A New Pressure Loss Equation

Basic principles of pneumatic conveying and equations are presented. A new pressure loss equation is presented with examples. 

The new pressure loss equation presented here is based on determining two parameters the velocity difference between gas and conveyed material and the falling velocity of the material. The advantage of this method is that no additional pressure loss coefficient is needed. The two parameters are physically clear and they are quite easily modeled for different cases by theoretical considerations, which makes the method reliable and applicable to various ap>-plications. The new calculation method presented here can be applied to cases where solids are conveyed in an apparently uniform suspension in a so-called lean or dilute-phase flow. 

Note that all the factors required for Eqs. (6.30) and (6.31) have been established in previous steps of this section. Thus, for any 90° standard ell using these two equations, we have the pressure loss established for two-phase flow acceleration. Simply multiply the calculated APen value by the number of 90° ells in the pipe segment. Remember that if a 15% pressure loss in a pipe segment results, a new pipe segment is required. 

These new equations, Eqs. (6.32) and (6.33), have now been applied to numerous field trials and tests, finding good results. Please note the resemblance to Eq. (6.6). The log D factor is a plot of pipe diameter vs. pressure loss on a log-log scale. 

The temperature is tentatively lowered by a few degrees. The loss of enthalpy of the liquid then serves for vaporization. The volume released is replaced by vapour, as long as there is still liquid and the quantity of vaporized liquid is sufficient. Otherwise this quantity is the upper limit. As a consequence we obtain a new value for the pressure. By iteration the temperature is subsequently modified until the values for pressure and temperature lie on the vapour pressure curve (vid. Fig. 10.4). The latter can be determined from approximate equations [13] or the Clausius-Clapeyron relation [19]. The connection between temperature and pressure is ensured by the equation of state for gases. 

Therefore, it is possible to increase throughput, and thus the speed of analysis without affecting the chromatographic performance. The advent of UPLC has demanded the development of a new instrumental system for LC, which can take advantage of the separation performance (by reducing dead volumes) and consistent with the pressures (8000-15,000 psi, compared with 2500 to 5000 psi in HPLC). Efficiency is proportional to column length and inversely proportional to the particle size [41], Smaller particles provide increased efficiency as well as the ability to work at increased linear velocity without a loss of efficiency, providing both resolution and speed. Efficiency is the primary separation parameter behind UPLC since it relies on the same selectivity and retentivity as HPLC. In the fundamental resolution (Rs) equation [38], resolution is proportional to the square root of N. 

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