Flow Through an Assembly of Pipes and Its Permeability

Consider the viscous flow through an assembly of pipes with an overall square cross section of side length D and an overall longitudinal length L (Fig. 5.7). The diameter of a single pipe is d, and for simplicity we ignore the thickness of the pipe wall. The boundary surface of each pipe is impervious. It should be noted that the porosity n = 1 - njA of the section is the same for any size of pipes. 

If the number of pipes is A = (D/df, and a flux through one pipe is given by (5.72), the total flux through this pipe assembly is 

From the above equation a hydraulic conductivity k of this system can be defined as 

3 Flow in a Tank Filled with Solid Particles and Its Permeability 

Consider the seepage flow problem in a tank that is Ailed with solid particles as shown in Fig. 5.9. The total volume of this tank is V and the volume of the voids is Fy, so that the porosity is n = V /V. The mass flow velocity V = Q/p is given by the flux Q. The total surface area of solid particles is Sp, and the surface area per unit volume of one particle is (if the particle is a sphere of diameter dp = 2r, Sy = Anr pj(AnTapi S) = ( ldp). Then the surface area per unit volume Sy of the total solid particles is calculated as 5 = vCl — ). 

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