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138 2 Mass transfer Table 2.2 Friction factor f Reynolds number Re ˆ vdH=ν Re 2500 Laminar 96/Re 2500 Re 3500 Critical 0:038…3500 Re† ‡ f T;Reˆ2500…Re 2500† Re> 3500 Turbulent fT Re≫3500 Stable turbulent fT=Cte, single function of roughness differential: Kxa ˆ a ΔPa … †b1 Flow Friction factor f 1000 where a is the air permeance coefficient for a 1 Pa pressure differential and b the air permeance exponent. For laminar flow, b is 1, for turbulent flow 0.5, and for transition flow 0.5 to 1. Most air permeances are only quantifiable by experiment. For joints, leaks, cavities and openings with known geometry, using hydraulics helps. The pressure losses are first of all frictional: ΔPa ˆ f L dH ρav2 2 0:42f L dH g2a (2.18) with f the friction factor, dH the hydraulic diameter of the section, L its length and v the average transfer velocity. Bends, widenings, narrowings, entrances and exits add local losses: ΔPa ˆ ξ ρav2 2 0:42 ξ g2a (2.19) with ξ the local loss factor. Values for the friction factor are given in Table 2.2. Table 2.3 collects some local loss factors. In the Reynolds number Re, v is the average flow velocity, ν the kinematic viscosity and dH the hydraulic diameter, for a circular section the diameter of the circle; for a rectangular section, dHˆ 2ab=…a ‡ b† where a and b are its sides, and for a cavity, dH=2b, where b is its width. The Reynolds number can be written as 56 000 ga dH, with ga the air flux. The turbulent friction factor f is given by: f T 2 ˆ 2 log 4:793 log 10 Re ‡ 0:2 ε Re ‡ 0:2698 ε where ε is the relative roughness (see Figure 2.5). Calculation of the air permeances stems from continuity, stating that in each section the same flow must pass. Total pressure loss, the sum of the frictional and local


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