Hydraulic Diameter Calculator Formula
Understand the math behind the hydraulic diameter calculator. Each variable explained with a worked example.
Formulas Used
Hydraulic Diameter
hyd_dia = 4 * (width_a * height_b) / (2 * (width_a + height_b))Cross-Sectional Area
area = width_a * height_bWetted Perimeter
perimeter = 2 * (width_a + height_b)Variables
| Variable | Description | Default |
|---|---|---|
width_a | Duct Width (a)(mm) | 400 |
height_b | Duct 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.
- 01Area = 400 x 300 = 120,000 mm^2
- 02Perimeter = 2 x (400 + 300) = 1,400 mm
- 03D_h = 4 x 120,000 / 1,400 = 342.9 mm
Frequently Asked Questions
Why not just use the average of width and height?
The hydraulic diameter accounts for the relationship between flow area and wall friction area (wetted perimeter). A simple average would not correctly represent the friction behaviour.
What is hydraulic diameter for a square duct?
For a square duct with side s, D_h = 4s^2 / (4s) = s. The hydraulic diameter equals the side length.
When is hydraulic diameter used?
Use it for computing Reynolds number, friction factor, and head loss in non-circular conduits: HVAC ducts, open channels, annular spaces, and non-standard piping cross-sections.
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