Velocity, mean flow rate

The mean flow rate velocity (V) is equal to 2/3 of the maximum velocity,... 

By using (1.5.5), we obtain the mean flow rate velocity... 

Table 1.2 presents values of the drag coefficients for tubes with various shapes of the cross-section (according to [80]). The Reynolds number Re[Pg.31]

A flow of fluid through a smooth tube of circular cross-section remains laminar while Re=a(V)/v < 1500 [427], where a is the tube radius and (V) the mean flow rate velocity of the fluid. For higher Reynolds numbers, the loss of stability of the laminar flow is observed and an intermediate regime occurs. For Re > 2500, a fully developed regime of turbulent flow is established which is characterized by a chaotic variation of the velocity and pressure in time and space. 

The mean flow rate velocity (U) of a particle, which is obtained in a large number of experiments when an arbitrarily oriented particle falls in a fluid, is determined for the Stokes flow by the formula [179] ... 

Let us consider the absorption of weakly soluble gases on the free surface of a liquid film in a laminar flow on an inclined plane. It follows from the results of Section 1.3 that for moderate velocities of motion, the steady-state distribution of the velocity inside the film has the form of a semiparabola with maximum velocity 17max on the free surface, which is one and a half of the mean flow rate velocity (V) ... 

The mean flow rate velocity of the film flow of a viscoplastic fluid is given by the formula... 

Mean flow rate velocity, (V) a2AP na ( aAP 1 a4AP a3To 2 L 3]... 

Up to the different notation (APjL -> pg sin a), formula (6.4.15) coincides with the expression (6.2.5) for shear stresses, which was obtained earlier for film flows. Therefore, we can calculate the velocity profile V in a plane channel (in the region 0 < < h), the maximum velocity f/max, and the mean flow rate velocity (V) for nonlinear viscous fluids by formulas (6.2.8)—(6.2.11) and for viscoplastic fluids by formulas (6.2.17)-(6.2.19) if we formally replace pg sin a by AP/L in these formulas. 

It follows from Tables 6.5 and 6.6 that the maximum temperature difference for a power-law fluid in a circular tube can be expressed via the mean flow rate velocity (V ) of the flow as follows ... 

The total number of openings N affects the flow rate, velocity, and Ret) in the region of the last opening, which is determined to (1/AO of the opening at the entrance of the distributor. So, ReD at die first and the last opening of the distributor can be calculated, and in turn, the corresponding values of the fanning friction factors can be estimated. The mean value of these two factors should be used in the calculations in diis procedure. 

NMR imaging techniques were applied to the measurements of velocity field in opaque systems such as tomato juice and paper pulp suspensions [58-60]. In both cases, the particle concentrations are sufficiently high that widely applied techniques such as hot film and laser Doppler anemometry could not be used. The velocity profile for a 6 % tomato juice slurry clearly showed a power-law behavior [58, 59]. Row NMR images for a 0.5 % wood pulp suspension provided direct visual of three basic types of shear flow plug flow, mixed flow and turbulent flow as mean flow rate was increased. Detailed analysis of flow NMR image is able to reveal the complex interaction between the microstructure of suspensions and the flow [60]. 

Now from all solutions in plane (5, s) we ll consider only those ones which have extremely properties, namely, their phase velocity c, amplitude a and mean flow rate qo are maximal at every fixed wave number s. We refer to this solutions as dominating waves. From Figure 6 it is clear that at (5 = 0.15 the set of dominating waves includes 4 pieces belonging to described families 7a, 7, 7c,i 7c,2- There are jumps of the dominating waves parameters at values of s dividing one piece from the other. 

The data points in the region of discontinuity represent mean flow rates calculated from the velocity of the driving piston. In reality, the output oscillates between the upper and lower branches of the flow curve. The bars on the stainless steel data in Figure 12.2 denote the range of pressure fluctuations during these oscillations. (The pressure fluctuations are small relative to the base pressure, so they do not affect the flow curve in any substantive way.) There is massive slip on the... 

