Where does the friction rate come from?

From your design — the pressure your blower has left for the ductwork, spread over the longest run (a Manual D worksheet does exactly that), or the figure on the job’s drawings. This page does not pick one: a friction rate is a design decision, and it changes with the equipment. Type yours and the page finds the duct that loses exactly that.

Velocity or friction — which should I size by?

Residential trunks and branches are usually sized by friction rate, then checked for velocity so the duct is not noisy. Some specs set a maximum velocity instead. The page does either and shows the other number at the size you would actually buy, so you can check both against your design.

How does it work out the friction?

The Darcy–Weisbach equation with the Colebrook friction factor, for standard air (1.204 kg/m³, 0.075 lb/ft³ — the density the paper friction charts and duct slide rules are drawn for) and the duct roughness you type. It matches a duct calculator slide rule within the width of its hairline: 1,000 cfm at 0.10 in. w.c. per 100 ft comes out 13.7 in at about 980 fpm.

What roughness should I type?

Galvanized steel duct is about 0.0003 ft (0.09 mm), which is where the page starts. Flex duct, duct board and lined duct are rougher — use the maker’s figure. A rougher duct needs a bigger size for the same friction, and the page shows how much.

How is the rectangular size worked out?

With Huebscher’s equal-friction formula, D = 1.30 × (a·b)^0.625 ÷ (a + b)^0.25: type one side and the page finds the other side that gives the same friction as the round size. The velocity in the rectangle is lower than in the round, because the rectangle has more area for the same friction.

Duct size calculator

Airflow

cfm

For the section you are sizing — the duct CFM calculator works it out.

Size by

Design friction rate, per 100 ft

in. w.c.

From your duct design or drawings — the page has none.

Duct comes in steps of

The page rounds up to the next size you can buy.

No design figure handy?

Rectangular duct & roughness (optional)

One side of a rectangular duct

The depth you have room for; the page finds the width.

Duct roughness

Galvanized steel is about 0.0003 ft (0.09 mm). Flex and duct board are rougher — use the maker’s figure.

— round

Standard air, 20 °C. Friction by Darcy–Weisbach at the roughness above.

Keep these results

We send this one email through our mail provider and don't keep your address.

Physics on your figures. The friction rate, velocity limits, duct materials and how the system is balanced come from your design, your equipment’s data and your local rules — this page does not choose any of them.

Type the airflow and the friction rate (or velocity) from your design. The page finds the exact round size, rounds it up to one you can buy, and shows the velocity and friction at that size; open the fold for the rectangular duct of equal friction and for a rougher duct material.

Worked example

A 400 cfm run designed at 0.10 in. w.c. per 100 ft in galvanized: the exact round is 9.69 in (781 fpm in it), so buy a 10 in round — at 400 cfm it runs 733 fpm and 0.086 in. per 100 ft, under the design rate. No room for a 10 in round? With an 8 in depth the equal-friction rectangle is 8 × 10.5, so 8 × 11, at 655 fpm.

Sized by velocity instead, at 700 fpm: 400 ÷ 700 = 0.571 ft², √(4 × 0.571 ÷ π) = 0.853 ft = 10.24 in, so an 11 in round — 606 fpm and 0.054 in. per 100 ft.

In metric: 190 L/s at 0.8 Pa/m is 248 mm exact, so a 250 mm round at 3.87 m/s and 0.76 Pa/m. With a 200 mm depth the rectangle is 200 × 263, so 200 × 275 in 25 mm steps.

Try one

Quick referencefor duct sizing

Velocity: flow ÷ area · cfm ÷ ft² = fpm · (L/s ÷ 1000) ÷ m² = m/s
Round area: π ÷ 4 × d² · 6 in 0.196 ft² · 8 in 0.349 · 10 in 0.545 · 12 in 0.785
Diameter: √(4 × flow ÷ (π × velocity))
Rectangle: D = 1.30 × (a·b)^0.625 ÷ (a + b)^0.25 — equal friction
Units: 1 in. w.c. = 249.1 Pa · per 100 ft → Pa/m: × 8.172 · 1 cfm = 0.4719 L/s · 1 m/s = 196.9 fpm

The formula

d = √(4Q ÷ πV) · Δp/L = f ÷ d × ρV²/2 · 1/√f = −2 log(ε/3.7d + 2.51/(Re√f))

Questions

Where does the friction rate come from?: From your design — the pressure your blower has left for the ductwork, spread over the longest run (a Manual D worksheet does exactly that), or the figure on the job’s drawings. This page does not pick one: a friction rate is a design decision, and it changes with the equipment. Type yours and the page finds the duct that loses exactly that.
Velocity or friction — which should I size by?: Residential trunks and branches are usually sized by friction rate, then checked for velocity so the duct is not noisy. Some specs set a maximum velocity instead. The page does either and shows the other number at the size you would actually buy, so you can check both against your design.
How does it work out the friction?: The Darcy–Weisbach equation with the Colebrook friction factor, for standard air (1.204 kg/m³, 0.075 lb/ft³ — the density the paper friction charts and duct slide rules are drawn for) and the duct roughness you type. It matches a duct calculator slide rule within the width of its hairline: 1,000 cfm at 0.10 in. w.c. per 100 ft comes out 13.7 in at about 980 fpm.
What roughness should I type?: Galvanized steel duct is about 0.0003 ft (0.09 mm), which is where the page starts. Flex duct, duct board and lined duct are rougher — use the maker’s figure. A rougher duct needs a bigger size for the same friction, and the page shows how much.
How is the rectangular size worked out?: With Huebscher’s equal-friction formula, D = 1.30 × (a·b)^0.625 ÷ (a + b)^0.25: type one side and the page finds the other side that gives the same friction as the round size. The velocity in the rectangle is lower than in the round, because the rectangle has more area for the same friction.

Related tools

Spot something wrong on this page? Report it

Thanks — your report was sent.

That didn’t send. Please try again later.