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A membrane consists of a rigid disk of ? = 10 µm thick polycarbonate with 108 identical cylindrical pores, each with ? = 30 nm diameter. The pores pass through the entire membrane thickness normal to the membrane surface. Water (? = 1000 kg/m3 , ? = 10−3 Pa∙s) is forced through the membrane by applying a pressure of 10 atm (absolute) upstream, with 1 atm (absolute) pressure downstream. The pores are sufficiently spaced that flow through each pore is independent of that through all other pores. Furthermore, the pores are sufficiently large that continuum fluid mechanics remains valid. (a) Neglecting minor losses, what is the volume flow rate of water through the membrane? (b) Assuming the flow remains incompressible, what is the maximum pressure difference across the membrane at which the flow would be laminar?