Forces gravitational

Settling and sedimentation. In settling processes, particles are separated from a fluid by gravitational forces acting on the particles. The particles can be solid particles or liquid drops. The fluid can be a liquid or a gas. 

A thin film of hydrocarbon spread on a horizontal surface of quartz will experience a negative dispersion interaction. Treating these as 1 = quartz, 2 = n-decane, 3 = vacuum, determine the Hamaker constant A123 for the interaction. Balance the negative dispersion force (nonretarded) against the gravitational force to find the equilibrium film thickness. 

CE uses holonomic constraints. In a constrained system the coordinates of the particles 5t independent and the equations of motion in each of the coordinate directions are cted. A second difficulty is that the magnitude of the constraint forces is unknown, in the case of the box on the slope, the gravitational force acting on the box is in the ction whereas the motion is down the slope. The motion is thus not in the same direc-s the gravitational force. As such, the total force on the box can be considered to arise wo sources one due to gravity and the other a constraint force that is perpendicular to otion of the box (Figure 7.8). As there is no motion perpendicular to the surface of the the constraint force does no work. 

It is easiest to appreciate what is meant by mass iadirecdy, by observing the influence of forces on objects, eg, by picking up an object and sensing the effect of the earth s gravitational force acting on it, and hence "feeling" its weight. 

Buoyant Effect of Air. Weighing operations performed m vacuo are not affected by buoyancy forces. An object in air, however, is subject to a buoyancy force that is equal and opposite to the gravitational force on the mass of air the object displaces (10). If the equal arm balance of Figure 1 is in balance with a test weight of mass, in one pan, and material of mass, m, in the other, m = m if they have the same density. If the densities are different, then the buoyancy forces acting on each pan affect the result. Taking moments about the center pivot point gives... 

Sedimentation (qv) techniques, whether based on gravitational forces or centrifugation, derive the particle size from the measured travel rates of particles in a Hquid. Before the particle analysis is carried out, the sample is usually dispersed in a medium to break down granules, agglomerates, and aggregates. The dispersion process might involve a simple stirring of the powder into a Hquid, but the use of an ultrasonic dispersion is preferred. 

Falling ball viscometers are based on Stokes law, which relates the viscosity of a Newtonian fluid to the velocity of the falling sphere. If a sphere is allowed to fall freely through a fluid, it accelerates until the viscous force is exactly the same as the gravitational force. The Stokes equation relating viscosity to the fall of a soHd body through a Hquid may be written as equation 34, where ris the radius of the sphere and d are the density of the sphere and the hquid, respectively g is the gravitational force and p is the velocity of the sphere. 

Power. The power requited to drive a belt conveyor is derived from the tensile forces requited to propel or restrain the belt at the design speed. These include the tensile forces produced by the frictional resistance of the drive, conveyor components, and material the acceleration of the material and the gravitational forces requited to lift or lower the material. Detailed information and methods of calculation can be found in belt conveyor design handbooks and in Reference 9. 

Another type of condensation, called dropwise, occurs when the wall is not uniformly wetted by the condensate, with the result that the condensate appears in many small droplets at various points on the surface. There is a growth or individual droplets, a coalescence of adjacent droplets, and finally a formation of a liviilet. Adhesional force is overcome by gravitational force, and the rivulet flows quickly to the bottom of the surface, capturing and absorbing all droplets in its path and leaving dry surface in its wake. 

G. Highly agitated systems solid particles, drops, and bubbles continuous phase coefficient [E] Use arithmetic concentration difference. Use when gravitational forces overcome by agitation. Up to 60% deviation. Correlation prediction is low (Ref. 118). (PA, ar.k) = power dissipated by agitator per unit volume liquid. [79][83]p.231 [91] p. 452... 

A particle falling under the action of gravity will accelerate until the drag force balances gravitational force, after which it falls at a constant terminal or free-settling velocity given by... 

Gravitational force favors the separation of gas from liquid in a disperse system, causing the bubbles to rise to the hquid surface and the liquid contained in the bubble walls to drain downward to the main body of the liquid. Interfacial tension favors the coalescence and ultimate disappearance of bubbles indeed, it is the cause of bubble destruction upon the rupture of the laminae. 

Planetary Ball Milling This is a method of increasing the gravitational force acting on balls in a ball mill. For example, refractoiy metals and carbides can be ground to 1 to 2.6 [Lm in 5 to 20 min in an apparatus capable of applying a centrifugal force of 10 to 50 G. [Dobrovol sldi, Poroshk. MetalL, 7(6), 1-7 (1967)]. 

The pour point is an indication of the lowest temperature at which a fuel oil can be stored and still be capable of flowing under gravitational forces. Fuels with higher pour points are permissible where the piping has been heated. Water and sediment in the fuel lead to fouling of the fuel system and obstruction in fuel filters. 

Both particle size and the liquid viscosity affect the rate of particle settling. The rate of settling due to gravitational force decreases with decreasing particle size and increasing viscosity. The process mechanisms are sensitive to the relative rates of filtration and gravity sedimentation. 

Look closely at the settling times in Table 1 - the times span from a fraction of a second to almost a lifetime A great deal of the suspended matter found in waste waters fall into the colloidal suspension range, so obviously we caimot rely on gravitational force alone to separate out the pollutants. 

---