Mean diameter

In all other cases the quantity / calculated from the specific surface is a mean diameter. Unless there is some definite and detailed evidence as to particle shape, the simplest such diameter to aim at is the mean diameter obtained by substituting the measured value of A in Equation (1.79)... 

Since the numerator of the right-hand side of (1.81) has the dimensions of volume and the denominator those of surface area, the quantity is termed the volume-surface mean diameter of the sample. 

For a longitudinal disturbance of wavelength 12 pm, the droplets have a mean diameter of about 3-4 pm. These very fine droplets are ideal for ICP/MS and can be swept into the plasma flame by a flow of argon gas. Unlike pneumatic forms of nebulizer in which the relative velocities of the liquid and gas are most important in determining droplet size, the flow of gas in the ultrasonic nebulizer plays no part in the formation of the aerosol and serves merely as the droplet carrier. 

S. Aureus Sausage Sausage casing Sausage casing material Sausages Sauter diameter Sauter mean diameter N.S. Savannah Savard-Lee injectors Savin ase... 

The role of coalescence within a contactor is not always obvious. Sometimes the effect of coalescence can be inferred when the holdup is a factor in determining the Sauter mean diameter (67). If mass transfer occurs from the dispersed (d) to the continuous (e) phase, the approach of two drops can lead to the formation of a local surface tension gradient which promotes the drainage of the intervening film of the continuous phase (75) and thereby enhances coalescence. It has been observed that d-X.o-c mass transfer can lead to the formation of much larger drops than for the reverse mass-transfer direction, c to... 

Particle Size. The soHds in a fluidized bed are never identical in size and foUow a particle size distribution. An average particle diameter, is generally used for design. It is necessary to give relatively more emphasis to the low end of the particle size distribution (fines), which is done by using the surface mean diameter, to calculate an average particle size ... 

The surface mean diameter is the diameter of a sphere of the same surface area-to-volume ratio as the actual particle, which is usually not a perfect sphere. The surface mean diameter, which is sometimes referred to as the Sauter mean diameter, is the most useful particle size correlation, because hydrodynamic forces in the fluid bed act on the outside surface of the particle. The surface mean diameter is directly obtained from automated laser light diffraction devices, which are commonly used to measure particle sizes from 0.5 to 600 p.m. X-ray diffraction is commonly used to measure smaller particles (see Size TffiASURETffiNT OF PARTICLES). 

Under turbulent flow conditions, the Sauter mean diameter from two static mixers can be obtained from the following ... 

Distribution Averages. The most commonly used quantities for describing the average diameter of a particle population are the mean, mode, median, and geometric mean. The mean diameter, d, is statistically calculated and in one form or another represents the size of a particle population. It is usefiil for comparing various populations of particles. 

The simplest calculation of the mean, referred to as arithmetic mean (count mean diameter) for data grouped in intervals, consists of the summation of all diameters forming a population, divided by the total number of particles. It can be expressed mathematically by equation 1 ... 

The mean volume (mass diameter) is the arithmetic mean diameter of all the particle volumes or masses forming the entire population and, for spherical particles, can be expressed as in equation 2 ... 

Another frequentiy used average is the geometric mean, which is particularly usehil for log-normal or wider (spanning over a decade) distributions. The geometric mean diameter, d is calculated usiag the logarithm values of the measured diameters ... 

Mea.il Diameters. Several mean diameters are frequendy used to represent the statistical properties of droplets produced by Hquid atomizers. These mean diameters may be expressed according to the following proposed notation (27) ... 

Thep and q denote the integral exponents of D in the respective summations, and thereby expHcitiy define the diameter that is being used. and are the number and representative diameter of sampled drops in each size class i For example, the arithmetic mean diameter, is a simple average based on the diameters of all the individual droplets in the spray sample. The volume mean diameter, D q, is the diameter of a droplet whose volume, if multiphed by the total number of droplets, equals the total volume of the sample. The Sauter mean diameter, is the diameter of a droplet whose ratio of volume-to-surface area is equal to that of the entire sample. This diameter is frequendy used because it permits quick estimation of the total Hquid surface area available for a particular industrial process or combustion system. Typical values of pressure swid atomizers range from 50 to 100 p.m. 

