STRESS AND PRESSURE

The forces that exist within a fluid at any point may arise from various sources. These include gravity, or the weight of the fluid, an external driving force such as a pump or compressor, and the internal resistance to relative motion between fluid elements or inertial effects resulting from variation in local velocity and the mass of the fluid (e.g., the transport or rate of change of momentum). 

Any or all of these forces may result in local stresses within the fluid. Stress can be thought of as a (local) concentration of force, or the force per unit area that bounds an infinitesimal volume of the fluid. Now both force and area are vectors, the direction of the area being defined by the normal vector that points outward relative to the volume bounded by the surface. Thus, each stress component has a magnitude and two directions associated with it, which are the characteristics of a second-order tensor or dyad. If the direction in which the local force acts is designated by subscript j (e.g., j = x, y, or z in Cartesian coordinates) and the orientation (normal) of the local area element upon which it acts is designated by subscript i, then the corresponding stress component (ay) is given by 

Note that since i and j each represent any of three possible directions, there are a total of nine possible components of the stress tensor (at any given point in a fluid). However, it can readily be shown that the stress tensor is symmetrical (i.e., the ij components are the same as the ji components), so there are at most six independent stress components. 

Thus the total stress, cry, at any point within a fluid is composed of both the isotropic pressure and anisotropic stress components, as follows  

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The majority of polymer flow processes are characterized as low Reynolds number Stokes (i.e. creeping) flow regimes. Therefore in the formulation of finite element models for polymeric flow systems the inertia terms in the equation of motion are usually neglected. In addition, highly viscous polymer flow systems are, in general, dominated by stress and pressure variations and in comparison the body forces acting upon them are small and can be safely ignored. 

When the operation of the hoUow-ftber membrane is to be reversed, and permeation from the bore to outer 2one is required, circumferential stress and pressure drop along the fiber capiUary (bore) must be considered in the design of the fiber unit. The circumferential stress, S is expressed as... 

The words stress and pressure are used interchangeably for fluids considered in this chapter, but the distinction is important and will be made in later chapters. 

Of particular interest in fluid flow is the distinction between shear stress and pressure (or pressure difference), both of which are defined as force per unit area. For steady-state... 

The calculation of pressure drop in vertical slug flow requires an understanding of the distribution of shear stress and pressure around a... 

Once the Reynolds number (based on the mean velocity) is known for a given tube and flow situation, the friction factor follows as / = Re//Re. From the friction factor the wall shear stress and pressure gradient are easily determined. 

It is crucial to define a reference configuration, or state, to which all tests can be reckoned. Such a reference state, referred to as hypertonic state, is defined as the state of maximum salinity of the extrafibrillar compartment then as the salt content overweights the presence of proteoglycans, the latter have a very small mechanical effect the hypertonic configuration is such that the stress is equal to the bath pressure. Therefore, stresses and pressures can be reckoned to their values at the hypertonic state from which all tests start and at which by convention the strain vanishes as well. 

Figure 2. Confined compression tests at given bath salinity correspond to a linear in-axis stress-strain relation. The maximal salinity is associated to the minimal elastic moduli, that is to A = 0, or to a zero intercept with the stress axis p =0 (reckoning stresses and pressures from the hypertonic state). A given bath salinity is also assumed to correspond to a given mass-content of sodium in the extrafibrillar phase mNa . The function pY (mNaE) embodies the monotonous increase of the slopes of the confined compression tests, as bath salinity decreases.

The development of membrane emulsification technologies permits production of small and uniform droplets and capsules, using mild conditions of temperature, shear stress and pressure. Furthermore, they are able to produce stable droplets with reduced stabilizers content, which will contribute to the manufacturing of improved food products with low-fat content. 

Here c is the solubility of hydrogen (g-atom H/cm3 metal) when the applied uniaxial stress (equivalent to pressure, see below) is a and c0 is the solubility when the applied stress is zero. The general relation between the applied stress and pressure or the equivalent hydrostatic stress ah, can be written as... 

Pipe stress and pressure vessel analysis Pressure, dead-weight, thermal expansion, vibration modal analysis of fatigue. Analysis to ensure that the piping and pressure vessels conform to the codes of ASME, API or WRC as the case may be... 

