Hydraulic definition

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

Re using the equivalent diameters defined in the following. This situation is, by arbitrary definition, opposite to that for the hydraulic diameter used for turbulent flow. 

Depth tends to be determined from the retention time and the surface overflow rate. As surface overflow rates were reduced, the depth of sedimentation tanks was reduced to keep retention time from being excessive. It was recognized that depth was a valid design parameter and was more critical in some systems than retention time. As mixed-liquor suspended-solids (MESS) concentrations increase, the depth should also be increased. Minimum sedimentation-tank depths for variable operations should be 3.0 m (10 ft) with depths to 4.5 m (15 ft) if 3000 mg/L MESS concentrations are to be maintained under variable hydraulic conditions. With MESS concentrations above 4000 mg/L, the depth of the sedimentation tank should be increased to 6.0 m (20 ft). The key is to keep a definite freeboard over the settled-sludge blanket so that variable hydraulic flows do not lift the solids over the effluent weir. 

The permeability relative to a pure liquid, usually water, may be determined with the help of different devices that operate on the principle of measurement of filtrate volume obtained over a definite time interval at known pressure drop and filtration area. The permeability is usually expressed in terms of the hydraulic resistance of the filter medium. This value is found from ... 

The characteristics of the pump relate the applied pressure on the cake to the flowrate at the exit face of the filter medium. The cake resistance determines the pressure drop. During filtration, liquid flows through the porous filter cake in the direction of decreasing hydraulic pressure gradient. The porosity (e) is at a minimum at the point of contact between the cake and filter plate (i.e., where x = 0) and at a maximum at the cake surface (x = L) where sludge enters. A schematic definition of this system is illustrated in Figure 2. 

Fluid power encompasses most applications that use liquids or gases to transmit power in the form of mechanical work, pressure and/or volume in a system. This definition includes all systems that rely on pumps or compressors to transmit specific volumes and pressures of liquids or gases within a closed system. The complexity of these systems range from a simple centrifugal pump used to remove casual water from a basement to complex airplane control systems that rely on high-pressure hydraulic systems. 

The connection that has been shown in Section VIII to exist between burn-out in a rod bundle and in an annulus leads to the question of whether or not a link may also exist between, for example, a round tube and an annulus. Now, a round tube has its cross section defined uniquely by one dimension—its diameter therefore if a link exists between a round tube and an annulus section, it must be by way of some suitably defined equivalent diameter. Two possibilities that immediately appear are the hydraulic diameter, dw = d0 — dt, and the heated equivalent diameter, dh = (da2 — rf,2)/ however, there are other possible definitions. To resolve the issue, Barnett (B4) devised a simple test, which is illustrated by Figs. 38 and 39. These show a plot of reliable burn-out data for annulus test sections using water at 1000 psia. Superimposed are the corresponding burn-out lines for round tubes of different diameters based on the correlation given in Section VIII. It is clearly evident that the hydraulic and the heated equivalent diameters are unsuitable, as the discrepancies are far larger than can be explained by any inaccuracies in the data or in the correlation used. 

Studies with rats and chickens given oral doses of TOCP and tn-/ ara-cresyl phosphate provide more definitive evidence that, following absorption, organophosphate esters in hydraulic fluids (or their metabolites) may be widely distributed among tissues with a preferential distribution to fatty tissues, the liver, and the kidneys (Abou-Donia et al. 1990a, 1990b Kurebayashi et al. 1985 Somkuti and Abou-Donia 1990 Suwita and Abou-Donia 1990). 

The expressions for the hydraulic diameter and the superficial velocity can be incorporated into the definition of the friction factor to give an equivalent expression for the porous medium friction factor ... 

Hydraulic conductivity is defined as volume units per square unit of medium face per unit of time under a unit hydraulic gradient (often expressed as units3/units2/time). However, many variations of this definition are used for convenience. For example, in the United States hydraulic conductivity is referred to in terms of gallons per day per square foot or, by the U.S. Geological Survey, as square feet per day. 

