Gravitational force defined

This number gives a correlation between the inertial and gravitational forces, defined by g, inside the fluid. 

P represents the combined effects of static pressure (P) and gravitational force and is defined as... 

In a hydrodynamically free system the flow of solution may be induced by the boundary conditions, as for example when a solution is fed forcibly into an electrodialysis (ED) cell. This type of flow is known as forced convection. The flow may also result from the action of the volume force entering the right-hand side of (1.6a). This is the so-called natural convection, either gravitational, if it results from the component defined by (1.6c), or electroconvection, if it results from the action of the electric force defined by (1.6d). In most practical situations the dimensionless Peclet number Pe, defined by (1.11b), is large. Accordingly, we distinguish between the bulk of the fluid where the solute transport is entirely dominated by convection, and the boundary diffusion layer, where the transport is electro-diffusion-dominated. Sometimes, as a crude qualitative model, the diffusion layer is replaced by a motionless unstirred layer (the Nemst film) with electrodiffusion assumed to be the only transport mechanism in it. The thickness of the unstirred layer is evaluated as the Peclet number-dependent thickness of the diffusion boundary layer. 

The force on a sedimenting particle increases with the velocity of the rotation and the distance of the particle from the axis of rotation. A more common measurement of F, in terms of the earth s gravitation force, g, is relative centrifugal force, RCF, defined by Equation 7.2. 

The shape of the melt-fluid interface in a meniscus-defined crystal growth system is set by surface tension, gravitational force, and viscous and dynamic pressure forces on the surface. The Bond number (Bo for hydro-... 

According to the hereby used theory of superluminal relativity [5], nuclear forces are explained by Newton s gravitational law and Einstein s general theory of relativity [10], with the gravitational constant defined and determined by the quantum mass theory [4], for masses and distances characteristic for nuclear structures. 

The dynamic response of a particle in gas-solid flows may be characterized by the settling or terminal velocity at which the drag force balances the gravitational force. The dynamic diameter is thus defined as the diameter of a sphere having the same density and the same terminal velocity as the particle in a fluid of the same density and viscosity. This definition leads to a mathematical expression of the dynamic diameter of a particle in a Newtonian fluid as... 

The moons of Saturn have a direct influence on Saturn s rings. A natural tendency of ring materials is to spread both toward and away from the planet, but the moons and a complex interplay of gravitational forces shape the rings and define their structure. Mimas. . . Tethys. . . Dione. . . Rhea. . . Enceladus. . . Iapetus. . . And Hyperion. . . ... 

The moons of Saturn have a direct influence on Saturn s rings. A natural tendency of ring materials is to spread both toward and away from the planet, but the moons and a complex tnterplay of gravitational forces shape the rings and define their structure. 

External fields are applied widely in separation systems. The most common fields used are based on electrical and sedimentation (both centrifugal and gravitational) forces. Gradients in solvent composition and temperature maintained by actions external to the system may also be considered as external fields defined in their broadest context (see Chapter 8). All of these fields are capable of changing the equilibrium distribution of chemical components. Furthermore, they may be selective, affecting one component differently from another, a basic requirement for separation. 

According to Newton s 2nd law of motion, the force, F, is expressed as a product of mass, m, and acceleration, a F = m a, having the dimension of [M LT 2]. According to Newton s law of gravitation, force is defined by F mi m2/r2, thus leading to completely another dimension [M2 L-2]. To remedy this, the gravitational constant G - a dimensional constant - had to be introduced to ensure the dimensional homogeneity of the latter equation ... 

In other words, the gravitational force can be defined thus ... 

Three forces act on a gaseous bubble in free liquid (without a solid phase) gravitational force (G = mg = Vpog) Archimedes force (F = Vpg) and the resistant force of the medium defined by Stake s law (R = bTiqroVo), where, g = acceleration due to gravity, ro = radius of bubble, V = volume of bubble, po = density of gases in bubble, p = density of liquid, q = dynamic viscosity of liquid, Vq = speed of bubble at equilibrium of the three forces. 

When studying the dependence of force on position, we must pay careful attention to how displacement is defined in each particular problem. The force and the acceleration at any point are parallel to each other, but the displacement (defined relative to some convenient origin of coordinates in each particular case) may point in a different direction. In applications concerned with the height of an object above the earth, the gravitational force is usually written as... 

The dimensionless source term essentially represents the ratio of generation to convection. For various generation terms, several additional dimensionless numbers may be defined. For example, if the generation of momentum due to gravitational forces is considered, a dimensionless number, called as the Froude number (Fr), is defined as the ratio of convection to gravitational factors. The dimensionless numbers discussed here along with other dimensionless numbers are listed in Table 2.1 together with their physical interpretation. 

---