Hydraulic Diameter Calculator Formula

Understand the math behind the hydraulic diameter calculator. Each variable explained with a worked example.

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Formulas Used

Hydraulic Diameter

hyd_dia = 4 * (width_a * height_b) / (2 * (width_a + height_b))

Cross-Sectional Area

area = width_a * height_b

Wetted Perimeter

perimeter = 2 * (width_a + height_b)

Variables

VariableDescriptionDefault
width_aDuct Width (a)(mm)400
height_bDuct Height (b)(mm)300

How It Works

Hydraulic Diameter

The hydraulic diameter allows non-circular conduits to be analysed using the same formulas developed for circular pipes.

Formula

D_h = 4 A / P

where A is the cross-sectional flow area and P is the wetted perimeter. For a rectangular duct with sides a and b: D_h = 4ab / (2(a+b)) = 2ab / (a+b). For a circle, D_h equals the actual diameter.

Worked Example

A rectangular HVAC duct 400 mm wide and 300 mm tall.

width_a = 400height_b = 300
  1. 01Area = 400 x 300 = 120,000 mm^2
  2. 02Perimeter = 2 x (400 + 300) = 1,400 mm
  3. 03D_h = 4 x 120,000 / 1,400 = 342.9 mm

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