Consider steady laminar flow in a network of 12 tubes forming a cube, driven by an effective pressure drop ?p = p(1) – p(8), where (1) is the (corner) inlet and (8) is the diagonally opposite outlet. (a) Find an expression for the mass flow rate m= m (?p; ?, , R, L) , where R and L are the same radius and length of each of the 12 tubes. (b) Convert this system to a simple flow-through porous media model by extracting Darcys velocity. Comment!
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