Pressure drop power dissipation

Equation (6-95) is valid for incompressible flow. For compressible flows, see Benedict, Wyler, Dudek, and Gleed (J. E/ig. Power, 98, 327-334 [1976]). For an infinite expansion, A1/A2 = 0, Eq. (6-95) shows that the exit loss from a pipe is 1 velocity head. This result is easily deduced from the mechanic energy balance Eq. (6-90), noting that Pi =pg. This exit loss is due to the dissipation of the discharged jet there is no pressure drop at the exit. 

Equation (11) shows that the pressure drop across the connecting tube increases inversely as the fourth power of the tube radius. It follows that, as it is impractical to dissipate a significant amount of the available pump pressure across a connecting tubing, there will be a limit to the reduction of (r) to minimize tube dispersion. 

Power input per unit mass of the system is equal to the rate of energy dissipation per unit mass of the liquid and it is estimated by considering the permanent pressure head loss across the orifice. The rate of energy dissipation due to eddy losses is the product of the head loss and the volumetric flow rate. Frictional pressure drop at downstream of the orifice can be calculated as,... 

The results are very revealing and instructive. The rate of melting increases with the total force Fn, but only to the one fourth power. The physical explanation for this is that with increasing force, the film thickness is reduced, thus increasing the rate of melting. However, the thinner the film, the larger the pressure drops that are needed to squeeze out the melt. The dependence on the plate temperature is almost linear. The inverse proportionality with R is perhaps the most important result from a design point of view. If viscous dissipation were included, some of these results would have to be modified. 

The increased interfacial area in the microreactor led to an increased pressure drop. The energy dissipation factor, the power unit per reactor volume, of the microreactor process was thus higher (sv = 2-5 kW/m3) than that of the laboratory trickle-bed reactors (sv = 0.01-0.2 kW/m3) [277]. This is, however, outperformed by the still larger gain in mass transfer so that the net performance of the microreactor is better. 

Figure 8.19 shows the flux-time profiles obtained in filtration of 5% yeast cell suspension using a mbular membrane of 6 mm i.d. (inside diameter) and 0.14 pm pore size with a helical baffle (HB), a rod baffle (RB), and the mbular membrane without baffle (NB) [35]. The comparison has been made at the same hydraulic-dissipated power, which is defined as the product of the flow rate and the pressure drop along the mbular membrane, or the energy consumed to generate the crossflow through the mbular membrane. Using the hydraulic-dissipated power rather than the crossflow rate as a control parameter for the comparison of the mbular membrane with and without inserts eliminates the effect of the reduced crossflow section by... 

The evaluation of diazotization reactions [41], which were carried out in Kenics and Sulzer SMXL mixers, provide a possible access to this parameter determination. For small throughputs and high viscosities the yield of the desired product was determined by micro-mixing. The power dissipation of 85-90% in both mixers indicated, that the engulfment model for micro-mixing prevailed. Faster micro- and meso-mixing was achieved in the Sulzer mixers, because larger pressure drops were also present in them, see Fig. 8.11 and 8.12. 

The caterpillar micromixer consists of a number of serial oriented unit cells that repeat and complete the same type of mixing process. Eight such cells are serially combined in the standard version that is commercially available. Dependent on the mixing problem, however, more or less units may be appropriate, which, especially for production, needs to be optimized to reduce the pressure drop to the limit really needed and for efficient power dissipation. For this reason, caterpillar devices (600 pm width and depth) with 0, 2, 4, 6, and 8 mixing cells have been manufactured to test mixing efficiency by a standardized protocol (Fig. 6.3) ]27]. 

In a pressure flow, the greatest power is dissipated near the channel walls where the shear strain rate is highest. Hence, the viscous heating will lead to temperature differences between the core and the surface of the melt. When a melt falls in passes down a flow channel, under the influence of a pressure drop Ap, we can assume adiabatic conditions, so that no heat is transferred to the channel walls the average temperature rise of the melt is... 

The advantages of structured catalysts are demonstrated by the successful use in environment-related processes such as the selective catalytic reduction of NO, in power plants and the elimination of volatile organic compound (VOC) and NO in exhaust emissions. Low pressure drop, thus low power dissipation, high conversion, and selectivity required are clear elements of PI as defined in the introduction. 

The specific power dissipation is proportional to the flow rate and the pressure drop. The pressure drop through open channels with laminar flow is given by the Hagen-Poiseuille equation [20] ... 

For micromixers for which experimental pressure drop data are available, it is possible to estimate the specific power dissipation from Equation (6.4) between the inlet and the outlet pressure measurement points. It is assumed here that the estimated specific power contributes to mixing, which is a rough estimation because of the pressure drop induced by the micromixer pipe connections. In Figure 6.9 is plotted the mixing time with respect to the specific power dissipation for several mixers. The experimental mixing times scale fairly well as a power law of the... 

The power density Py is the characteristic quantity of turbulent flow. It determines the size of the smallest eddies and the intensity of microturbulence. In addition, it is a measure of the shear intensity in laminar flows or the intensity of cavitation in ultrasonic fields (see above). The power input P in the dispersion zone can be derived from the pressure drop (e.g. in pipes and nozzles) or can be measured caloricafly (e.g. for rotor-stator systems and ultrasonication Pohl 2005 Kuntzsch 2004). Additionally, P can be roughly approximated by the electric power consumption of the dispersion machine (e.g. for ultrasonication Mandzy et al. 2005 Sauter et al. 2008), even though the real values may be lower by a factor of 2 to 5. A further source of uncertainty is the volume of the dispersion zone (Vdisp). since the stress intensities are not uniformly distributed in dispersion apparatuses. In particular, this applies to agitated vessels, where the highest dissipation rates are obtained in the vicinity of the stirring instmment (Henzler and Biedermann 1996),... 

The total amount of power dissipated in the flow channel of a die is simply determined by the product of flow rate and pressure drop along the flow channel. Thus ... 

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