as fish and dolphins, who exude viscous solutions from their skin to aid flow over their bodies while swimming.Reynolds Number
It has been used in yacht racing by owners who want to gain a speed advantage by pumping a polymer solution such as low molecular weight polyoxyethylene in water, over the wetted surface of the hull.
It is, however, a problem for mixing of polymers, because turbulence is needed to distribute fine filler for example through the material. Inventions such as the "cavity transfer mixer" have been developed to produce multiple folds into a moving melt so as to improve mixing efficiency. The device can be fitted onto extruders to aid mixing.
Sphere in a fluid[ edit ] For a sphere in a fluid, the characteristic length-scale is the diameter of the sphere and the characteristic velocity is that of the sphere relative to the fluid some distance away from the sphere, such that the motion of the sphere does not disturb that reference parcel of fluid. The density and viscosity are those belonging to the fluid.
Under the condition of low Re, the relationship between force and speed of motion is given by Stokes' law. Such considerations are important in natural streams, for example, where there are few perfectly spherical grains. For grains in which measurement of each axis is impractical, sieve diameters are used instead as the characteristic particle length-scale.
Both approximations alter the values of the critical Reynolds number.
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Fall velocity[ edit ] The particle Reynolds number is important in determining the fall velocity of a particle. When the particle Reynolds number indicates laminar flow, Stokes' law can be used to calculate its fall velocity.
When the particle Reynolds number indicates turbulent flow, a turbulent drag law must be constructed to model the appropriate settling velocity.