Static fluid

In a static fluid an important property is the pressure in the fluid. Pressure is familiar as a surface force exerted by a fluid against the walls of its container. Also, pressure exists at any point in a volume of a fluid. 

In order to understand pressure, which is defined as force exerted per unit area, we must first discuss a basic law of Newton s. This equation for calculation of the force exerted by a mass under the influence of gravity is 

Another system of units sometimes used in Eq. (2.2-1) is that where thefts is omitted and the force (F = mg) is given as lb , ft/s, which is called poundals. Then 1 lb acted on by gravity will give a force of 32.174 poundals(lb ft/s ). Or if I g mass is used, the force (F = mg) is expressed in terms of dynes (g - cm/s ). This is the centimeter-gram-second (cgs) systems of units. 

Conversion factors for different units of force and of force per unit area (pressure) are given in Appendix A.I. Note that always in the SI system, and usually in the cgs system, the term g is not used. 

Calculate the force exerted by 3 lb mass in terms of the following. 

This equation and its applications are almost the whole of fluid statics. 

In Chap. 7 we apply Newton s law of motion to moving fluids. What we do in this chapter is really only part of the more general application in Chap. 7. In Chaps. 4, 5, and 6, however, we will need some of the results from this chapter, and the kinds of problem we deal with here are different from (and simpler than) those in Chap. 7 for these reasons a separate chapter on fluid statics is practical at this point. Remember, all we do in this chapter is apply F= ma to a. static fluid the more general application, covering both moving and static fluids, is discussed in Chap. 7. [ 

For a simple fluid at rest the pressure is the same in shear stresses. These facts lead to the basic equation small block of fluid which is part of a large mass of fluid at rest in a gravity 

This is the basic equation of fluid statics, also called the barometric equation. It is correct only if there are no shear stresses on the vertical faces of the cube in Fig. 2.1. If there are such shear stresses, then they may have a component in the vertical direction, which must be added to the sum of forces in Eq. 2.1. For simple newtonian fluids, shear stresses in the vertical direction can exist only if the fluid has a different vertical velocity on one side of the cube from that on the other side (see Eq. 1.5). Thus this equation is correct if the fluid is not moving at all, which is the case in fluid statics, or if it is moving but only in the X and y directions, or if it has a uniform velocity in the z direction. In this chapter, we apply it only when a fluid has no motion relative to its container or to some set of fixed coordinates. In later chapters, we apply it to flows in which there is no motion in the z direction or a motion with a uniform z component. 

For complicated fluids, such as toothpaste, paints, and jellies, Eq. 2.1 is not correct, because the fluids can sustain small but finite shear stresses without any motion. The equation simply is not applicable. To find its equivalent, it is necessary to make up a sum of forces which includes shear forces on the vertical sides of the cube. 

If water should rise to the top of the dam, then the moment about O due to water pressure would increase to P a It is important that this moment about O not exceed the opposing moment due to the weight of the dam. Otherwise, the dam would tend to rotate counterclockwise about O allowing water under high pressure to penetrate below the dam causing a catastrophic failure. 

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Fluid statics, discussed in Sec. 10 of the Handbook in reference to pressure measurement, is the branch of fluid mechanics in which the fluid velocity is either zero or is uniform and constant relative to an inertial reference frame. With velocity gradients equal to zero, the momentum equation reduces to a simple expression for the pressure field, Vp = pg. Letting z be directed vertically upward, so that g, = —g where g is the gravitational acceleration (9.806 mVs), the pressure field is given by... 

Static temperature is the temperature of the flowing fluid. Like static pressure, it arises because of the random motion of the fluid molecules. Static temperature is in most practical instaUations impossible to measure since it can be measured only by a thermometer or thermocouple at rest relative to the flowing fluid that is moving with the fluid. Static temperature will increase in a diffuser and decrease in a nozzle. 

Friction head loss develops as fluids flow through the various pipes, elbows, tees, vessel connections, valves, etc. These losses are expressed as loss of fluid static head in feet of fluid flowing. 

In fluid mechanics the principles of conservation of mass, conservation of momentum, the first and second laws of thermodynamics, and empirically developed correlations are used to predict the behavior of gases and liquids at rest or in motion. The field is generally divided into fluid statics and fluid dynamics and further subdivided on the basis of compressibility. Liquids can usually be considered as incompressible, while gases are usually assumed to be compressible. 

Besson, U., Viennot, L. (2004). Using models at the mesoscopic scale in teaching physics two experimental interventions in solid friction and fluid statics. International Journal of Science Education, 26(9), 1083-1110. 

Spinning disc reactor Supercritical fluids Static mixer reactor Reactor... 

Having obtained two simultaneous equations for the singlet and doublet correlation functions, X and, these have to be solved. Furthermore, Kapral has pointed out that these correlations do not contain any spatial dependence at equilibrium because the direct and indirect correlations of position in an equilibrium fluid (static structures) have not been included into the psuedo-Liouville collision operators, T, [285]. Ignoring this point, Kapral then transformed the equation for the singlet density, by means of a Laplace transformation, which removes the time derivative from the equation. Using z as the Laplace transform parameter to avoid confusion with S as the solvent index, gives... 

Ii the analysis of piping systems, pressure losses are commonly expressed in terms of the equivalent fiiid column height, called the head loss / ,. Noting from fluid statics that AP = pgh and thus a pressure difference of AP corresponds to a fluid height of h = Plpg, the pipe head loss is obtained by dividing APt by pg to give... 

Mass transfer through the membrane can be adjusted by changing two major variables of the acceptor (upper) chamber. Thus, Xhe flow-rate of the acceptor fluid is a key to improved pervaporation this can be achieved through a displacement in the mass transfer equilibrium resulting from the continual use of fresh acceptor fluid — which maximizes the concentration gradient between both chambers. Keeping the fluid static facilitates attainment of an equilibrium or near-equilibrium state for mass transfer. 

As described in Problem CLM.3, the fundamental equation of fluid statics indicates that the rate of change of the pressure P is directly proportional to the rate of change of the depth Z, or... 

F. Fluid Statics - The Stress Tensor for a Stationary Fluid... 

F. FLUID STATICS - THE STRESS TENSOR FOR A STATIONARY FLUID... 

We have said that the Young Laplace equation cannot be satisfied unless V n = constant. The proof is more or less trivial. Let us suppose that u = 0. Then, according to the equation of fluid statics, (2 61),... 

Problem 2-16. Fluid Statics (Archimedes Principle). Assume that we have a spherical coordinate system defined with respect to a Cartesian system according to x = r sin0 cos(j), y = r sin0 sin, andz = rcos0 ... 

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