Velocity settling

Equation 10.10 can be used to estimate the settling velocity of the liquid droplets, for the design of separating vessels. 

If a demister pad is not used, the value of u, obtained from equation 10.10 should be multiplied by a factor of 0.15 to provide a margin of safety and to allow for flow surges. 

For those applications where a more complete design is required, the starting point for the entrainment reduction check is the droplet settling velocity. 

Droplets in the 3 to 100 micron (1 micron = 1/25,400 in.) range settle under the action of gravity at a rate given by Stokes law. The settling velocity is found by the equation 

Free-settling (terminal) velocity of the liquid entrainment under the action of gravity in feet per second. 

Enter the nomograph at the left with the Pv difference (a mental subtraction should be good enough). 

Draw a line from the density difference to the vapor viscosity. Mark the intersection with Index Line A. 

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Figure 3.1a shows a flash drum used to separate by gravity a vapor-liquid mixture. The velocity of the vapor through the flash drum must be less than the settling velocity of the liquid drops. Figure 3.11) shows a simple gravity settler for removing a... 

Measurement of single particle settling velocity in a turbulent field is not easy. However, it is known to be a function of free settling velocity which for spherical particles can be estimated from the following ... 

Fig. 14. Drag coefficient for terminal settling velocity correlation (single particle) where A represents Stokes law B, intermediate law and C, Newton s...

Quite often the settling velocity is modified by the presence of a large number of particles. This hindered settling velocity is a function of soHds concentration and should be measured experimentally or estimated from Hterature correlations (1). 

This relationship is exponential with respect to time t and with increasing time quickly approaches equation 7, where is known as the terminal settling velocity under gravity. 

The settling velocity, is relative to the continuous Hquid phase where the particle or drop is suspended. If the Hquid medium exhibits a motion other than the rotational velocity, CO, the vector representing the Hquid-phase velocity should be combined with the settling velocity (eq. 2) to obtain a complete description of the motion of the particle (or drop). 

The feed rate corresponding to this condition is related to the bowl geometry r, and /, the bowl angular speed, CO and the Stokes settling velocity. 

Here again an equation is estabUshed (2) to describe the trajectory of a particle under the combined effect of the Hquid transport velocity acting in the x-direction and the centrifugal settling velocity in thejy-direction. Equation 13 determines the minimum particle size which originates from a position on the outer radius, and the midpoint of the space, between two adjacent disks, and just reaches the upper disk at the inner radius, r. Particles of this size initially located above the midpoint of space a are all collected on the underside of the upper disk those particles initially located below the midpoint escape capture. This condition defines the throughput, for which a 50% recovery of the entering particles is achieved. That is,... 

Equipment. Centrifugation equipment that separates by density difference is available in a variety of sizes and types and can be categorized by capacity range and the theoretical settling velocities of the particles normally handled. Centrifuges that separate by filtration produce drained soflds and can be categorized by final moisture, drainage time, G, and physical characteristics of the system, such as particle size and Hquid viscosity. 

Fig. 8. Sedimentation equipment performance where the particles have a A5 value of 1.0 g/cm and a viscosity, p., value of 1 mPa-s(=cP). The value of is twice the settling velocity at G = 1, and Q = overflow discharge rate in measurements given.

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... 

Pettyjohn and Christiansen Chem. Eng. Prog., 44, 157-172 [1948]) present correlations for the effect of particle shape on free-settling velocities of isometric particles. For Re < 0.05, the terminal or free-setthng velocity is given oy... 

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