Volume dux is the volume contained by the droplets passing through a unit cross-sectional area per unit interval of time. It can be calculated as follows, where is the volume mean diameter and n is the total number of droplets. 

Figure 4 shows a three-dimensional distribution of the Sauter mean diameter, measured 38.1-mm downstream from the nozzle using a Delavan 1 GPH-80°A pressure atomizer. The operating pressure was 690 kPa (100 psi). TypicaUy, the mean diameters graduaUy increase with an increase in radial... 

Fig. 4. Three-dimensional distribution of Sauter mean diameter (SMD) in a typical hoUow-cone spray.

Using equations 11 and 12, the estimated Sauter mean diameters agree quite weU with experimental data obtained for a wide range of atomizer designs. Note that the two constants in equation 11 differ from those shown in Lefebvre s equation (32). These constants have been changed to fit a wide range of experimental data. 

For airblast-type atomizers, it has been speculated (33) that the Sauter mean diameter is governed by two factors, one controlled by air velocity and density, the other by Hquid viscosity. Equation 13 has been proposed for the estimation of equation 13, and B are constants whose values depend... 

Fig. 6. Activation energy for diffusion in poly(vinyl chloride) as a function of penetrant mean diameter (19). To convert to cal, divide by 4.184.

Stainless steel flat six-blade turbine. Tank had four baffles. Correlation recommended for ( ) < 0.06 [Ref. 156] a = 6( )/<, where d p is Sauter mean diameter when 33% mass transfer has occurred. dp = particle or drop diameter <3 = iuterfacial tension, N/m ( )= volume fraction dispersed phase a = iuterfacial volume, 1/m and k OiDf implies rigid drops. Negligible drop coalescence. Average absolute deviation—19.71%. Graphical comparison given by Ref. 153. ... 

Volume mean diameter e Entrainment, mass liquid/mass gas... 

AP is the pressure drop, cm of water p and Pg are the density of the scrubbing liquid and gas respectively, g/cm L/g is the velocity of the gas at the throat inlet, cm/s QtIQg is the volumetric ratio of liquid to gas at the throat inlet, dimensionless It is the length of the throat, cm Coi is the drag coefficient, dimensionless, for the mean liquid diameter, evaluated at the throat inlet and d[ is the Sauter mean diameter, cm, for the atomized liquid. The atomized-liquid mean diameter must be evaluated by the Nuldyama and Tanasawa [Trans. Soc Mech Eng (Japan), 4, 5, 6 (1937-1940)] equation ... 

Most of the investigators have assumed the effective drop size of the spray to be the Sauter (surface-mean) diameter and have used the empirical equation of Nuldyama and Tanasawa [Trons. Soc. Mech. Eng., Japan, 5, 63 (1939)] to estimate the Sauter diameter ... 

Average Particle Size A powder has many average sizes hence it is essential that they be well specified. The median is the 50 percent size half the distribution is coarser and half finer. The mode is a high-density region if there is more than one peak in the frequency cui ve, the distribution is said to be multimodal. The mean is the center of gravity of the distribution. The center of gravity of a mass (volume) distribution is defined by. Xyw = X XdV/X dV where dV = X dN dV is the volume of dN particles of size X This is defined as the volume-moment mean diameter and differs from the mean for a number or surface distribution. 

For obtaining a self-inductance of 42.93 pH consider a coil of 15 cm mean diameter (r= 7.5 cm) made of the same cable that is connecting each capacitor bank through the switching device. 

By providing 12 turns of 150 mm mean diameter of the 50 mm flexible copper cable connecting each 60 kVAr capacitor bank a self-inductance of roughly 42.93 x 10 H can be introduced into each switching circuit, which will limit the switching inrush current to almost the permissible value of the making current (/, ) of the switching device. 

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