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

Exam areas

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

p_s

is the pressure the air exerts on the duct walls — what a manometer tap flush with the wall reads. Velocity pressure

p_v

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

p_t

, 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.

p_t = p_s + p_v

Velocity pressure and the 4005 constant

Velocity pressure in inches of water is

p_v = \rho\,(V/1097)^2

with

V

in fpm and

\rho

\text{lbm/ft}^3

; the constant

1097

already buries the

1/2

and the unit conversion. For standard air (

\rho = 0.075\ \text{lbm/ft}^3

) this collapses to the form every examinee memorizes,

p_v = (V/4005)^2

, because

1097/\sqrt{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

\rho

form. Velocity itself comes from continuity,

V = Q/A

, with

Q

in cfm and

A

\text{ft}^2

p_v = \left(\dfrac{V}{4005}\right)^2 \quad(\text{standard air}), \qquad V = \dfrac{Q}{A}

The friction chart and the Darcy relation

Straight-duct loss is computed from the Darcy equation,

\Delta p_f = f\,(12L/D_h)\,p_v

, where

D_h

is in inches,

L

in feet, and the friction factor

f

comes from the Moody/Colebrook relation at the chart roughness

\varepsilon = 0.0003\ \text{ft}

(galvanized). You rarely evaluate this by hand on the exam: the handbook's Friction Chart for Round Duct plots it for

\rho = 0.075\ \text{lbm/ft}^3

, so you read friction rate (in. wg per 100 ft) directly from any two of airflow, velocity, and diameter. For example,

1000\ \text{cfm}

in a

12\text{-in.}

round duct runs at

1273\ \text{fpm}

and about

0.19\ \text{in. wg}/100\ \text{ft}

\Delta p_f = f\,\dfrac{12L}{D_h}\,p_v \qquad (\varepsilon = 0.0003\ \text{ft})

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

D_e

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

D_e

. 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.

D_e = 1.30\,\dfrac{(ab)^{0.625}}{(a+b)^{0.25}}

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

0.12\ \text{in. wg}/100\ \text{ft}

) 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

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.

\Delta p_{s,\text{regain}} = R\left(p_{v,1} - p_{v,2}\right)

Exam strategy

Anchor every duct problem with

V = Q/A

and

p_v = (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

D_e

before touching the chart, and remember

D_e

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 = \dfrac{Q}{A}

$V$ in fpm, $Q$ in cfm, $A$ in $\text{ft}^2$ . The first line of nearly every duct calculation.

Velocity pressure (general)

p_v = \rho\left(\dfrac{V}{1097}\right)^2

$p_v$ in in. wg, $V$ in fpm, $\rho$ in $\text{lbm/ft}^3$ . Use this form whenever air is non-standard (altitude, hot air).

Velocity pressure (standard air)

p_v = \left(\dfrac{V}{4005}\right)^2

Valid only at $\rho = 0.075\ \text{lbm/ft}^3$ ; $4005 = 1097/\sqrt{0.075}$ .

Total pressure

p_t = p_s + p_v

Total = static + velocity, all in in. wg. Fans and Bernoulli work in total pressure; friction consumes it.

Darcy friction loss

\Delta p_f = f\,\dfrac{12L}{D_h}\,p_v

$\Delta p_f$ in in. wg; $L$ in ft, $D_h$ in in., $f$ from Colebrook at $\varepsilon=0.0003\ \text{ft}$ . The friction chart evaluates this for you.

Hydraulic diameter

D_h = \dfrac{4A}{P}

For non-circular duct; $A$ = area, $P$ = wetted perimeter (consistent units). Used inside the Darcy relation.

Circular equivalent diameter

D_e = 1.30\,\dfrac{(ab)^{0.625}}{(a+b)^{0.25}}

Round diameter (in.) giving equal airflow, friction, and length to a rectangle of sides $a,b$ (in.). Equal friction, NOT equal area.

Equal-friction principle

\dfrac{\Delta p_f}{L} = \text{constant for every section}

Hold one friction rate (e.g. $0.10\ \text{in. wg}/100\ \text{ft}$ ); read each section's size from the chart at its airflow.

Static-regain recovery

\Delta p_{s,\text{regain}} = R\,(p_{v,1} - p_{v,2})

Static recovered as air slows; recovery factor $R\approx 0.5$ – $0.75$ . Set equal to downstream friction to keep static constant.

Local loss coefficient

C = \dfrac{\Delta p_t}{p_v}

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 $18\ \text{in.}$ in diameter carries $4{,}000\ \text{cfm}$ of standard air. A wall tap reads a static pressure of $1.20\ \text{in. wg}$ . Find the velocity, the velocity pressure, and the total pressure at that point.

