Required minimum flow velocity

TABLE 18.2 Required Minimum Flow Velocity (RMFV) of Slurry Blend in the Global Loop, Abrasive Settling Rate (SR), and Stokes Number (St) for Tested CMP Slurries. SR Values Depend on Selected Transmission and Back-Scattering Zones. (A) = Slurry Abrasive Component Only and (B) = Slurry Blend. 

An estimate of the minimum required mud flow velocity in annular space to assure adequate cuttings transport can be estimated from... 

A minimum flow velocity was required to maintain a flame. When the flow velocity of the feed was increased, the location of the flame first moved upstream and then downstream again, while the width of the reaction zone decreased and the maximum... 

Many of the above factors that affect column operation are due to vapor flow conditions being either excessive or too low. Vapor flow velocity is dependent on column diameter. Weeping determines the minimum vapor flow required while flooding determines the maximum vapor flow allowed, hence column capacity. Thus, if the column diameter is not sized properly, the column will not perform well. Not only will operational problems occur, the desired separation duties may not be achieved. 

Piping systems should be designed for an economic flow velocity. For relatively clean fluids, a recommended velocity range where minimum corrosion can be expected is 2 to 10 fps. If piping bores exist, maximum fluid velocities may have a mean velocity of 3 fps for a 3/8-in. bore to 10 fps for an 8-in.-diameter bore. Higher flow velocities are not uncommon in situations that require uniform, constant oxygen supply to form protective films on active/passive metals. 

In the flow of a gas through a nozzle, the pressure falls from its initial value Pi to a value P2 at some point along the nozzle at first the velocity rises more rapidly than the specific volume and therefore the area required for flow decreases. For low values of the pressure ratio P2/P1, however, the velocity changes much less rapidly than the specific volume so that the area for flow must increase again. The effective area for flow presented by the nozzle must therefore pass through a minimum. It is shown that this occurs if the pressure ratio P2/P1 is less than the critical pressure ratio (usually approximately 0.5) and that the velocity at the throat is then equal to the velocity of sound. For expansion... 

It should be noted that at a flow rate of 2 ml/min., the mobile phase velocity will be well above that of the optimum and so the maximum efficiency will not be realized. Generally, when there are more theoretical plates available than required, the flow rate is increased until the separation required is just realized. This procedure trades efficiency for time and allows the separation to be achieved in the minimum time given the column and phase system that has been chosen. It must be emphasized that the minimum analysis time can... 

As the fluid velocity is increased the drag on the particles increases and a point is reached where the pressure drop balances the effective weight of bed per unit cross-sectional area. At this point the fluid drag just supports the solid particles. A small increase in the flow rate causes a slight expansion of the bed from its static, packed state. Further increase in the flow rate allows the bed to expand more and the particles become free to move around and the bed is said to be fluidized. The state when the bed just becomes fluidized is known as incipient, or minimum, fluidization. The fluid velocity required to cause incipient fluidization is called the minimum fluidization velocity and is denoted by umf. 

The flow required to maintain a complete homogeneous bed of solids in which coarse or heavy particles will not segregate from the fluidized portion is very different from the minimum fluidizing velocity. See... 

In the last 25 years, calculations of the detonation properties of condensed explosives from their chemical compositions and densities have been approached in various ways.2 All have used the necessary conservation conditions for steady flow with the detonation discontinuity satisfying the Chapman-Jouguet hypothesis (minimum detonation velocity compatible with the conservation conditions or sonic flow behind the discontinuity in a reference frame where the discontinuity is at rest). In order to describe the product state and the thermodynamic variables which fix its composition, an equation of state applicable to a very dense state is required. To apply this equation to a mixture of gaseous and solid products, a mixing rule is also needed and the temperature must be explicitly defined. Of the equations of state for high-density molecular states which have been proposed, only three or four have been adapted to the calculation of equilibrium-product compositions as well as detonation parameters. These are briefly reviewed in order to introduce the equation used for the ruby computer code and show its relation to the others. 

Principally, investigations have been conducted of suitable linear velocities and power requirements. Slurries of 40-50 vol% solids can be handled satisfactorily, with particle sizes less than 24-48 mesh or so (0.7-0.3 mm). At low line velocities, particles settle out and impede the flow of the slurry, and at high velocities the frictional drag likewise increases. An intermediate condition exists at which the pressure drop per unit distance is a minimum. The velocity at this condition is called a critical velocity of which one correlation is... 

Ordinarily under practical conditions the flow rate is at most a few multiples of the minimum fluidizing velocity so the local maximum bed level at the minimum bubbling velocity is the one that determines the required vessel size. The simplest adequate equation that has been proposed for the ratio of voidages at minimum bubbling and fluidization is... 

---