Pressure Drop in a Filter

The flow pattern in a filter is complex as a result of the intricate structure of the fiber, which is further complicated by the particle deposition. Consequently, the pressure 

Assume that the fibers in a filter are cylindrical they are parallel to each other and are uniformly assembled. Consider cake filtration in which particles are collected with the deposited particles forming a layer of porous structure as shown in Fig. 7.13(a). Thus, to account for the total pressure drop, three basic flow modes are pertinent (1) flow is parallel to the axis of fibers (2) flow is perpendicular to the axis of the cylinder and (3) flow passes through a layer of a homogeneous porous medium. In the analysis of the first two modes given later, Happel s model [Happel, 1959] is used, while for the third mode, Ergun s approach [Ergun, 1952] is used. 

consider the case where the flow is parallel to the cylinders. It is assumed that the fluid is moving through the annular space between the cylinder of radius a and the fluid envelope of equivalent radius b, as shown in Fig. 7.14. Assume that the fluid motion is in the creeping flow regime so that inertia terms can be omitted from the Navier-Stokes equations. Thus, in cylindrical coordinates, we have 

The axial fluid velocity inside the annular space is obtained as 

The fluid flow rate through the entire annulus is given by 

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