Stress static fluid

The pressure acting on a surface in a static fluid is the normal force per unit area, ie the normal stress. The pressure of the surrounding fluid acts inwards on each face of a fluid element. Consequently, with the negative sign convention the normal stress components may be identified with the pressure. With the positive sign convention, the normal stress components may be identified with the negative of the pressure positive normal stresses correspond to tension with this convention. 

In the case of a flowing fluid the mechanical pressure is not necessarily the same as the thermodynamic pressure as is the case in a static fluid. The pressure in a flowing fluid is defined as the average of the normal stress components. In the case of inelastic fluids, the normal stress components are equal and therefore, with the negative sign convention, equal to the pressure. It is for this reason that the pressure can be used in place of the normal stress when writing force balances for inelastic liquids, as was done in Examples 1.7-1.9. 

The profiles of pendant and sessile bubbles and drops are commonly used in determinations of surface and interfacial tensions and of contact angles. Such methods are possible because the interfaces of static fluid particles must be at equilibrium with respect to hydrostatic pressure gradients and increments in normal stress due to surface tension at a curved interface (see Chapter 1). It is simple to show that at any point on the surface... 

Consider first the trivial case of a static fluid. Here there can only be normal forces on a fluid element and they must be in equilibrium. If this were not the case, then the fluid would move and deform. Certainly any valid relationship between stress and strain rate must accommodate the behavior of a static fluid. Hence, for a static fluid the strain-rate tensor must be exactly zero e(/- = 0 and the stress tensor must reduce to... 

Pascal s law states that the pressure in a static fluid is the same in all directions. This condition is different from that for a stressed solid in static equilibrium. In such a solid, the stress on a plane depends upon the orientation of that plane, A liquid m contact with the atmosphere is sometimes called a free surface. A static liquid has a horizontal free surface if gravity is the only type of force acting. 

This quantity has the following desirable properties. First, it is invariant under rotation of the coordinate axes (unlike the individual components of T). Second, for a static fluid — 1/3 tr T = p, the thermodynamic pressure. And third, p has a physical significance analogous to pressure in a static fluid in the sense that it is precisely equal to the average value of the normal component of the stress on a surface element at position x over all possible orientations of the surface (alternatively, we may say that 1 /3 tr T is the average magnitude of the normal stress on the surface of an arbitrarily small sphere centered at point x). 

Fluid mechanics has two branches important to the study of unit operations fluid statics, which treats fluids in the equilibrium state of no shear stress, and fluid dynamics, which treats fluids when portions of the fluid are in motion relative to other parts. 

The polyacrylate polymers and a derivative of a vinyl acetate maleic anhydride copolymer cause V30 to decrease monotonically with increasing polymer concentration, similar to the CMC polymers (Figure 46). The polymers PVA and poly(vinyl pyridinium) (PVP) hydrochloride markedly increased V30 at low concentration at concentrations above 1 g of polymer per gram of added bentonite PVA functions as a static fluid loss additive. The maximum in the API fluid loss at low PVA concentrations approximately coincides with the maximum in the yield stress and plastic viscosity found by Heath and Tadros (75). The increased static fluid loss is consistent with Heath and Tadros s conclusion that bentonite is flocculated by low concentrations of PVA. The concentration of PVA required to decrease V30 below that of the neat bentonite suspension is significantly larger than the concentration of CMC, where effective static fluid loss control can be achieved at polymer bentonite weight ratios of about 0.1 g/g. More effective fluid loss control has been achieved with other synthetic polymers such as poly(vinyl sulphonate)-poly(vinyl amide) copolymer (40) and other sulphonated polymers (39). 

At the thin film limit, the hydrodynamic pressure will approach a distribution that is consistent with the pressure between the two solid surfaces in dry static contact, while the shear stress experienced by the fluid film will reach a limiting value that is equal to the shear strength of a boundary film. 

Predictions on the effectiveness of a fluid loss additive formulation can be made on a laboratory scale by characterizing the properties of the filter-cake formed by appropriate experiments. Most of the fluids containing fluid loss additives are thixotropic. Therefore the apparent viscosity will change when a shear stress in a vertical direction is applied, as is very normal in a circulating drilling fluid. For this reason, the results from static filtering experiments are expected to be different in comparison with dynamic experiments. 

Static leak-off experiments with borate-crosslinked and zirconate-cross-Unked hydroxypropylguar fluids showed practically the same leak-off coefficients [1883]. An investigation of the stress-sensitive properties showed that zirconate filter-cakes have viscoelastic properties, but borate filter-cakes are merely elastic. Noncrosslinked fluids show no filter-cake-type behavior for a large range of core permeabilities, but rather a viscous flow dependent on porous medium characteristics. 

We are interested in final states of stellar evolution. Therefore we can restrict ourselves to static configurations. Also, fluid-like behavior seems appropriate in the microscopical dimensions. Therefore we are looking for static configurations. Also, some fluid-like behavior is expected in the sense that stresses in the macroscopical directions freely equilibrate. Then in 3 spatial directions isotropy is expected and thence spherical symmetry. Finally, in the lack of any information so far, we may assume symmetry in the extra dimension. Then in... 

By virtue of its yield stress, an unsheared viscoelastic material is capable of supporting the immersed weight of a particle for an indefinite period of time, provided that the immersed weight of the particle does not exceed the maximum upward force which can be exerted by virtue of the yield stress of the fluid. The conditions for the static equilibrium of a sphere are now discussed. 

Framework of load compensator on plane wings injection moulding of carbon fibre reinforced PEEK replaces the aluminium alloy previously used. This part plays a critical role in plane safety and must resist the static and dynamic stresses and hydraulic fluids. The grade selected after many tests has a high fluidity allowing the manufacture of parts with dimensions of 200 mm by 400 mm. With 30% carbon fibre reinforcement, this PEEK grade ... 

The concept ofmetastability in this elementary setting has exactly the same meaning as in the closely related case of van der Waals s fluid. Consider the simplest equilibrium treatment of a bar loaded by a constant stress Oo,. The static problem reduces to the minimization of the functional... 

PRESSURE. If a body of fluid is at rest, the forces are in equilibrium or the fluid is in static equilibrium. The types of force that may aci on a body are shear or tangential force, tensile force, and compressive force. Fluids move continuously under the action of shear or tangential forces. Thus, a fluid at rest is free in each part from shear forces one fluid layer does not slide relative to an adjacent layer. Fluids can be subjected to a compressive stress, which is commonly called pressure. The term may be defined as force per unit area. The pressure units may be dynes per square centimeter, pounds per square foot, torr. mega-Pascals, etc. Atmospheric pressure is the force acting upon a unit area due to the weight of the atmosphere. Gage pressure is the difference between the pressure of the fluid measured (at some point) and atmospheric pressure. Absolute pressure, which can be measured by a mercury barometer, is the sum of gage pressure plus atmospheric pressure. 

In this paper a static linear elastic deformation problem for a fluid saturated solid is formulated in which the behavior of the solid matrix is described by a second gradient model. The non-deformed configuration, chosen as a reference configuration, for the considered mixture can not be stress-free indeed the saturating fluid must exhibit internal stresses acting both on the solid constituent and on its sub-bodies. 

For the momentum conservation of a single-phase fluid, the momentum per unit volume / is equal to the mass flux pU. The momentum flux is thus expressed by the stress tensor i/r = (pi — t). Here p is the static pressure or equilibrium pressure / is a unit tensor and r is the shear stress tensor. Since <1> = —pf where / is the field force per unit mass, Eq. (5.12) gives rise to the momentum equation as... 

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