The nomenclature selected for the Dimensional Data Group (Grotq> C) was adcqjted fiom the Hydraulic Institute Standards for Centrifugal, Rotary, and Reciprocating Pumps. For example, the field number COOl, "Width of base srqrport", has the field name definition of "HIS A . This corresponds to dimension "A" in the Hydraulic Institute Standards. 

Perhaps the simplest classification of flow regimes is on the basis of the superficial Reynolds number of each phase. Such a Reynolds number is expressed on the basis of the tube diameter (or an apparent hydraulic radius for noncircular channels), the gas or liquid superficial mass-velocity, and the gas or liquid viscosity. At least four types of flow are then possible, namely liquid in apparent viscous or turbulent flow combined with gas in apparent viscous or turbulent flow. The critical Reynolds number would seem to be a rather uncertain quantity with this definition. In usage, a value of 2000 has been suggested (L6) and widely adopted for this purpose. Other workers (N4, S5) have found that superficial liquid Reynolds numbers of 8000 are required to give turbulent behavior in horizontal or vertical bubble, plug, slug or froth flow. Therefore, although this classification based on superficial Reynolds number is widely used... 

The resin internal porosity can be evaluated by using the definition of the hydraulic density (eq. 3.558) ... 

Beginning with the definition of a hydraulic diameter (Dh = 4Ac/P), show that the hydraulic diameter of the annular channel may be written as... 

D.J. Mason, P. Marjanovic, Re-visit to the fundamental definitions of fluid-solids flow properties in conveying pipelines, Proceedings of the 2nd International Conference on Pneumatic and Hydraulic Conveying Systems. UEF Conf. Davos, Switzerland, June 1999. 

SQ iL/KAP)yi. Equivalent diameters are not the same as hydraulic diameters. Equivalent diameters yield the correct relation between flow rate and pressure drop when substituted into Eq. (6-36), but not Eq. (6-35) because V Q/(kDe/4). Equivalent diameter De is not to be used in the friction factor and Reynolds number f 16/Re using the equivalent diameters defined in the following. This situation is, by arbitrary definition, opposite to that for the hydraulic diameter DH used for turbulent flow. 

For cavitation in flow through orifices, Fig. 6-55 (Thorpe, Int. J. Multiphase Flow, 16, 1023-1045 [1990]) gives the critical cavitation number for inception of cavitation. To use this cavitation number in Eq. (6-207), the pressure p is the orifice backpressure downstream of the vena contracta after full pressure recovery, and V is the average velocity through the orifice. Figure 6-55 includes data from Tullis and Govindarajan (ASCE J. Hydraul. Div., HY13, 417-430 [1973]) modified to use the same cavitation number definition their data also include critical cavitation numbers for 30.50- and 59.70-cm pipes... 

This was one of the earliest rational laws of hydraulics (1643), known as Torricelli s theorem from its discoverer, who was a student of Galileo. According to the definitions just given, the actual velocity of the jet is... 

Transition from laminar to turbulent flow within the condensed film can occur when the vapor is condensed on a tall surface or on a tall vertical bank of horizontal tubes [45] to [47]. It has been found that the film Reynolds number, based on the mean velocity in the film, um, and the hydraulic diameter, D, can be used to characterize the conditions under which transition from laminar flow occurs. The mean velocity in the film is given by definition as ... 

Geological information of the rock sequence and tectonic settings may be instructive but not definitive, as it is hard to translate field data into hydraulic conductivity values a shale bed may be fractured and let water flow through in one case, and a clay bed may be weathered and act as an aquiclude in another. In addition, a variety of processes lower the local water conductance, occasionally preventing lateral flow. An example of such a process is chemical clogging (Goldenberg et al., 1983). 

Pascal 3. The hydraulic lever. The hydraulic jack is a problem in fluid equilibrium, just as a pulley system is a problem in mechanical equilibrium (no accelerations involved). It s the static situation in which a small force on a small piston balances a large force on a large piston. No change of pressure need be involved here. A constant force on one piston slowly lifts a different piston with a constant force on it. At all times during this process the fluid is in near-equilibrium. This principle is no more than an application of the definition of pressure as F/A, the quotient of... 

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