Dimensionless Reynolds

Reynolds Number. The Reynolds number, Ke, is named after Osborne Reynolds, who studied the flow of fluids, and in particular the transition from laminar to turbulent flow conditions. This transition was found to depend on flow velocity, viscosity, density, tube diameter, and tube length. Using a nondimensional group, defined as p NDJp, the transition from laminar to turbulent flow for any internal flow takes place at a value of approximately 2100. Hence, the dimensionless Reynolds number is commonly used to describe whether a flow is laminar or turbulent. Thus... 

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU p/ I where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. 

A generalized equation for the limiting-current response of different detectors, based on the dimensionless Reynolds (Re) and Schmidt (Sc) numbers has been derived by Hanekamp and co-workers (62) ... 

For an incompressible viscous fluid (such as the atmosphere) there are two types of flow behaviour 1) Laminar, in which the flow is uniform and regular, and 2) Turbulent, which is characterized by dynamic mixing with random subflows referred to as turbulent eddies. Which of these two flow types occurs depends on the ratio of the strengths of two types of forces governing the motion lossless inertial forces and dissipative viscous forces. The ratio is characterized by the dimensionless Reynolds number Re. 

An indicator of the validity of the creeping flow approximation is the dimensionless Reynolds number ... 

The dimensionless Reynolds number (Re) is used to characterize the laminar-turbulent transition and is commonly described as the ratio of momentum forces to viscous forces in a moving fluid. It can be written in the form... 

A characteristic quantity describing the viscous flow state is the dimensionless Reynolds number Re. 

Laminar flow to turbulent flow transition — When increasing the velocity of the flow, a transition from -> laminar flow to rippling and finally to turbulent flow will occur [i]. The transition from laminar to turbulent flow is governed by the dimensionless -> Reynolds number. Ref [i] Levich VG (1962) Physicochemical hydrodynamics. Prentice-Hall, Englewood Cliffs... 

Rapid and complete mixing in cylindrical channels d > 100 pm) is obtained in the tmbulent regime. Turbulence is expressed by the dimensionless Reynolds number, Re, according to... 

Reducing the bed length while keeping the space velocity the same will reduce the fluid velocity proportionally. This will affect the fluid dynamics and its related aspects such as pressure drop, hold-ups in case of multiphase flow, interphase mass and heat transfer and dispersion. Table II shows the large variation in fluid velocity and Reynolds number in reactors of different size. The dimensionless Reynolds number (Re = u dp p /rj, where u is the superficial fluid velocity, dp the particle diameter, p the fluid density and t] the dynamic viscosity) generally characterizes the hydrodynamic situation. 

We start this chapter with a general physical description of the convection mechanism. We then discuss (he velocity and thermal botmdary layers, and laminar and turbitlent flows. Wc continue with the discussion of the dimensionless Reynolds, Prandtl, and Nusselt nuinbers, and their physical significance. Next we derive the convection equations on the basis of mass, momentiim, and energy conservation, and obtain solutions for flow over a flat plate. We then nondimeiisionalizc Ihc convection equations, and obtain functional foiinis of friction and convection coefficients. Finally, we present analogies between momentum and heat transfer. 

B Gain a working knowledge of the dimensionless Reynolds, Prandtl, and Nusselt numbers, B Distinguish betvreen laminar and turbulent llovrs, and gain an understanding of the mechanisms of momentum and heat transfer In turbulent flow,... 

For external flow, the dimensionless Reynolds number is expressed as... 

What are the conditions for flow to become turbulent This depends on the preponderance of inertial stresses—proportional to pv2—over frictional or viscous stresses. The latter are equal to j/ P in laminar flow is proportional to v/L, where L is a characteristic length perpendicular to the direction of flow. The ratio is proportional to the dimensionless Reynolds number, given by... 

Transition from laminar to turbulent flow Reynolds number. The factors that determine the point at which turbulence appears in a laminar boundary layer are coordinated by the dimensionless Reynolds number defined by the equation... 

It is useful to relate the relative magnitudes of the inertial and viscous forces as a dimensionless Reynolds number... 

Turbulent Flow. The dimensionless Reynolds number Re of a Newtonian fluid flowing in a pipe of radius R can be defined by... 

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