Air Distribution & Ductwork · Study · PE Mechanical: HVAC and Refrigeration · FE → PE Prep
Air Distribution & Ductwork
6% of exam
Duct sizing and friction, equal-friction and static-regain methods, fan total/static pressure, terminal devices, diffusers, and VAV airflow.
5 concepts
A. Air Distribution Systems and Ductwork
Duct Sizing: Friction, Velocity Pressure, Equal-Friction and Static Regain
How the friction chart, velocity pressure (V/4005)², equivalent diameter, and the equal-friction and static-regain methods turn an airflow schedule into a sized, balanced duct system.
Duct sizing is where a cooling load becomes hardware. You know the airflow each space needs; the duct system has to deliver it at a pressure the fan can produce, quietly, and without one branch hogging the air while another starves. The PE Mechanical HVAC exam tests this directly — a handful of A-area questions reduce to reading the friction chart, converting velocity to velocity pressure, swapping a round size for a rectangular one, or splitting total pressure into static and velocity parts. The methods live in the PE Mechanical Reference Handbook — §9.3.6 Duct Design, which gives you the Bernoulli/total-pressure relations, the friction chart for round duct, and the round-to-rectangular equivalency. Everything in this concept is fluency with those few tools.
Total pressure is static plus velocity
Air in a duct carries two kinds of pressure. Static pressure ps
is the pressure the air exerts on the duct walls — what a manometer tap flush with the wall reads. Velocity pressure
pv
is the kinetic energy of the moving stream, the pressure you would recover if you brought the air to rest. Their sum is the total pressure
pt
, and it is total pressure — not static — that the fan must supply and that Bernoulli conserves between two points minus losses. Keeping these three straight is the single most useful habit in duct work: friction and fittings consume total pressure, while transitions trade static for velocity and back.
pt=ps+pv
Velocity pressure and the 4005 constant
Velocity pressure in inches of water is pv=ρ(V/1097)2 with V in fpm and ρ in lbm/ft3; the constant 1097 already buries the 1/2 and the unit conversion. For standard air (ρ=0.075lbm/ft3) this collapses to the form every examinee memorizes, pv=(V/4005)2, because 1097/0.075=4005. That single substitution — standard air — is exactly what makes 4005 valid; at altitude or in hot air you must go back to the ρ form. Velocity itself comes from continuity, V=Q/A, with Q in cfm and A in ft2.
pv=(4005V)2(standard air),V=AQ
The friction chart and the Darcy relation
Straight-duct loss is computed from the Darcy equation, Δpf=f(12L/Dh)pv, where Dh is in inches, L in feet, and the friction factor f comes from the Moody/Colebrook relation at the chart roughness ε=0.0003ft (galvanized). You rarely evaluate this by hand on the exam: the handbook's Friction Chart for Round Duct plots it for ρ=0.075lbm/ft3, so you read friction rate (in. wg per 100 ft) directly from any two of airflow, velocity, and diameter. For example, 1000cfm in a 12-in. round duct runs at 1273fpm and about 0.19in. wg/100ft.
Δpf=fDh12Lpv(ε=0.0003ft)
Round-to-rectangular equivalent diameter
Most chart work is in round duct, but real systems are often rectangular to fit above ceilings. The circular equivalent De is the round diameter that carries the same airflow at the same friction rate — NOT the same cross-sectional area. Size the round duct on the chart, then convert to a rectangle of equal De. A rectangle always needs more metal and more area than its round equivalent because its larger perimeter adds friction; flatter aspect ratios make this penalty worse, which is why designers keep aspect ratios below about 4:1.
De=1.30(a+b)0.25(ab)0.625
The equal-friction method
Equal-friction sizing — the workhorse for low- and medium-pressure supply and all return/exhaust — picks one friction rate (often 0.08 to 0.12in. wg/100ft) and sizes every section to it. Because airflow drops at each branch takeoff while the friction rate is held fixed, velocity automatically tapers from the fan toward the ends, which keeps noise down at the outlets. The name 'equal-friction' is an ASHRAE method applied on top of the handbook's §9.3.6 friction data — the chart gives the friction rate, the method tells you to hold it constant. Its weakness: it does nothing to balance branches of very different length, so short, low-resistance runs still need dampers, and the index (longest, highest-loss) run sets the fan pressure.
The static-regain method
On long high-velocity trunks, the static-regain method sizes each downstream section so that the static pressure regained as the air slows (velocity pressure converting back to static) just offsets the friction loss to the next takeoff. The result is nearly constant static pressure along the trunk, so every branch sees the same entering condition and self-balances. Only a fraction R (typically 0.5 to 0.75) of the velocity-pressure change is actually recovered — the rest is lost in the expansion. Regain trades fan energy and balancing labor for larger, costlier downstream duct.
Δps,regain=R(pv,1−pv,2)
Exam strategy
Anchor every duct problem with V=Q/A and pv=(V/4005)2, and write down whether a stated pressure is static, velocity, or total. For chart problems, fix two of {airflow, velocity, diameter, friction rate} and read the rest — do not try to back out f by hand. When a problem gives a rectangle, convert to De before touching the chart, and remember De matches friction, not area. If the method is named, equal-friction means 'same in. wg/100 ft everywhere,' and static-regain means 'recovered static cancels friction so static stays constant.' Default to standard air and sea level unless told otherwise.
