流体力学与 及传热课件Filtration Operations-Basic Equations.pptVIP

3.4.3 Filtration Operations-Basic Equations ;where Vm is the medium resistance, which is equal to;3.4.4 Constant pressure filtration ;Using equation (3.4-17 ) either t or V can be calculated from the value of the other variable. ;Substitution of K from equation (3.4-18 ) in equation (3.4-17 ) gives an equation for constant pressure filtration: ;Which gives a straight line if Δt/ΔV is plotted against V, shown in figure. The equation (3.4-20) and the figure are used to predict the filtration constants. ;3.4.5 Constant rate filtration ; Where V is simply ;A plot of Δp against t as in figure3.22, will, from equation (3.4-22), be a straight line. ;3.4.6 Constant rate followed by constant pressure operation ;As the cake becomes thicker and offers more resistance to the flow, the pressure developed by the pump becomes a limiting factor and the filtration proceeds at a nearly constant pressure.; For such a combined operation, the plot Δp versus time is as shown in figure3.23 . ; will be as shown in figure ;3.4.7 Vacuum Filtration-Drum Continuous Filtration ; The process consists of several steps in series —cake formation, washing, drying and discharging. The pressure drop across the filter during cake formation is, however, held constant. ;Automatic valve ; Thus the foregoing equations for discontinuous constant-pressure filtration may, with some modification, be applied to continuous filters. ; If t is the actual filtering time (i.e., the time any filter element is immersed in the slurry), then from Eq. (3.4-19) ;where V is the volume of filtrate collected during time t. Solving Eq. (3.4-23) for V, as a quadratic equation, gives; Where V is the volume of filtrate collected during time t that it is the actual filtration time. If the fraction of the drum submerged is φ, and drum speed is n ; Substituting t from Eq. (3.4-25) in Eq. (3.4-24) for the volume of filtrate;The capacity of drum filter Q in m3/s can be derived by equation (3.4-26) ;In continuous