流体力学与 及传热课件Flow Rate-Pressure Drop Relationships.pptVIP

3.4.2 Flow Rate-Pressure Drop Relationships ; As the pores in the medium are normally small and rate of flow of filtrate is low, laminar flow conditions are almost invariably obtained. ; So, the relationship between the superficial velocity u and the pressure drop can be described by Kozeny-Carman equation ; The linear velocity u is given by the equation ;Substituting u from Eq. (3.4-3 ) into Eq. (3.4-2 ) gives ; This equation relating the flow rate of a filtrate with viscosity μ through a bed of thickness L and face area A to the driving pressure Δp is called Darcy’s basic filtration equation. ;Equation (3.4-7) is often written in the form. ; Where R is called the resistance (and is equal to L/k, the thickness divided by the permeability of the bed) ;Filter medium resistance ; In practice, however, the assumption made above that the medium resistance is constant is rarely true because some penetration and blocking of the medium inevitably occurs when particles impinge on the medium ; As the resistance of the cake may be assumed to be directly proportional to the amount of cake deposited (only true for incompressible cakes) it follows that for a given filtration area A. ; Where L is the width of cake deposited and r is the specific cake resistance. Similarly for the filtration medium of width Lm;;The thickness of cake deposited and other parameters, some of which can , in certain circumstances, be assumed to be constant. ;1. Pressure drop The pressure drop Δp may be constant or variable with time depending on the characteristics of the pump used or on the driving force applied. ;2. Face area of the filter medium The face area of the medium A is usually constant, but with a few exceptions such as in the case of equipment with an appreciable cake build-up on a tubular medium or a rotary drum. ;3. Liquid viscosity The liquid viscosity μ is constant provided that the temperature remains constant during the filtration cycle and that the liquid is Newto