Solution. Area:

A = \frac{\pi}{4}(1.5\ \text{ft})^2 = 1.767\ \text{ft}^2

. Velocity:

V = Q/A = 4000/1.767 = 2{,}264\ \text{fpm}

. Velocity pressure (standard air):

p_v = (2264/4005)^2 = 0.319\ \text{in. wg}

. Total pressure:

p_t = p_s + p_v = 1.20 + 0.319 = 1.52\ \text{in. wg}

. Sanity check:

2{,}264\ \text{fpm}

is a normal trunk velocity and a velocity pressure near

0.3\ \text{in. wg}

is typical for it; units are consistent (in. wg throughout). Final:

p_v = 0.319\ \text{in. wg}

p_t = 1.52\ \text{in. wg}

p_v = \left(\dfrac{2264}{4005}\right)^2 = 0.319\ \text{in. wg}

Round-to-rectangular conversion

Problem. The chart sizes a section as $20\text{-in.}$ round duct, but only $10\ \text{in.}$ of vertical space is available. Choose a rectangular duct $a \times 10\ \text{in.}$ that carries the same airflow at the same friction rate.

Solution. Require

D_e = 20\ \text{in.}

with

b = 10\ \text{in.}

. Solve

20 = 1.30\,(10a)^{0.625}/(a+10)^{0.25}

by trial. Try

a = 26\ \text{in.}

D_e = 1.30\,(260)^{0.625}/(36)^{0.25} = 1.30(32.3)/(2.449) = 17.2

— too small. Try

a = 34\ \text{in.}

D_e = 1.30\,(340)^{0.625}/(44)^{0.25} = 1.30(38.2)/2.576 = 19.3

— closer, still short. Try

a = 37\ \text{in.}

D_e = 1.30\,(370)^{0.625}/(47)^{0.25} = 1.30(40.3)/2.618 = 20.0

— match. So

a \approx 37\ \text{in.}

gives the equal-friction equivalent. Rounding up to the nearest standard size, a

38 \times 10\ \text{in.}

duct (

D_e = 20.2\ \text{in.}

) is the nearest conservative selection. Sanity check: the rectangle's area

370\ \text{in}^2

exceeds the round area

\frac{\pi}{4}(20)^2 = 314\ \text{in}^2

— expected, because a flat duct needs more metal for the same friction. Final: about

37 \times 10\ \text{in.}

(specify

38 \times 10\ \text{in.}

20 = 1.30\,\dfrac{(37\cdot 10)^{0.625}}{(37+10)^{0.25}}

Static regained as a trunk slows

Problem. In a static-regain trunk, velocity drops from $2{,}000\ \text{fpm}$ upstream of a takeoff to $1{,}400\ \text{fpm}$ downstream. Using a recovery factor $R = 0.75$ , how much static pressure is regained, and what friction loss can it offset?

Solution. Velocity pressures:

p_{v,1} = (2000/4005)^2 = 0.249\ \text{in. wg}

;

p_{v,2} = (1400/4005)^2 = 0.122\ \text{in. wg}

. Regained static:

\Delta p_{s} = R(p_{v,1}-p_{v,2}) = 0.75(0.249 - 0.122) = 0.75(0.127) = 0.0954\ \text{in. wg}

. The section length to the next takeoff is sized so its friction loss equals

0.0954\ \text{in. wg}

, keeping static pressure constant. Sanity check: only

75\%

of the

0.127\ \text{in. wg}

velocity-pressure change is recovered; the remaining

0.032\ \text{in. wg}

is the expansion loss. Final:

0.0954\ \text{in. wg}

regained.

\Delta p_{s} = 0.75\,(0.249 - 0.122) = 0.0954\ \text{in. wg}

Common pitfalls

•Using $p_v = (V/4005)^2$ for non-standard air. The $4005$ is hard-wired to $\rho = 0.075\ \text{lbm/ft}^3$ ; at altitude or in hot supply air, revert to $p_v = \rho(V/1097)^2$ or the answer is high by the density ratio.
•Treating the circular equivalent $D_e$ as the equal-AREA diameter. $D_e$ matches friction and airflow; a rectangle of equal $D_e$ always has MORE cross-sectional area than the round duct.
•Confusing static, velocity, and total pressure. Friction and fittings consume total pressure; a flush wall tap reads static. Forgetting to add $p_v$ understates total pressure (and fan pressure) at high velocity.
•Reading the friction chart with cfm but rectangular dimensions. Convert the rectangle to $D_e$ 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 $R\approx 0.5$ – $0.75$ 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.

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