c02.qxd
5/25/2004
4:31 PM
Page 25
PRESSURE RELATIONSHIPS
25
Reynolds number (Re), which is computed as
ρ Re ⫽ VD ᎏµᎏ
(2.23)
where V ⫽ average velocity of the fluid ρ ⫽ density of the fluid µ ⫽ viscosity of the fluid D ⫽ diameter of the conduit If a consistent set of units is used (e.g., [ D ] ⫽ ft, [ V ] ⫽ ft/s, [ ] ⫽ lbm/ft3, and [ µ ] ⫽ lbm/ft-s), the Reynolds number is dimensionless. In general, if the Reynolds number for a given flow regime is less than 2000, the flow will probably be laminar. If Re is greater than 4000, the flow will be turbulent. When 2000 ⬍ Re ⬍ 4000, the type of flow is less predictable, depending on other factors, such as obstructions or directional changes in flow. Because the relationship between static pressure losses and velocity depends on the type of flow encountered, the derivation of a general formula requires one to know whether normal ventilation systems operate in the laminar or turbulent flow regions. To gain a better appreciation of the relationship between velocity and Reynolds number for air, Eq. 2.23 can be rearranged to
µ VD ⫽ Re ᎏρᎏ
(2.24)
The viscosity of air at standard conditions is 1.2 ⫻ 10⫺5 lbm/ft-s and the density is 0.075 lbm/ft3. Substituting these values into Eq. 2.24 yields (1.2 ⫻ 10⫺5 lbmⲐft-s) (60 sⲐmin) VD ⫽ ᎏᎏᎏᎏ Re 0.075 lbmⲐft3
冤
冥
(2.25)
⫽ 9.6 ⫻ 10⫺3 Re ft2Ⲑmin ⫽ 1.5 ⫻ 10⫺5 Re m2/s For air at standard conditions, turbulent flow will exist when 4000 ⬍ Re VD ⬍ ᎏ⫺ᎏ 9.6 ⫻ 10 3 ft2Ⲑmin or, VD ⬎ 40 ft2Ⲑmin (0.06 m2/s)
(2.26)
Thus any flow with a velocity–diameter product greater than 40 ft2/min (0.06 m2/s) would be turbulent. Because industrial ventilation systems typically operate at velocities greater than 1000 fpm (5 m/s) and duct diameters are usually at least 0.25 ft