Rectangular duct pressure drop calculator

This free rectangular duct pressure drop calculator finds the friction loss of a rectangular duct from its width, height, length and flow rate. It works for air as well as liquids (choose Custom under Fluid and enter the density and kinematic viscosity from the air properties table below), in metric or imperial units. Non-circular ducts do not have a single bore, so the friction is evaluated on the hydraulic diameter D_h = 4A/P and the true flow area, feeding the ordinary Darcy-Weisbach method.

Method

For a rectangular duct of width w and height h, the flow area and hydraulic diameter are:

A   = w h
P   = 2 (w + h)
D_h = 4 A / P = 2 w h / (w + h)

The mean velocity is V = Q / A, the Reynolds number is Re = V D_h / nu, and the Darcy friction factor comes from the Churchill correlation on Re and the relative roughness eps / D_h. The head loss is the standard Darcy-Weisbach expression on the hydraulic diameter:

hf = f (L / D_h) V^2 / (2 g),   dp = rho g hf

This is the same hydraulic-diameter path the Studio uses for non-circular ducts, and it is one of the element-reference cases on the verification page, where it agrees to within 0.5% of an independent closed-form calculation on the same hydraulic diameter. It captures the friction effect of the shape only, not shape-specific secondary or corner flows.

Inputs

• Duct width w and height h, and the length L.
• Flow rate Q, the fluid, and the wall roughness (a material preset or a Custom value).

Outputs

• Hydraulic diameter D_h and flow area A.
• Mean velocity, Reynolds number, flow regime and Darcy friction factor.
• Head loss and pressure drop.

Duct and pipe wall roughness

Standard ASHRAE Handbook - Fundamentals and Moody roughness classes. Pick the closest material in the Roughness (material) dropdown, or enter a Custom absolute roughness (for example about 3 mm for fully-extended flexible duct, and more when compressed).

Air properties for the Custom fluid fields

Dry air at 101.325 kPa, standard handbook values. Enter them in the Custom fluid fields (always in these SI units, on either unit system). Density falls with altitude and temperature, so correct it for site conditions. Treating duct air as incompressible is standard at normal duct velocities.

Hydraulic diameter of common rectangular duct sizes

Exact geometry from D_h = 2wh/(w+h) and A = wh, the same expressions the calculator evaluates. For a given area, the closer to square the section, the larger D_h and the lower the friction loss, which is why high aspect ratios cost pressure.

Recommended duct air velocities

Practice ranges aligned with the ASHRAE Handbook - Fundamentals duct design guidance: noise and fan energy set the limit, not the duct itself. Equal-friction designs commonly target 0.8 to 1.5 Pa per metre of straight run, so compare the calculator's pressure drop divided by length.

Worked example

A 200 x 100 mm duct carrying 50 L/s of water over 10 m:

A   = 0.2 x 0.1 = 0.020 m^2
D_h = 2 x 0.2 x 0.1 / (0.2 + 0.1) = 0.133 m
V   = 0.050 / 0.020 = 2.5 m/s
Re  = 2.5 x 0.133 / 1.0e-6 = 3.3e5  (turbulent)
f   = 0.0172   (Churchill, on eps/D_h = 3.4 x 10^-4)
hf  = 0.410 m,   dp = 4.0 kPa

These are the figures the calculator above returns for the same inputs, evaluated on the same Churchill correlation.

Frequently asked questions

Can I use this calculator for air ducts?

Yes. Choose Custom under Fluid and enter air's density and kinematic viscosity from the air properties table (1.204 kg/m3 and 1.51 x 10^-5 m2/s for 20 degree air). Darcy-Weisbach on the hydraulic diameter is the standard method for duct friction at normal HVAC velocities.

What is the hydraulic diameter of a rectangular duct?

D_h = 4A/P = 2wh/(w+h), the length scale that makes a non-circular duct behave like a round pipe for friction. The calculator reports it for your size, and the quick-reference table above lists it for common duct sizes.

Is the hydraulic diameter the same as the equivalent diameter?

No. The hydraulic diameter 2wh/(w+h) is the friction length scale, while the equal-area diameter and ASHRAE's equal-friction equivalent diameter are different quantities. This calculator uses D_h for friction and the true w x h area for velocity.

How accurate is the hydraulic-diameter method?

In turbulent flow it is the accepted engineering method, and this implementation is cross-checked on the verification page to within 0.5% of an independent closed-form calculation on the same hydraulic diameter. In laminar flow the true friction constant is shape-dependent (roughly f.Re 57 to 96 across rectangles against 64 for a circle), so treat laminar results as approximate.

What pressure drop should a duct run aim for?

Equal-friction practice for commercial air systems targets about 0.8 to 1.5 Pa per metre of straight run. Divide the calculator's pressure drop by the length to compare, and check the reported velocity against the recommended ranges for your application.

Can I use it for a square or oval duct?

A square duct is a rectangle with equal sides, so enter the side length as both width and height. Oval (flat-oval) ducts run on the same hydraulic-diameter basis in the Studio.

References

• ASHRAE, Handbook - Fundamentals, for the duct roughness classes, the equal-friction design targets and the recommended velocity ranges. ashrae.org
• Churchill, S. W. (1977), "Friction-factor equation spans all fluid-flow regimes", Chemical Engineering, Vol. 84, No. 24, pp. 91-92. The friction correlation evaluated here.
• Colebrook, C. F. (1939), Journal of the Institution of Civil Engineers, and Moody, L. F. (1944), Transactions of the ASME, for the underlying friction relationship. Colebrook, Moody
• Crane Co., Technical Paper No. 410: Flow of Fluids Through Valves, Fittings and Pipe, which also sets out the hydraulic-diameter treatment of non-circular sections. tp410.com

Related

• Darcy friction factor calculator
• Reynolds number calculator
• Pipe pressure drop calculator
• Fan and duct worked example and the compressed air system design guide
• Open the Studio to size ducts and pipes together in a full network.