The correction factor

To enable us to compare the long-pipe approximation with the exact solution valid for a horizontal pipe, we substitute equation (A2.29) into (A2.13) with the additional condition that zi = Zs. i-e.  

Defining the long-pipe approximation function, fipa, as the dimensionless function 

Comparing equations (A2.33) and (A2.7), it is clear that the correction factor, o. is simply the ratio of the exact pipe-flow function, /p,, to its approximate equivalent just defined  

As we would expect from the assumptions made in the derivation of the long-pipe approximation, bo is close to unity when the change in pressure with distance, dp/dx, is relatively low, namely when the pipe is long and/or the pressure drop small. The contours show how bo increases towards unity as pn/p 1.0 and Kt - 00. In fact at Kr = 128 and Pa/P = 0.95, bo is already greater than 0.99. But the deviations from unity grow when dp/dx is large, namely when the pipe is short, or the pressure ratio is small. 

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Since the known stress calibration method was adopted to perform the SPATE setting, the calibration factor was directly obtained from the preliminary tests above mentioned. However, it is interesting to observe that assuming the correction factor equal to 1 at 10 Hz, the ratio of Cf at the others investigated frequencies (2 and 5 Hz) to the calibration factor at 10 Hz gives ... 

Harkins and Jordan [43] found, however, that Eq. 11-26 was generally in serious error and worked out an empirical correction factor in much the same way as was done for the drop weight method. Here, however, there is one additional variable so that the correction factor/ now depends on two dimensionless ratios. Thus... 

The third term in Equation (11.52) is the correction factor corresponding to the work done creating the charge distribution of the solute within the cavity in the dielectric medium. the gas-phase wavefimction. 

In this expression, cos 0 is the average value of cos 0 the weighting factor used to evaluate the average is given by the Boltzmann factor exp(-V /RT), where R is the gas constant in the units of and T is in degrees Kelvin. Note that the correction factor introduced by these considerations reduces to unity if... 

NTU p is the "exterior apparent" overall gas-phase number of transfer units calculated neglecting axial dispersion simply on the basis of equation 56, whereas NTU stands for the higher real number of transfer units (Nq ) which is actually required under the influence of axial dispersion. The correction factor ratio can be represented as a function of those parameters that are actually known at the outset of the calculation... 

The correction factor (NTU) p/NTU as a function of Pe rather than Pe is shown in Figure 19b. The correction factors given in Figures 19a and 19b can roughly be estimated as... 

Inclined belts provide additional areas of contact with the pulley magnetic field and can tolerate higher capacities than normal for a magnetic pulley apphcation. Table 3, which iadicates the correction factor to be appHed to the capacity, can be used with Table 2 to make the magnetic pulley diameter selection for an inclined belt. The initial cost of units can be related to the capacity or volume throughput. Costs mn about 35 for each m /h on the smaller units about 50 for each m /h on larger units. 

For pressui es greater than 3.5 MPa, the correction factor suggested by Missenard " may be used to obtain the thermal conductivity of pure component nonhydrocarbon liquids. Thus ... 

The correction factor C still applies. Spectral data for water vapor, tabulated for 371 wavelength intervals from 1 to 40 Im, are also available [Ferriso, Ludwig, and Thompson, J. Quant. Spectm.s. Radiat. Tran.sfer, 6, 241-273 (1966)]. The principal emission is in bands at about 2.55 to 2.84, 5.6 to 7.6, and 12 to 25 jlm. 

Thus the factors vaiy with the type of processing, although the boundaries between the classifications are not clear-cut and considerable judgment is required in selection of the correct factor. 

Find the correction factor for baffle-leakage effects J[ from Fig. 11-11. 

Find the correction factor for adverse temperature-gradient buildup at low Reynolds number J/. 

Find the correction factor for the effect of baffle leakage on pressure drop Ri from Fig. 11-16. Cni ves shown are not to be extrapolated beyond the points shown. 

When straight or serrated segmental weirs are used in a column of circiilar cross secdion, a correction may be needed for the distorted pattern of flow at the ends of the weirs, depending on liquid flow rate. The correction factor F from Fig. 14-33 is used direcdly in Eq. (14-112) or Eq. (14-119). Even when circular downcomers are utilized, they are often fed by the overflow from a segmental weir. When the weir crest over a straight segmental weir is less than 6 mm V in), it is desirable to use a serrated (notched) weir to provide good liquid distribution. Inasmuch as fabrication standards permit the tray to be 3 mm Vh in) out of level, weir crests less than 6 mm V in) can result in maldistribution of hquid flow. 

