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The Hydraulic Diameter Calculator determines the hydraulic diameter for non-circular conduits and ducts, a key parameter for applying pipe-flow equations (Reynolds number, Darcy-Weisbach, Nusselt correlations) to non-circular geometries. The hydraulic diameter is defined as: $$D_h = \frac{4A}{P}$$ where A is the cross-sectional flow area and P is the wetted perimeter.
For a circular pipe, D_h reduces to the actual diameter D. For non-circular shapes, D_h provides an equivalent circular dimension that preserves the area-to-perimeter ratio. This calculator supports four modes: custom (enter A and P directly), rectangular duct, annular (concentric pipes), and circular pipe (verification).
The hydraulic diameter is essential in HVAC engineering (rectangular and oval ductwork), heat exchanger design (annular passages, plate channels), process piping (non-standard cross-sections), and microfluidics. It allows engineers to use the vast body of circular-pipe correlations for any geometry by substituting D_h for D in the Reynolds number, friction factor, and heat transfer calculations.
The general definition is: $$D_h = \frac{4A}{P}$$
Rectangular duct (width a, height b): $$D_h = \frac{4ab}{2(a+b)} = \frac{2ab}{a+b}$$ For a square duct (a = b): D_h = a.
Annular passage (outer diameter D_o, inner diameter D_i): $$A = \frac{\pi}{4}(D_o^2 - D_i^2), \quad P = \pi(D_o + D_i)$$ $$D_h = D_o - D_i$$
Circular pipe (diameter D): $$D_h = \frac{4 \cdot \pi D^2/4}{\pi D} = D$$
The factor of 4 in the definition ensures that D_h equals the actual diameter for a circular pipe, making it a natural generalization. The hydraulic diameter is then used in: $$Re = \frac{\rho v D_h}{\mu}, \quad h_f = f \frac{L}{D_h} \frac{v^2}{2g}$$
The hydraulic diameter indicates how efficiently a cross-section transports fluid relative to its boundary friction. A circular pipe has the maximum D_h for a given perimeter (most efficient). Flat rectangular ducts with high aspect ratios have low D_h values, meaning more friction per unit of flow area. For annular passages, D_h = D_outer − D_inner, so a thin annular gap has a very small hydraulic diameter and correspondingly high friction losses.
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A 600 × 300 mm rectangular duct has Dh = 2(0.6)(0.3)/(0.6+0.3) = 0.40 m. This equivalent diameter is used for duct sizing and fan selection.
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An annular passage with 100 mm outer and 60 mm inner diameter: Dh = 100 − 60 = 40 mm. The small Dh indicates relatively high friction in the narrow annulus.
The hydraulic diameter Dh = 4A/P is a generalized characteristic length for non-circular conduits. It allows circular-pipe correlations for friction factor, Reynolds number, and heat transfer to be applied to any cross-section shape by replacing the pipe diameter D with Dh.
The factor of 4 ensures that Dh equals the actual diameter D for a circular pipe: Dh = 4(πD²/4)/(πD) = D. This makes the hydraulic diameter a natural extension of the diameter concept to non-circular geometries.
No. The hydraulic radius is Rh = A/P (used mainly in open-channel flow), while the hydraulic diameter is Dh = 4A/P = 4Rh. They are simply related by a factor of 4. Open-channel formulas typically use Rh; pressurized-flow formulas use Dh.
For turbulent flow, the Dh concept works well (within ~5–15% accuracy for friction factor) for most shapes except very elongated ones (aspect ratio > 8:1). For laminar flow, shape-specific friction factors should be used because the actual velocity profile depends strongly on geometry.
For a square duct with side length a: Dh = 4a²/(4a) = a. The hydraulic diameter equals the side length, which is about 13% larger than the diameter of an equal-area circle (D = a√(4/π) ≈ 1.128a).
Yes. Nusselt number correlations developed for circular pipes (e.g., Dittus-Boelter, Gnielinski) can be used for non-circular geometries by substituting Dh for D. Accuracy is generally good for turbulent flow but less reliable for laminar flow in highly non-circular cross-sections.
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