Reynolds criterion

This also is refetTed to as the Reynolds criterion. Reynolds numbers are only comparable when they refer to geometrically similar flows and. provided that all the boundary conditions can be described by the scale velocity and scale length, flows of the same Reynolds number are dynamically similar. For an airfoil, it is... 

In passing it is of interest to point out that Reynolds criterion for turbulent motion of vibrating particles has been found by Andrade (1936) to occur when... 

We observe that Reynolds criterion for pipes which distinguishes... 

Swindin had long been impressed with the reputation of Osborne Reynolds—the more so since he actually had heard the great man lecture. However, as he says, he truly did not understand the implications of Reynolds work on fluid flow until it was explained to him by GrifiBths in his Battersea lectures. Once he realized the power of the flow criterion particularly to characterize the multifarious fluids with which he had to deal, he was quick to exploit it. His book well may be the flrst published practical application of the Reynolds criterion to processing problems. Certainly no mention of the Reynolds number or its application to fluid flow appears in Liddell s Handbook, published the same year... 

The usable range of unburnt gas velocities depends on the interaction of several factors. If the velocity is too high, the flame may blow off, or flow within the burner may exceed the Reynolds criterion and become turbulent. If too low, the flame will either flash back, with wide burner tubes, or be extinguished if the tubes are below the extinction diameter. Each factor depends on the burner design, and on the flame composition, but the overall result is not too restrictive, particularly for... 

One of the most recent areas to be attacked is the turbulent regime. Turbulent flames are of dominant importance, and are typically emitters of audible noise. Since Reynolds criterion for turbulence... 

Actual speed is 1 - 4 m/s, already exceeding the critical speed. The model Reynolds criterion cannot be considered. In addition, the porosity of experimental models and prototypes is small and substantially equal, so the formula (6), (7) can be further simplified to... 

The fact that in highly turbulent flows liquid viscosity doesn t influence on main volume medium movement is interesting and important enough [3, 135]. In this case they say that flow is self-simila in relation to viscosity and the influence of the last one is displayed in a narrow enough wall layer. The value of Reynolds criterion above which the self-simila field is observed in many respects is determined by flow geometry. For example, in [3] they showed that under sphere flow the... 

It is well known that fundamental criterion of hydrodynamic similarity is Reynolds criterion characterizing the influence of frictional force on liquid movement [3,12,135,202,204] ... 

Figure 3.18. Dependence of critical value of Reynolds criterion (Recr) and parameter f on divergent opening angle (y) in reactor of divergent-convergent type.

Figure 4.20. Dependence of heat-transfer coefficient K on the rate of internal flow wb and Reynolds criterion Re in apparatus of cylindrical (1) and divergent-convergent (2) designs.

FIGURE 1.7 Relationships between (a) the flow velocity Vf and the specific surface area (5 ) or the primary particle diameter, d, and (b) the Reynolds criterion (RJ and the value for several series of nanosilica samples synthesized under different conditions that result in a certain scatter in the data. 

In order to simulate the action of a flow on an adhering particle we must maintain geometric, kinematic (velocity ratio), and dynamic (mass and force) similarity. We cannot choose these conditions in detail. We can only note that for river-type flows the Froude criterion Fr = v /gZ ensures d5mamic similarity and the Reynolds criterion Re = vd/ v kinematic similarity. Since the forces of gravity prevail over viscosity, the decisive factor in simulating river flows will be the Froude criterion. 

A criterion for the namre of flow, either laminar or mrbulent flow in fluid systems is the value of the Reynolds number. This number, Rg is defined by the equation... 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

The group udp/p, known as the Reynolds number, is one which frequently arises in the study of fluid flow and affords a criterion by which the type of flow in a given geometry may be characterised. Equation 1.8 involves the reciprocal of the Reynolds number, although this may be rewritten as ... 

Reynolds, O. Papers on Mechanical and Physical Subjects 2 (1881-1901) 51. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and the law of resistance in parallel channels. 535. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. 

Thus, the available data related to transition in circular micro-tubes testify to the fact that the critical Reynolds number, which corresponds to the onset of such transition, is about 2,000. The evaluation of critical Reynolds number in irregular micro-channels will entail great difficulty since this problem contains a number of characteristic length scales. This fact leads to some vagueness in definition of critical Reynolds number that is not a single criterion, which determines flow characteristics. 

Flow of the liquid past the electrode is found in electrochemical cells where a liquid electrolyte is agitated with a stirrer or by pumping. The character of liquid flow near a solid wall depends on the flow velocity v, on the characteristic length L of the solid, and on the kinematic viscosity (which is the ratio of the usual rheological viscosity q and the liquid s density p). A convenient criterion is the dimensionless parameter Re = vLN, called the Reynolds number. The flow is laminar when this number is smaller than some critical value (which is about 10 for rough surfaces and about 10 for smooth surfaces) in this case the liquid moves in the form of layers parallel to the surface. At high Reynolds numbers (high flow velocities) the motion becomes turbulent and eddies develop at random in the flow. We shall only be concerned with laminar flow of the liquid. 

Below and to the right of this line, the Klimov-Williams criterion is satisfied and wrinkled laminar flames may occur. The figure shows that this region includes both large and small values of turbulence Reynolds numbers and velocity ratios (VISA) both greater and less than 1, but predominantly large Da. 

The internal resistance is always decreased substantially when a bubble or drop oscillates, but the external resistance may be unaffected if the Reynolds number is high enough. A rough criterion can be obtained from Eq. (11-63) for vibration of a particle in an axial stream. Oscillation has negligible effect on the external resistance if... 

At this point, it is also important to check the plug-flow assumption as the simple model assumes plug flow for the liquid. For the specified Reynolds number, the Peclet number is found to be 0.59 using the Michell-Furzer correlation (eq. 3.417). The minimum value of Z/d, evaluated using the Mears criterion, is 15.87 (eq. (3.421)), lower than the value used in the experiments, which is about 30. Thus, the operation can be assumed as plug flow. 

Since the velocity profile approaches the Hagen-Poiseuille profile asymptotically, the factor 0.05 depends on a criterion for deciding how close the profile needs to be to the Hagen-Poiseuille profile (e.g., the maximum velocity is within 1% of the steady state maximum velocity). In any case, the entry length scales linearly with the Reynolds number. 

According to Rivin and Shchelkin, if one considers a wider interval of pressures and diameters (i.e., of values of the Reynolds number) than that with which Breton [39] worked, the relation between the spin and the limit ceases to be single-valued. Such a single-valued relation would necessarily follow from a theory with only the Rivin-Sokolik criterion Dr /d in which we make only the wave front width concrete, replacing it with the tube diameter d or the braking distance d/ = df (Re). One might think that when the Rivin-Sokolik criterion is increased we will move from the classical picture with a narrow plane front and a velocity which does not differ from the calculated value, to appearance of spin at one value of the criterion, and to the detonation limit at an even larger value of Dr /d. Such simple behavior is indeed observed in series of experiments performed in tubes of constant diameter at constant pressure (Breton), i.e., at a practically constant value of the Reynolds number. 

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