Magnetic pulleys. These vary in size from 0.203 to 1.219 m in diameter and from 2.03 to 1.526 m in width. The acceptable depth of the material on the conveyor belt depends on the diameter of the pulley and the linear velocity of the belt (see Table 19-18). Table 19-19 indicates the maximum capacity for such units. Depending on the apphcation, the correction factors given in Table 19-20 should be apphed. For sizing and maximum efficiency, multiply the actual volume of material to be handled by the correction factor shown and select the magnetic pulley having a capacity equal to or greater than the resultant volume. 

Because the crack penetrates a long way into the wall of the vessel, it is necessary to take into account the correction factor Y (see Chapter 13). Figure 16.3 shows that Y = 1.92 for our crack. The critical stress for fast fracture is given by... 

A similar expansion can be written in the vicinity of Q = 0. Path integration amounts to the Gaussian integration over the Q , whereas the integration over the unstable mode Qq is understood as described in section 3.3. In that section we also justified the correction factor (f) = T /T = X l2n which should multiply the Im F result in order to reproduce the correct high-temperature behavior. Direct use of the Im F formula finally yields... 

Interestingly, the correction factor is to a good accuracy approximated by the Wigner formula (2.15) and it is practically independent of friction [Hanggi 1986], by contrast with the relatively strong dependence of on r. ... 

Correction factors are also provided in ASME PTC Test Code-46. The correction factors for ambient temperature, ambient pressure, and relative humidity are presented in this chapter. 

The correction factor can be quite low requiring an uneconomically large area. 

For Figure 1, assuming one shell pass and two or more tube passes, the correction factor is roughly 0.7. This... 

Since the composition of the unknown appears in each of the correction factors, it is necessary to make an initial estimate of the composition (taken as the measured lvalue normalized by the sum of all lvalues), predict new lvalues from the composition and the ZAF correction factors, and iterate, testing the measured lvalues and the calculated lvalues for convergence. A closely related procedure to the ZAF method is the so-called ())(pz) method, which uses an analytic description of the X-ray depth distribution function determined from experimental measurements to provide a basis for calculating matrix correction factors. 

It is now necessary to derive an expression for (Pr) and then the correction factor —... 

Figure 55 indicates that the level of percent solids is extremely important in determining the proper separation, the higher the concentration, the coarser the separation. The correction factor is a relative measure of slurry viscosity and is affected by such parameters as particle present and particle shape. A feed that contains a large amount of clay would tend to shift the curve to the left, resulting in a coarser separation. In contrast, the absence of fines would shift the curve to the right and result in a finer separation. 

Measurements of the effective viscosity as a function of composition may be fitted to equation 80 or presented in graphic form as in Figure 16. The correction factor, R, also may be determined by accounting for the volume fraction, ti , of particles through the Andress formula ... 

Figure 17. Variable or constant back pressure sizing factor, Kw for 25% overpressure on balanced bellows safety relief valves (liquids only). The curve represents conqiromise of the valves reconunended by a number of relief valve manufacturers. This curve may be used wiien the make of dw valve is not known. When the make is known, the manufacturer should be consulted for the correction factor.

The correction factor for converting apparent shear rates at the wall of a circular cylindrical capillary to true shear rates is (3n + l)/4n, where n is the power law index of the polymer melt being extruded. 

A slit die is designed on the assumption that the material is Newtonian, using apparent viscous properties derived from capillary rheometer measurements, at a particular wall shear stress, to calculate the volumetric flow rate through the slit for the same wall shear stress. Using the correction factors already derived, obtain an expression for the error involved in this procedure due to the melt being non-Newtonian. Also obtain an expression for the error in pressure drop calculated on the same basis. What is the magnitude of the error in each case for a typical power law index n = 0.377... 

For some fluids, such as oils, the viscosity is temperature dependent. Here the correction factor pp/is used, where r)p is the viscosity at the mean fluid temperature and is the viscosity at the wall temperature. 

It is not uncommon to supply air into the room with jets attached both to the ceiling and to the wall surfaces. Air jets can be parallel to both surfaces or be directed at some angle to one or both surfaces (Fig. 7.28). Studies of compact wall jets supplied parallel to both surfaces reported by Grimitlyn show that the correction factor value is in the range from 1.6 to 1.7, which means that restriction of entrainment from two sides reduces velocity decay by 20% to 30% compared to the case of a wall jet. 

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