Hydraulic criteria

The Reynolds number characterizing laminar-turbulent transition for bulk flow in a pipe is about Re 2300 provided that the fluid moves unidirectionally, the pipe walls are even and behave in a hydraulically smooth manner, and the internal diameter remains constant. However, intestinal walls do not fulfill these hydraulic criteria due to the presence of curvatures, villi, and folds of mucous membrane, which are up to 8 mm in the duodenum, for instance (Fig. 18). Furthermore, the internal diameter of the small intestine is estimated to... 

Summary. The third trial checks well against the various hydraulic criteria. Column capacity is limited by downcomer backup flood in the bottom section center-to-side trays (i.e., side downcomers). All trays will operate in the emulsion regime. 

The design of centrifugal pumps involves a combination of mathematical and empirical formulae and models. Although water pumps have been the subject of extensive research in the past, slurry pumps have been designed based on a compromise of what can be cast with hard alloys, molded in rubber, and what can meet the hydraulic criteria. 

The design approaches to filters are usually grouped into geometticaT and hydraulic criteria. Geometrical criteria define limit values for void diameters to hinder the transport of finer particles through them. Hydraulic criteria define a limit value for the hydraulic gradient at which the transport of particles begins. In most cases. 

The development of the power limits safety criteria is a two-step process (1) the extent of acceptable core damage, a macro consideration, must be defined and (2) the specific thermal hydraulic criteria that will conservatively bound the accident envelope within this acceptable core damage criteria must be established. 

A significant consideration is the thermal-hydraulic criterion for limiting power for the FI phase of the accident. Initially, a "no bulk boiling" criterion was assumed to apply to the individual annular coolant channels within the fuel assemblies. Locally, subchannels could produce steam prior to the channel mixing cup temperature reaching the saturation temperature. 

Hydraulic Gradient Hydraulic gradient, the head of hquid necessary to overcome the frictional resistance to hquid (froth) passage across the plate, is impoiTant for plate stabihty inasmuch as it is the only liquid head that varies across the length of passage. If the gradient is excessive, the upstream portion of the plate may be rendered inoperative because of increased resistance to gas flow caused by increased liqmd head (Fig. 14-34). In general the empirical criterion for stable operation is /j > 2.5/j/,g. 

It may be used, the relation of the time-averaged heat transfer coefficients on the top and bottom, as a criterion for determination of dryout. It was assumed that the relation he/hi < 1 indicates dryout, i.e., the surface superheat Tw -7f is greater than that, when the surface contacts single-phase water only (hg is the heat transfer at the bottom of the channel). This method can be applied to connect dryout with hydraulic conditions, if the value of he may be associated with intermittent flow parameters. 

As will be outlined below, the computation of compressible flow is significantly more challenging than the corresponding problem for incompressible flow. In order to reduce the computational effort, within a CED model a fluid medium should be treated as incompressible whenever possible. A rule of thumb often found in the literature and used as a criterion for the incompressibility assumption to be valid is based on the Mach number of the flow. The Mach number is defined as the ratio of the local flow velocity and the speed of sound. The rule states that if the Mach number is below 0.3 in the whole flow domain, the flow may be treated as incompressible [84], In practice, this rule has to be supplemented by a few additional criteria [3], Especially for micro flows it is important to consider also the total pressure drop as a criterion for incompressibility. In a long micro channel the Mach number may be well below 0.3, but owing to the small hydraulic diameter of the channel a large pressure drop may be obtained. A pressure drop of a few atmospheres for a gas flow clearly indicates that compressibility effects should be taken into account. 

The most important criterion to assure that hydraulic control of the contaminated area is maintained during the remediation program is the proper layout of injection and extraction wells. This is important obviously to minimize and exclude the significant spreading of contaminants into clean areas and to ensure the focus of bioremediation efforts in the areas of highest concentration of contaminants. Important parameters to be considered are as follows ... 

From the analysis presented in the last two paragraphs, it is evident that the gravitational force acting upon the particle is used for the derivation of the equations for the terminal velocity and the pressure drop in the fluidized bed. Then, it is clear that the hydraulic density should be used in these equations as well as in any other equations that are derived from a similar force-balance analysis. For instance, this is the case of the Foscolo-Gibilaro criterion for determining the fluidization pattern (Section 3.8.2). 

Hydraulic analysis and controlling mechanism For the determination of the mass transfer coefficient, and the case of wastewater treatment, the correlation proposed by Chern and Chien (eq. (3.345)) is used. As a criterion, the Biot number as defined by Hand et al. (eq. (4.105)) is used. 

Hydraulic parameters and Mears criterion for plug flow... 

Note that the swollen particle density, which is 158.4 kg/m3, is used for all calculations except the hydraulic ones, where the hydraulic density is used. Then, we have K = 22.61 and = 0.0006. According to the mechanical parameter criterion, if is zero (practically much lower than 1), then fluid-film diffusion controls the process rate, while if infinite (practically much higher than 1), then solid diffusion is controlling the process rate. It is obvious that the controlling mechanism is the fluid-film diffusion. 

The various hydraulic stability analyses mentioned in Section III, C lead to the criterion NFr > n, where n = 0.58-2.0, instead of 1.0 as assumed above, and these reduce to conditions similar to Eq. (Ill) for the onset of rippling, but with numerical constants other than 3. 

