Rectangular duct pressure drop calculator

Find the friction pressure drop of a rectangular duct from its width, height, length and flow, using the hydraulic diameter. 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, cross-checked in Verification Part N to within 0.5% of the reference. It captures the friction effect of the shape only, not shape-specific secondary or corner flows.

Inputs

• Duct width w (mm) and height h (mm), and the length L (m).
• Flow rate Q (L/s), the fluid, and the wall material roughness.

Outputs

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

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)
hf  = 0.410 m,   dp = 4.0 kPa

Frequently asked questions

What is the hydraulic diameter?

The hydraulic diameter D_h = 4A/P is the length scale that makes a non-circular duct behave like a round pipe for friction. For a rectangle it is 2wh/(w+h); for a square of side a it is a; for a circle of diameter D it is D.

Does this capture everything about a non-circular duct?

No. It captures the friction effect of the shape through the hydraulic diameter and the true area. It does not model the secondary and corner flows specific to a particular cross-section, which are second-order for pressure drop but real.

Can I use it for an oval or square duct?

A square is just a rectangle with equal sides. The Studio also handles oval (elliptical) ducts on the same hydraulic-diameter basis; open it for those.

Related

• Pipe flow and pressure drop calculator
• Orifice plate loss coefficient calculator
• How the elements are verified against NASA GFSSP.
• Open the Studio to size ducts and pipes together in a full network.