Hydrostatic pressure force

Hydrostatic pressure Force generated by a fluid at rest, directed perpendic-... 

A capillary system is said to be in a steady-state equilibrium position when the capillary forces are equal to the hydrostatic pressure force (Levich 1962). The heating of the capillary walls leads to a disturbance of the equilibrium and to a displacement of the meniscus, causing the liquid-vapor interface location to change as compared to an unheated wall. This process causes pressure differences due to capillarity and the hydrostatic pressures exiting the flow, which in turn causes the meniscus to return to the initial position. In order to realize the above-mentioned process in a continuous manner it is necessary to carry out continual heat transfer from the capillary walls to the liquid. In this case the position of the interface surface is invariable and the fluid flow is stationary. From the thermodynamical point of view the process in a heated capillary is similar to a process in a heat engine, which transforms heat into mechanical energy. 

Since the fluid is at rest, the hydrostatic pressure forces must just balance the weight of the fluid. Hence, if dA is the horizontal cross-sectional area of the control volume and if po is the density of the fluid in this unheated state, then the force balance requires that ... 

Introductorily we examine a generally accepted momentum balance formulation for a small (point) particle generally referred to as Newton s second law. The net force is conventionally split into the uncoupled effects of drag, gravity (fc), body forces other than gravity hydrostatic pressure force... 

Hydrostatics. Hydrostatics is a subdiscipline of fluid mechanics that examines the pressures in water at rest and the forces on floating bodies or bodies submerged in water. When water is at rest, as in a tank or a large reservoir, it does not experience shear stresses therefore, only normal pressure is present. When the pressure is uniform over the surface of a body in water, the total force applied on the body is a product of its surface area times the pressure. The direction of the force is perpendicular (normal) to the surface. Hydrostatic pressure forces can be mathematically determined on any shape. Buoyancy, for instance, is the upward vertical force applied on floating bodies (such as boats) or submerged ones (such as submarines). Hydraulic engineers use... 

Gasket seating force) — (Hydrostatic pressure force)... 

The buoyancy force is the resultant of hydrostatic pressure forces exerted on a domain V, under the action of gravity, by the surrounding fluid. In the absence of flow, the pressure inside the fluid is the hydrostatic pressure, pi j, associated with the weight of the water colunrn. Navier-Stokes equations now reduce to ... 

In Chapter III, surface free energy and surface stress were treated as equivalent, and both were discussed in terms of the energy to form unit additional surface. It is now desirable to consider an independent, more mechanical definition of surface stress. If a surface is cut by a plane normal to it, then, in order that the atoms on either side of the cut remain in equilibrium, it will be necessary to apply some external force to them. The total such force per unit length is the surface stress, and half the sum of the two surface stresses along mutually perpendicular cuts is equal to the surface tension. (Similarly, one-third of the sum of the three principal stresses in the body of a liquid is equal to its hydrostatic pressure.) In the case of a liquid or isotropic solid the two surface stresses are equal, but for a nonisotropic solid or crystal, this will not be true. In such a case the partial surface stresses or stretching tensions may be denoted as Ti and T2-... 

Gravity, or centrifugation rarely provide enough hydrostatic pressure to force Hquid into nonwetting pores. If the Hquid wets the soHd the clump density increases as gas is displaced from the interior. It is best if submersion does not occur until the Hquid has completely displaced gas from the pores (Fig. 2). For wetting Hquids and pores with average diameter, D-pQ- y and tortuosity,the length, to which Hquid is pulled into a bed of powder by... 

In the large-diameter vertical cylindrical tanks, because hoop stress is proportional to diameter, the thickness is set by the hydrostatic hoop stresses. Although the hydrostatic forces increase proportionally with the depth of Hquid in the tank, the thickness must be based on the hydrostatic pressure at the point of greatest depth in the tank. At the bottom, however, the expansion of the shell owing to internal hydrostatic pressure is limited so that the actual point of maximum stress is slightly above the bottom. Assuming this point to be about 1 ft (0.305 m) above the tank bottom provides tank shells of adequate strength. The basic equation modified for this anomaly is... 

