A hollow-fiber module has 4,000 ft² of membrane surface area based on the size of the fibers, which are 42 mm i.d. x 85 mm o.d. x1.2 m long each. Determine the: 

(a) Number of hollow fibers in the module; 

(b) Diameter of the module, assuming the fibers are on a square spacing of 120 mm center-to-center; and 

(c) membrane surface area per unit volume of module (packing density) m²/m³. Compare your result with that in Table 14.4.

Table 14.4 Typical Characteristics of Membrane Modules Plate-and-Frame 30 to 500 Good Good Spiral-Wound 200 to 800 Moderate Fair Low D, RO, GP, UF, MF Tubular 30 to 200 Very good Packing density, m/m Resistance to fouling Ease of cleaning Relative cost High Main applications D, RO, PV, UF, MF Note: D, dialysis; RO, reverse osmosis; GP, gas permeation; PV, pervaporation; UF, ultrafiltration; MF, microfiltration. Excellent High RO, UF Hollow-Fiber 500 to 9,000 Poor Poor Low D, RO, GP, UF