34.1 CHAPTER 34 DUCT DESIGN BERNOULLI EQUATION ...................................................... 34.1 Head and Pressure .................................................................. 34.2 SYSTEM ANALYSIS ................................................................ 34.2 Pressure Changes in System ................................................... 34.6 FLUID RESISTANCE ............................................................. 34.7 Friction Losses ........................................................................ 34.7 Dynamic Losses ...................................................................... 34.8 Ductwork Sectional Losses ................................................... 34.12 FAN-SYSTEM INTERFACE ................................................. 34.12 DUCT SYSTEM DESIGN ...................................................... 34.14 Design Considerations .......................................................... 34.14 Duct Design Methods ............................................................ 34.18 HVAC Duct Design Procedures ............................................ 34.20 Industrial Exhaust System Duct Design ....................................................................... 34.22 FITTING LOSS COEFFICIENTS ......................................... 34.29 OMMERCIAL, industrial, and residential air duct system Cdesign must consider (1) space availability, (2) space air diffu- sion, (3) noise levels, (4) duct leakage, (5) duct heat gains and losses, (6) balancing, (7) fire and smoke control, (8) initial invest- ment cost, and (9) system operating cost. Deficiencies in duct design can result in systems that operate incorrectly or are expensive to own and operate. Poor air distribu- tion can cause discomfort, loss of productivity and even adverse health effects; lack of sound attenuators may permit objectionable noise levels. Poorly designed ductwork can result in unbalanced systems. Faulty duct construction or lack of duct sealing produces inadequate airflow rates at the terminals. Proper duct insulation eliminates the problem caused by excessive heat gain or loss. In this chapter, system design and the calculation of a system’s frictional and dynamic resistance to airflow are considered. Chap- ter 16 of the 2000 ASHRAE Handbook—Systems and Equipment examines duct construction and presents construction standards for residential, commercial, and industrial heating, ventilating, air- conditioning, and exhaust systems. BERNOULLI EQUATION The Bernoulli equation can be developed by equating the forces on an element of a stream tube in a frictionless fluid flow to the rate of momentum change. On integrating this relationship for steady flow, the following expression (Osborne 1966) results: (1) where v = streamline (local) velocity, m/s P = absolute pressure, Pa (N/m 2 ) ρ = density, kg/m 3 g = acceleration due to gravity, m/s 2 z = elevation, m Assuming constant fluid density within the system, Equation (1) reduces to (2) Although Equation (2) was derived for steady, ideal frictionless flow along a stream tube, it can be extended to analyze flow through ducts in real systems. In terms of pressure, the relationship for fluid resistance between two sections is (3) where V = average duct velocity, m/s Δp t,1-2 = total pressure loss due to friction and dynamic losses between sections 1 and 2, Pa In Equation (3), V (section average velocity) replaces v (streamline velocity) because experimentally determined loss coefficients allow for errors in calculating ρv 2 /2 (velocity pressure) across streamlines. On the left side of Equation (3), add and subtract p z1 ; on the right side, add and subtract p z2 , where p z1 and p z2 are the values of atmo- spheric air at heights z 1 and z 2 . Thus, (4) The atmospheric pressure at any elevation ( p z1 and p z2 ) expressed in terms of the atmospheric pressure p a at the same datum elevation is given by (5) (6) Substituting Equations (5) and (6) into Equation (4) and simpli- fying yields the total pressure change between sections 1 and 2. Assume no change in temperature between sections 1 and 2 (no heat exchanger within the section); therefore, ρ 1 = ρ 2 . When a heat exchanger is located within the section, the average of the inlet and outlet temperatures is generally used. Let ρ = ρ 1 = ρ 2 . (P 1 - p z1 ) and (P 2 - p z2 ) are gage pressures at elevations z 1 and z 2 . (7a) (7b) The preparation of this chapter is assigned to TC 5.2, Duct Design. v 2 2 ---- P d ρ ------ ∫ gz + + constant, N m ⋅ kg / = v 2 2 ---- P ρ --- gz + + constant, N m ⋅ kg / = ρ 1 V 1 2 2 ----------- P 1 g ρ 1 z 1 + + ρ 2 V 2 2 2 ----------- P 2 g ρ 2 z 2 p t 1-2 , Δ + + + = ρ 1 V 1 2 2 ----------- P 1 p z 1 p z 1 – ( ) g ρ 1 z 1 + + + ρ 2 V 2 2 2 ----------- P 2 + = p z 2 p z 2 – ( ) g ρ 2 z 2 p t 1-2 , Δ + + + p z 1 p a g ρ a z 1 – = p z 2 p a g ρ a z 2 – = p t 1-2 , Δ p s 1 , ρ V 1 2 2 --------- +       p s 2 , ρ V 2 2 2 --------- +       – = g ρ a ρ – ( ) z 2 z 1 – ( ) + p t 1-2 , Δ p t Δ p se Δ + =