Tangential stress

The stresses acting normal to the surface Tn,r22, r33 or Tl j with i = j are known as normal stresses, the stresses tangential to the surface TtJ with i, A J are called... 

Radial Stress Tangential Stress Von Mises Stress... 

Here, is the shear stress tangential to the cell boundary that is, the outer cell boundary is assumed to be a free surface. By this artifice the cell model accounts in an approximate way for the interference effects of the neighboring particles. 

Tensile stress Shear stress (tangential) Torque (rotational shear stress) Compressive stress... 

Viscosity coefficient (coefficient of viscosity)—The shearing stress tangentially applied that will induce a velocity gradient. A material has a viscosity coefficient of one poise when a shearing stress of one dyne per square centimeter produces a velocity gradient of 1 cm/s/cm. 

For the pendant drop in figure I, the equations above are subjected to the no-slip boundary conditions at solid surfaces and the kinematic condition on the free surfaces. The kinematic condition implies that there is no liquid crossing the boundary into the gas phase, or in other words forms a definite boundary between the phases. For creeping flows into an atmosphere of gas with minimal velocities there will be no interfacial shear stress tangential to the surface and the normal stress inside the fluid is balanced by the surface tension as described by the famous Young-Laplace equation. 

TANG STRESSES tangential STRESSesalong edgeof eccentric bore... 

Imposition of no-slip velocity conditions at solid walls is based on the assumption that the shear stress at these surfaces always remains below a critical value to allow a complete welting of the wall by the fluid. This iraplie.s that the fluid is constantly sticking to the wall and is moving with a velocity exactly equal to the wall velocity. It is well known that in polymer flow processes the shear stress at the domain walls frequently surpasses the critical threshold and fluid slippage at the solid surfaces occurs. Wall-slip phenomenon is described by Navier s slip condition, which is a relationship between the tangential component of the momentum flux at the wall and the local slip velocity (Sillrman and Scriven, 1980). In a two-dimensional domain this relationship is expressed as... 

Elastic Behavior. In the following discussion of the equations relevant to the design of thick-walled hoUow cylinders, it should be assumed that the material of which the cylinder is made is isotropic and that the cylinder is long and initially free from stress. It may be shown (1,2) that if a cylinder of inner radius, and outer radius, is subjected to a uniform internal pressure, the principal stresses in the radial and tangential directions, and <7, at any radius r, such that > r > are given by... 

Partially Plastic Thick-Walled Cylinders. As the internal pressure is increased above the yield pressure, P, plastic deformation penetrates the wad of the cylinder so that the inner layers are stressed plasticady while the outer ones remain elastic. A rigorous analysis of the stresses and strains in a partiady plastic thick-waded cylinder made of a material which work hardens is very compHcated. However, if it is assumed that the material yields at a constant value of the yield shear stress (Fig. 4a), that the elastic—plastic boundary is cylindrical and concentric with the bore of the cylinder (Fig. 4b), and that the axial stress is the mean of the tangential and radial stresses, then it may be shown (10) that the internal pressure, needed to take the boundary to any radius r such that is given by... 

Thermal Stresses. When the wak of a cylindrical pressure vessel is subjected to a temperature gradient, every part expands in accordance with the thermal coefficient of linear expansion of the steel. Those parts of the cylinder at a lower temperature resist the expansion of those parts at a higher temperature, so setting up thermal stresses. To estimate the transient thermal stresses which arise during start-up or shutdown of continuous processes or as a result of process intermptions, it is necessary to know the temperature across the wak thickness as a function of radius and time. Techniques for evaluating transient thermal stresses are available (59) but here only steady-state thermal stresses are considered. The steady-state thermal stresses in the radial, tangential, and axial directions at a point sufficiently far away from the ends of the cylinder for there to be no end effects are as fokows ... 

The theoretical value of the coefficient Y ranges from 0 to 1. If V = 0, equation 9 reduces to the Barlow or outside diameter formula. The Barlow formula is always conservative and for large D/1 the error is small. The value Y = 0.4 gives the Boardman approximation of the Lame tangential stress (27)... 

A Hquid is a material that continues to deform as long as it is subjected to a tensile and/or shear stress. The latter is a force appHed tangentially to the material. In a Hquid, shear stress produces a sliding of one infinitesimal layer over another, resulting in a stack-of-cards type of flow (Fig. 1). 

The geometry of the bowl parts is important, and for intermittently discharging centrifuges, fatigue strength must be considered. In general the tangential stress in a bowl wall is CJ. ... 

Other dimensional systems have been developed for special appHcations which can be found in the technical Hterature. In fact, to increase the power of dimensional analysis, it is advantageous to differentiate between the lengths in radial and tangential directions (13). In doing so, ambiguities for the concepts of energy and torque, as well as for normal stress and shear stress, are eliminated (see Ref. 13). 

These important results can be combined by superposition to compute the displacement for any arbitrary normal stress distribution applied to the free surface. Similar approaches can be taken for arbitrary tangential stress distributions. 

Since/is a tangential force, only the vector projection of the area is effective. Integrating these forces from 0 to Ti/2,f s given by equation 9.1-1 which is more easily done by a change of variables giving/= p r, and the stress is j Equation 9.1-2 gives... 

Substituting Equation 4-55 and Equation 4-56 into Equation 4-54 and putting = 0 (tangential stress equals zero in this case), the following formulas are obtained ... 

If the drill string is thought to be a thin wall cylinder with closed ends, then the drill pipe pressure produces the axial stress and tangential stress given by the following formulas ... 

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