There are four commonly occurring states of stress, shown in Fig. 3.2. The simplest is that of simple tension or compression (as in a tension member loaded by pin joints at its ends or in a pillar supporting a structure in compression). The stress is, of course, the force divided by the section area of the member or pillar. The second common state of stress is that of biaxial tension. If a spherical shell (like a balloon) contains an internal pressure, then the skin of the shell is loaded in two directions, not one, as shown in Fig. 3.2. This state of stress is called biaxial tension (unequal biaxial tension is obviously the state in which the two tensile stresses are unequal). The third common state of stress is that of hydrostatic pressure. This occurs deep in the earth s crust, or deep in the ocean, when a solid is subjected to equal compression on all sides. There is a convention that stresses are positive when they pull, as we have drawn them in earlier figures. Pressure,... 

Another property of importance is the pore volume. It can be measured indirectly from the adsorption and/or desorption isotherms of equilibrium quantities of gas absorbed or desorbed over a range of relative pressures. Pore volume can also be measured by mercury intrusion techniques, whereby a hydrostatic pressure is used to force mercury into the pores to generate a plot of penetration volume versus pres- sure. Since the size of the pore openings is related to the pressure, mercury intrusion techniques provide information on the pore size distribution and the total pore volume. 

From this relatively simple test, therefore, it is possible to obtain complete flow data on the material as shown in Fig. 5.3. Note that shear rates similar to those experienced in processing equipment can be achieved. Variations in melt temperature and hypostatic pressure also have an effect on the shear and tensile viscosities of the melt. An increase in temperature causes a decrease in viscosity and an increase in hydrostatic pressure causes an increase in viscosity. Topically, for low density polyethlyene an increase in temperature of 40°C causes a vertical shift of the viscosity curve by a factor of about 3. Since the plastic will be subjected to a temperature rise when it is forced through the die, it is usually worthwhile to check (by means of Equation 5.64) whether or not this is signiflcant. Fig. 5.2 shows the effect of temperature on the viscosity of polypropylene. 

Hydraulic lift must also be taken into account when using diamond bits and PDC bits. The weight-on-bit varies between 0 and 100,000 lb or 0 and 50 ton-force. The end effect is due to the differential pressure between the drill collar internal pressure and the external hydrostatic pressure. This differential pressure acts on the sub internal cross-sectional area. 

The hydrostatic pressure has two effects an upward force acting on the wall cross-section of the sub, and a downward stress due to the lateral compression of the subwall. 

The following factors affect net diffusion of a substance (1) Its concentration gradient across the membrane. Solutes move from high to low concentration. (2) The electrical potential across the membrane. Solutes move toward the solution that has the opposite charge. The inside of the cell usually has a negative charge. (3) The permeability coefficient of the substance for the membrane. (4) The hydrostatic pressure gradient across the membrane. Increased pressure will increase the rate and force of the collision between the molecules and the membrane. (5) Temperature. Increased temperature will increase particle motion and thus increase the frequency of collisions between external particles and the membrane. In addition, a multitude of channels exist in membranes that route the entry of ions into cells. 

In arterioles, the hydrostatic pressure is about 37 mm Hg, with an interstitial (tissue) pressure of 1 mm Hg opposing it. The osmotic pressure (oncotic pressure) exerted by the plasma proteins is approximately 25 mm Hg. Thus, a net outward force of about 11 mm Hg drives fluid out into the interstitial spaces. In venules, the hydrostatic pressure is about 17 mm Hg, with the oncotic and interstitial pressures as described above thus, a net force of about 9 mm Hg attracts water back into the circulation. The above pressures are often referred to as the Starling forces. If the concentration of plasma proteins is markedly diminished (eg, due to severe protein malnutrition), fluid is not attracted back into the intravascular compartment and accumulates in the extravascular tissue spaces, a condition known as edema. Edema has many causes protein deficiency is one of them. 

In 1861, Georg Hermann Quincke described a phenomenon that is the converse of electroosmosis When an electrolyte solution is forced through a porous diaphragm by means of an external hydrostatic pressure P (Fig. 31.1ft), a potential difference called the streaming potential arises between indicator electrodes placed on different sides of the diaphragm. Exactly in the same sense, in 1880, Friedrich Ernst Dorn described a phenomenon that is the converse of electrophoresis During... 

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