For ducts with other cross-sejtional shapes, it is common to assume that the same criterion as that given in Eq. (5.96) applies provided the hydraulic diameter is used in place of the diameter. The hydraulic diameter, as previously discussed, is defined by ... 

Much attention shonld be given to conelations for liquid-solid suspensions or fluidizing systems derived experimentally. If the experimental data have been conelated to particle density, this kind of density and not the hydraulic density should be used. For instance, this is the case of the Lin-Kwank-Li criterion for determining the flnidization pattern (Section 3.8.2). However, for correlations that have been derived nsing nonporons paiticles, the hydraulic density shonld be nsed. This is becanse the correlation acconnts for the whole mass included in the volnme of the particle, which is the snm of the solid mass and liquid mass in the pores for porons particles. 

The occurrence condition of shear fracture is examined on the basis of the Coulomb criterion. The averaged shear stress across the fracture plane in the simulated hydraulic stimulation tests is plotted in Fig. 5, as a function of the effective normal stress across the fracture plane. The steady-stale pore pressure distribution given from Equation (1) is averaged over the fracture plane and is used to compute the effective normal stress. Triaxial compression tests have been performed on the granite using the same apparatus shown in Fig. 

I (Takahashi, 2000). The peak shear stresses obtained from the triaxial compression tests are also plotted in Fig. A2. In the plot of Fig. 5, there is general agreement between the two types of the experimental results. Thus, it is thought that the occurrence of the shear fracture in the simulated hydraulic stimulation tests can be approximately predicted by the Coulomb criterion. Based on the comparison, the critical condition for the shear fracture due to hydraulic stimulation was estimated using the experimental results of the triaxial compression tests, as given in Fig. A2, and the averaged value of pore pressure. The detailed discussion of the triaxial compression tests can be found elsewhere (Takahashi, 2000.). 

Test Criterion of Concrete Used in Hydraulic Engineering (SDI05-82). Beijing Chinese Water Conservancy and Hydro-electric Power Publishers. [In Chinese]... 

Hydraulic reliability is reflected in the pump s ability to maintain steady discharge pressures and corresponding flow rates in the range of outputs desired. Relatively high flow rates and impeller speeds are conducive to the production of a cavitating flow. Such conditions become critical and hydraulic-flow deterioration occurs when the inlet pressure becomes inadequate for vapor suppression. A criterion for establishing the vulnerability of the pump to incipient cavitation is the well-known dimensionless parameter called suction specific speed. 

Although the exact position of the transition boundaries between the flow patterns are inherently related to the liquid-liquid system studied, the arrangement of the regions of the different flow patterns are similar to a number of systems. Models based on the Capillary, Reynolds and Weber numbers have been developed in order to allow an a priori prediction of the flow patterns using fluid properties and flow velocities. A general criterion for flow pattern identification in a given micro-channel was given in terms of dimensionless ratio of Reynolds to Capillary (ReJ Ca< ) numbers as a function of the product of Reynolds number and hydraulic diameter (Readh/Cd) by Kashid and Kiwi-Minsker (2011) and was applied to different literature data which are summarised in Fig. 2.5. 

In order to consider the applicability related to microchannels of the proposed criterion, the value of the minimum Reynolds number (linked to the minimum Brinkman number indicated in Eq. 20) for which k becomes equal to 5 % is computed as a function of the hydraulic diameter for a rectangular microchannel having a = 3. In Fig. 3 the minimum Reynolds number is shown for water and isopropanol as working fluids in rectangular and trapezoidal microchannels having an aspect ratio a = 3. A constant wall heat flux equal to 90 W/cm is cmisidered. It is evident that the viscous effects are more important for isopropanol than for water because the isopropanol is characterized by a lower value of... 

Equation 24 can be adopted as a criterion to predict the upper limit of significance of viscous dissipation in a microchannel. Equation 24 allows, for a fixed microchannel geometry and hydraulic diameter, the calculation of the values of the Reynolds number for which the temperature rise between inlet and outlet is equal to or greater than 1 K. 

The change in the expected downtime 0 by using a data selection criterion based on 6 /2" hydraulic drilling jars in the North Sea area. 

The chan in the e7q>ected downtime by excluding specific tests from the test data The chan in the e7q>ected downtime by using a data selection criterion based on 6 hydraulic drilling jars in the North Sea area The change in e7q>ected downtime 0 by using data that reflect also non-jarring activities... 

With reference to our case of thermal-hydraulic passive system, let s consider the characteristic time-variant parameter W t) (its evolution during time will depend on the transient/accident scenario under consideration). The lower hoimd for natural circulation operation is denoted as Wi t), which, according to the failure criterion provided above (see chapter 4), is a fraction (0,8) of the flow-rate in nominal conditions. 

During an accident, a channel tube rupture may be expected either on account of a steep pressure rise at near operational temperatures or as a result of thermomechanical deformation at rather high pressures in the circuit. The admissible pressure of hydraulic tests, equal to 13.4 MPa, may be taken as a conservative acceptance criterion for cases when the tube temperatures are close to their operating values (i.e. 50°C). The conservatism of this value can be easily proven by evaluating the pressure corresponding to the onset of plastic deformation of a tube. For the temperature of 300°C, the result is 20 MPa, and a real threat of pressure tube rupture will not appear until this pressure is exceeded. 

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