The term in brackets is positive and independent of r. Hence the velocity on the free surface is constant but smaller than the velocity of the solid plate. The speed of a fluid particle that travels along the interface must therefore increase discontinuously as it reaches the plate and turns the corner - that is, it must undergo an infinite acceleration. This infinite acceleration is produced by an infinite stress and pressure, 0(r 1), on the plate in the limit r —> 0. Again, we conclude that the solution breaks down in the limit r —r 0. 

We denote the characteristic length and velocity scales as tc and uc, the characteristic time scale as lc/uc> and the characteristic stress and pressure scales as fj,uc/ic and X luc/Ic for the fluid outside and inside the drop, respectively. We express the interfacial tension in the form... 

Pascal Dimension for mechanical stress and pressure in bonding technology for example, dimension for bond strength (MPa = 106 Pa). 

A new coarse grained molecular dynamics model was developed to study the role of thermal, mechanical and chemical reactions in the onset of the ablation process of PMMA [58]. In this model, the laser energy is absorbed in different ways, i.e. pure heating and Norrish type I and II reactions. Mechanical stresses and pressure are dominant for very short pulses in the stress confinement regime and can initiate... 

The influence of shear stress and pressure drawdown on solids production has been demonstrated in large-scale laboratory tests (38). Short bursts of solids, from perforation clean-up, and productivity improvement occurred after each increase in effective stress or drawdown. 

Most work on SD focuses on the effects of temperature and composition on phase equilibria in binary polymer mixmres. However, in industrial processes other variables may be of equal importance, e.g., the shear stress and pressure. It is known that these variables are important for miscibility, hence for the morphology and performance. For example, during extrusion of PC/PBT blends the LCST was increased by at least 60°C, causing miscibility. The blend coming out from the extruder phase separated by the SD mechanism. The co-continuity of phases resulted in excellent performance. 

Let us denote the force per unit area exerted on the interface from the viscous stresses and pressures associated with the boundary fluids as f and f. The superscripts a and jS refer to the two different fluids on each side of the interface. With n the unit normal vector into the fluid /3, the forces may be written (Newman 1991, Edwards et al. 1991)... 

A horizontal circular tunnel is considered. It is assumed that the rock is initially saturated and the stress state is supposed to be isotropic. This assumption allows us to simplify the geometric configuration and to make an axisymmetrical mono-dimensional calculation as shown in figure 2. The initial values of stress and pressure are given by ... 

Terri gallery in Switzerland. It is located in the Opalinus clay made of argilites at a depth of 250 meters. A horseshoe shape is assumed in this case. The initial state of the stress and pressure is given by ... 

The flow velocity, shear stress and pressure fields in the immediate vicinity of a given heart valve prosthesis design are directly related to the fluid dynamic characteristics of the prosthesis. Therefore, detailed in vitro fluid dynamic studies should help predict potential problems and complications that may arise in vivo with different designs of prosthetic heart valves. 

Lee, C.S. and Chandran, K.B. 1995. Numerical simulation of instantaneous backflow through central clearance of bileaflet mechanical heart valves at the moment of closure shear stress and pressure fields within the clearance. Med. Biol. Eng. Comp. 33 257-263. 

In 1992, McManus and Springer [5, 6] presented a thermomechanical model that considered the interaction between mechanically induced stresses and pressures created by the decomposition of gases within the pyrolysis front. Again, temperature-dependent mechanical properties were determined at several specified temperature points as stepped functions. The issue of degradation of material properties at elevated temperatures was considered in Dao and Asaro s [7] thermo-mechanical model in 1999. The degradation curves used in the model were, once again, obtained by curve fitting of limited experimental data. 

In designing the containment, the effect of ambient temperature extremes on resultant surface temperatures, contents, thermal stresses and pressure variations should be considered to ensure containment of the radioactive material. 

Viscoelastic effects alter the steady drop shape from being ellipsoidal to drop shapes with more blunt ends. The results reflect a balance between the direct tensile stress contribution of the viscoelastic fluid to the normal stress balance and modifications of the viscous (i.e., Newtonian) stress and pressure due to viscoelastic changes in the flow Hsu and Leal 2009... 

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