Key equations
Continuity (duct velocity)V=AQ
V in fpm, Q in cfm, A in ft2. The first line of nearly every duct calculation.
Velocity pressure (general)pv=ρ(1097V)2
Velocity pressure (standard air)pv=(4005V)2
Total pressurept=ps+pv
Total = static + velocity, all in in. wg. Fans and Bernoulli work in total pressure; friction consumes it.
Equal-friction principleLΔpf=constant for every section
Hold one friction rate (e.g. 0.10in. wg/100ft
Static-regain recoveryΔps,regain=R(pv,1−pv,2)
Local loss coefficientC=pvΔpt
Dimensionless ratio of a fitting's total-pressure loss to the reference velocity pressure; ties duct loss to fittings (see the fittings concept).
Worked examples
Velocity pressure and total pressure in a trunk
Problem. A round supply trunk 18in. in diameter carries 4,000cfm of standard air. A wall tap reads a static pressure of 1.20in. wg. Find the velocity, the velocity pressure, and the total pressure at that point.
Solution. Area: A=4π(1.5ft)2=1.767ft2.
Velocity: V=Q/A=4000/1.767=2,264fpm.
Velocity pressure (standard air): pv=(2264/4005)2=0.319in. wg.
Total pressure: pt=ps+pv=1.20+0.319=1.52in. wg.
Sanity check: 2,264fpm is a normal trunk velocity and a velocity pressure near 0.3in. wg is typical for it; units are consistent (in. wg throughout). Final: pv=0.319in. wg, pt=1.52in. wg.
pv=(40052264)2=0.319in. wg
Round-to-rectangular conversion
Problem. The chart sizes a section as 20-in. round duct, but only 10in. of vertical space is available. Choose a rectangular duct a×10in. that carries the same airflow at the same friction rate.
Solution. Require De=20in.
Static regained as a trunk slows
Problem. In a static-regain trunk, velocity drops from 2,000fpm upstream of a takeoff to 1,400fpm downstream. Using a recovery factor R=0.75, how much static pressure is regained, and what friction loss can it offset?
Solution. Velocity pressures: pv,1=(2000/4005)2=0.249in. wg
Common pitfalls
•Using pv=(V/4005)2 for non-standard air. The 4005 is hard-wired to ρ=0.075lbm/ft3; at altitude or in hot supply air, revert to pv=ρ(V/1097)2 or the answer is high by the density ratio.
•Treating the circular equivalent De as the equal-AREA diameter. De matches friction and airflow; a rectangle of equal De
•Confusing static, velocity, and total pressure. Friction and fittings consume total pressure; a flush wall tap reads static. Forgetting to add pv understates total pressure (and fan pressure) at high velocity.
•Reading the friction chart with cfm but rectangular dimensions. Convert the rectangle to De first, then enter the round-duct chart.
•Assuming equal-friction self-balances. It only equalizes friction RATE; branches of unequal length still need balancing dampers, and the longest/highest-loss run sets fan pressure.
•Crediting 100% static regain. Only R≈0.5–0.75 of the velocity-pressure drop is recovered — the expansion loss is real and must stay in the total-pressure budget.
References
NCEES PE Mechanical Reference Handbook — §9.3.6 Duct Design
ASHRAE Handbook—Fundamentals, Ch. 21 Duct Design — Source of the friction chart, rectangular-equivalent table, and fitting loss coefficients.
ASHRAE Standard 90.1 — Energy Standard — Fan power and duct-leakage limits that constrain friction-rate selection.
Fan Total and Static Pressure and VAV Airflow
Fan total vs static pressure, the system pressure profile and external static pressure, fan power, and how a VAV box turns down airflow as the zone load falls.
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Diffusers, Throw and the Air Diffusion Performance Index (ADPI)
How throw, the T50/L ratio, drop and spread govern room air motion, and how ADPI and the characteristic room length let you select a diffuser for comfort.
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Terminal Devices and VAV Boxes (Single-Duct, Fan-Powered, Dual-Max)
Single-duct vs series and parallel fan-powered VAV boxes, minimum/maximum airflow setpoints, dual-maximum control, and how primary and secondary airflow mix.
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Duct Fittings, Dynamic Losses and System Effect
Fitting loss coefficients and dynamic pressure loss, equivalent length, system effect at the fan inlet and outlet, and how to add fitting losses to the straight-run friction.
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pv in in. wg, V in fpm, ρ in lbm/ft3. Use this form whenever air is non-standard (altitude, hot air).
Valid only at ρ=0.075lbm/ft3; 4005=1097/0.075.
Δpf in in. wg; L in ft, Dh in in., f from Colebrook at ε=0.0003ft. The friction chart evaluates this for you.
= wetted perimeter (consistent units). Used inside the Darcy relation.
Round diameter (in.) giving equal airflow, friction, and length to a rectangle of sides a,b (in.). Equal friction, NOT equal area.
); read each section's size from the chart at its airflow.
Static recovered as air slows; recovery factor R≈0.5–0.75. Set equal to downstream friction to keep static constant.