Computer Models, The actual residence time for waste destmction can be quite different from the superficial value calculated by dividing the chamber volume by the volumetric flow rate. The large activation energies for chemical reaction, and the sensitivity of reaction rates to oxidant concentration, mean that the presence of cold spots or oxidant deficient zones render such subvolumes ineffective. Poor flow patterns, ie, dead zones and bypassing, can also contribute to loss of effective volume. The tools of computational fluid dynamics (qv) are useful in assessing the extent to which the actual profiles of velocity, temperature, and oxidant concentration deviate from the ideal (40). 

Because of the complexity of designs and performance characteristics, it is difficult to select the optimum atomizer for a given appHcation. The best approach is to consult and work with atomizer manufacturers. Their technical staffs are familiar with diverse appHcations and can provide valuable assistance. However, they will usually require the foUowing information properties of the Hquid to be atomized, eg, density, viscosity, and surface tension operating conditions, such as flow rate, pressure, and temperature range required mean droplet size and size distribution desired spray pattern spray angle requirement ambient environment flow field velocity requirements dimensional restrictions flow rate tolerance material to be used for atomizer constmction cost and safety considerations. 

Circulating fluidized-beds do not contain any in-bed tube bundle heating surface. The furnace enclosure and internal division wall-type surfaces provide the required heat removal. This is possible because of the large quantity of soflds that are recycled internally and externally around the furnace. The bed temperature remains uniform, because the mass flow rate of the recycled soflds is many times the mass flow rate of the combustion gas. Operating temperatures for circulating beds are in the range of 816 to 871°C. Superficial gas velocities in some commercially available beds are about 6 m/s at full loads. The size of the soflds in the bed is usually smaller than 590 p.m, with the mean particle size in the 150—200 p.m range (81). 

For small downdraft tables used for chemical work, a flow rate of 0.28 m s and m- table is used. This gives a mean velocity immediately above the surface of approximately 0.3 m s h This is a very low velocity, which can not capture moving contaminants. When these values are used, a maximum use height of 0.15 m is recommended, which should result in a small leakage from the source to the surrounding. This presumes there is at least 0.1 m of uncovered surface between the worker and the source and that the surface is covered to less than 30%. For these tables the pressure difference is between 50 and 100 Pa, depending on the density of holes. ... 

The vane anemometer s physical dimensions are often quite large (compared with other local velocity measurement instruments). It does not strictly measure a local velocity at all, but rather provides a spatially integrated mean value. This is an advantage in many cases where the air volume flow rate has to be predicted using local velocities and an integration principle. 

The graphical integration method is based on graphical presentation of the average flow profile. For a circular duct, the cross-section is virtually divided into several concentric ring elements. The spatial mean velocity of such an element is determined as an arithmetical mean of local velocities along the circumference of the corresponding radius. For a circular cross-section the flow rate can be expressed as... 

The volume flow rate is calculated as the arithmetical mean of the measured velocities multiplied by the duct cross-sectional area. The number of diameters along which the traversing occurs is not defined. If a near-symmetrical velocity profile is expected, an even travetse along one diameter may be sufficient. In case of a more disturbed profile, traversing along two or more diameters is recommended. 

There is also a standardized method based on the estimation of the flow rate on one measurement point only, In this method the velocity probe is placed in the duct so that the measured local velocity is equal to the mean axial velocity. In fully developed turbulent duct flow, this distance from the wall... 

A reduced scale of the model requires an increased velocity level in the experiments to obtain the correct Reynolds number if Re < Re for the prob lem considered, but the experiment can be carried out at any velocity if Re > RCj.. The influence of the turbulence level is shown in Fig. 12.40. A velocity u is measured at a location in front of the opening and divided by the exhaust flow rate in order to obtain a normalized velocity. The figure show s that the normalized velocity is constant for Reynolds numbers larger than 10 000, which means that the flow around the measuring point has a fully developed turbulent structure at that velocity level. The flow may be described as a potential flow with a normalized velocity independent of the exhaust flow rate at large distances from the exhaust opening— and far away from surfaces. 

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