Vortex pressure

Comparison of Equations 4-66 and 4-69 shows that 9p(x,y)/9x = 9 F(x,y)/9y, while Equations 4-65 and 4-68 show that 9p(x,y)/9y = -9 F(x,y)/9x. Hence, the Cauchy-Riemann conditions are identically satisfied, so that the streamfunction in Equation 4-67 is complementary to the vortex pressure in Equation 4-64. These results provide expressions for streamline tracing in the presence of distributed singularities. In general, as we will show in Chapter 5, the flow past (or from) an arbitrary entity can be represented by superpositions of line sources and vortexes, respectively, having strengths f(x) and g(x). The net pressure field... 

Thermochemical Liquefaction. Most of the research done since 1970 on the direct thermochemical Hquefaction of biomass has been concentrated on the use of various pyrolytic techniques for the production of Hquid fuels and fuel components (96,112,125,166,167). Some of the techniques investigated are entrained-flow pyrolysis, vacuum pyrolysis, rapid and flash pyrolysis, ultrafast pyrolysis in vortex reactors, fluid-bed pyrolysis, low temperature pyrolysis at long reaction times, and updraft fixed-bed pyrolysis. Other research has been done to develop low cost, upgrading methods to convert the complex mixtures formed on pyrolysis of biomass to high quaHty transportation fuels, and to study Hquefaction at high pressures via solvolysis, steam—water treatment, catalytic hydrotreatment, and noncatalytic and catalytic treatment in aqueous systems. 

Flow. The principal types of flow rate sensors are differential pressure, electromagnetic, vortex, and turbine. Of these, the first is the most popular. Orifice plates and Venturi-type flow tubes are the most popular differential pressure flow rate sensors. In these, the pressure differential measured across the sensor is proportional to the square of the volumetric flow rate. 

In a submerged-tube FC evaporator, all heat is imparted as sensible heat, resulting in a temperature rise of the circulating hquor that reduces the overall temperature difference available for heat transfer. Temperature rise, tube proportions, tube velocity, and head requirements on the circulating pump all influence the selec tion of circulation rate. Head requirements are frequently difficult to estimate since they consist not only of the usual friction, entrance and contraction, and elevation losses when the return to the flash chamber is above the liquid level but also of increased friction losses due to flashing in the return line and vortex losses in the flash chamber. Circulation is sometimes limited by vapor in the pump suction hne. This may be drawn in as a result of inadequate vapor-liquid separation or may come from vortices near the pump suction connection to the body or may be formed in the line itself by short circuiting from heater outlet to pump inlet of liquor that has not flashed completely to equilibrium at the pressure in the vapor head. 

Another common situation is batch hydrogenation, in which pure hydrogen is introduced to a relatively high pressure reactor and a decision must be made to recycle the unabsorbed gas stream from the top of the reactor or use a vortexing mode for an upper impeller to incorporate the gas from the surface. 

The sharpness of separation of the mineral from the gangue is dependent on (1) the stability of the suspension, which is influenced by the size of the medium (2) the specific gravity of the medium (3) the cleanliness of the medium (4) the cone angle (5) the size and ratios of the internal openings in the cyclone (inlet, apex, and vortex) and (6) the pressure at which the pulp is introduced into the cyclone. A 20° cone angle is the most common. Cyclone diameter will be determined by the separation to be made as well as by the capacity required. The 0.5- and 0.6-m (20- and 24-in) cyclones are most common in coal plants, whereas multiple cones of 0.25- or 0.3-m (10- or 12-in) diameter are used in higher-gravity separations. 

When the pressure relief device is set to open at greater than 15 psig (critical flow will result), it is normally not uecessaiy to be concerned about the pressure drop in the separator. If the hquid is to be drained from the separator during the emergency blowdown, a vortex breaker and false bottom should be used (Fig. 26-18, view BB). 

The nozzles, used to aeeelerate the flow toward the impeller tip, are usually straight vanes with no airfoil design. The vortex is a vaneless spaee and allows an equalization of the pressures. The flow enters the rotor radially at the tip with no appreeiable axial veloeity and exits the rotor through the exdueer axially with little radial veloeity. 

Cyclone Separators Cyclone separators are described in Chapter 7. Typically used to remove particulate from a gas stream, the gas enters tangentially at the top of a cylinder and is forced downward into a spiral motion. The particles exit the bottom while the gas turns upward into the vortex and leaves through the top of the unit. Pressure drops through cyclones are usually from 13 to 17 mm water gauge. Although seldom adequate by themselves, cyclone separators are often an effective first step in pollution control. 

A vertical cylindrical, and mechanical agitated pressure vessel, equipped with baffles to prevent vortex formation is the most widely used fermenter configuration. The baffles are typically one-tenth of the fermenter diameter in widtli, and are welded to supports tliat extend from the sidewall. A small space between the sidewall and the baffle enables cleaning. Internal heat transfer tube bundles can also be used as baffles. The vessels must withstand a 45 psig internal pressure and full vacuum of -14.7 psig, and comply with the ASME code. 

The T-connection in the original vortex exhaust will increase the pressure loss and increase the consumption of energy. Measurements of the pressure difference in the two versions show a sevenfold higher pressure difference in the original version (Fig. 12.396) compared with the pressure difference in the simplified version (Fig. 12.39c). This fact is very important in connection with selection of a given solution. 

As liquid flows out of the exit nozzle, it will swirl and create a vortex. Vortexing would carry the gas out with the liquid. Therefore, all liquid outlet nozzles should be equipped with a vortex breaker. Figure 12-0 shows several vortex breaker designs. Additional designs can be found in the Pressure Vessel Handbook. Most designs depend on baffles around or above the outlet to prevent swirling. 

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