Stream surfaces, volume flow rate

From the definition of the axisymmetric stream function and elementary continuity considerations, the volume flow rate between any two stream surfaces is simply IttA I. It follows that the mass flux of particles intercepted by the spherical collector is... 

By its physical meaning, the difference 2n y/- - y/2) is equal to the volume flow rate of liquid between two stream surfaces y/ = y/i and y/ = y/2. If the particles distribution far from the sphere is homogeneous, with mass concentration / q, the mass flux of the particles to the sphere is equal to... 

Cf, C y, and Cq are the concentrations of the substance in question (which may be a colligend or a surfactant) in the feed stream, bottoms stream, and foamate (collapsed foam) respectively. G, F, and Q are the volumetric flow rates of gas, feed, and foamate respectively, is the surface excess in equilibrium with C y. S is the surface-to-volume ratio for a bubble. For a spherical bubble, S = 6/d, where d is the bubble diameter. For variation in bubble sizes, d should be taken as YLnid fLnidj, where n is the number of bubbles with diameter dj in a representative region of foam. 

When bubbles burst at the surface of the fluidized bed, solid material carried along in their wake is ejected into the freeboard space above the bed. The solids are classified in the freeboard particles whose settling velocity ut is greater than the gas velocity fall back into the bed, whereas particles with u < u are elutriated by the gas stream. As a result, both the volume concentration of solids cy and the mass flow rate of entrained solids in the freeboard show a characteristic exponential decay... 

The region of space identified for analysis of open systems is called a control volume it is separated from its surroundings by a control surface. The fluid witliin the control volume is the themiodynamic system for wliich mass and energy balances are written. The control volume shown schematically in Fig. 2.5 is separated from its surroundings by an extensible control surface. Two streams with flow rates rh i and m2 are shown directed into the control volume, and one stream with flow rate m3 is directed out. Since mass is conserved, the rate of change of mass witliin the control volume, dm ldt, equals the net rate of flow of mass into the control volume. Tire convention is that flow is positive when directed into the control volume and negative when directed out. Tire mass balance is expressed mathematically by ... 

The next column parameters were imposed as follows feed specification liquid at bubble point feed flow rate 0.0053 kmol s" side stream flow rate 0.001455 kmol s" type of condenser total condenser pressure 760 mm Hg reflux ratio 3 type of reboiler total reboiler heat duty 417 kW bottom liquid volume 0.146 m tray surface (for top and bottom sections) 0.451 m tray surface (for right and left side of the dividing wall) 0.2255 m weir height 0.025 m hole diameter 0.002 m. 

According to the above equations, we can estimate the performance of a particle bed cathode that treats a 667 ppm (667 mg/1) Cu aqueous waste stream and generates a product effluent containing 1 ppm Cu, as was done in [125]. The cathode bed particles in the reactor are assumed to have a surface area/volume ratio of 25 cm" with a bed porosity of 0.3. The reactor operates with a superficial solution velocity of 0.0036 cm/sec and a 0.2 V potential variation in the cathode bed, i.e., the front face potential of the cathode is 0.2 V more negative (more cathodic) than the back of the bed. For these conditions, the cathode bed thickness should be 5.0 cm. The length and width of the bed are determined by the volumetric feed flow rate into the reactor, hence, the flow... 

The interfacial surface area per unit volume, a, in many types of packing materials used in industrial towers is virtually impossible to measure. Both a and the mass-transfer coefficient depend on the physical geometry of the equipment and on the flow rates of the two contacting, immiscible streams. Accordingly, they are normally correlated together as the volumetric mass-transfer coefficient, kca. 

Activity tests - A detailed description of the two apparatuses has been reported elsewhere [7], Experiments were carried out in the presence of steam and SO2 at varying temperature in the range 300-390°C, that is under realistic conditions of power plant flue gas treatment. In DeNOx tests the feed stream consisted of 500 ppm NO, 550 ppm T 3, 500 ppm SO2, 10% by volume H2O and 2% by volume O2 in N2. The SO2 oxidation activity was measured in a dedicated apparatus wherein 1000 ppm SO2, 10% H2O, 2% O2 were fed in a N2 stream. Total flow rates were such that the resulting values of Area Velocity, AV (the ratio between the volumetric flow rate and the geometric surface of the monolith), equaled 33 or 10 mNTP/h (NTP = 273K and 1 atm). 

The transient isotope-switching apparatus has been described previously. The reactor was a plug-flow, fixed-bed quartz microreactor, 8 mm in diameter, with a total volume of 0.8 cc. Approximately 0.4 g of catalyst was supported in the middle of the reactor on a fused quartz frit. Temperature in the catalyst bed was measured with a chromel-alumel thermocouple shielded in a quartz jacket. The reactant gas stream was controlled by a mass flow control switching system capable of switching one or more of the reactants to its isotopically labelled counterpart in approximately 1 s. The partial pressures and flow rates of the reactants are not altered by this switch so that the steady-state concentrations of reactants and products in the gas phase, and on the catalyst surface, are not disturbed. 

From the formula (20.8), it follows that the length at which absorption occurs becomes smaller with the increase of absorbent flow rate q and velocity U, and also with the reduction of pipe diameter d. An increase of the flow rate results in an increased volume concentration Wo of the absorbent, and hence in a larger phase contact surface area. Similarly, a velocity increase and reduction of the pipe diameter wUl reduce the size of drops in the gas stream, thus increasing the contact surface area. 

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