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Mechanical Engineering2D

Hydraulic Diameter Calculator

Calculate hydraulic diameter for non-circular ducts and pipes used in Reynolds number and pressure drop.

Inputs
Enter your values below
Result
Hydraulic Diameter
—
Enter values and click Calculate
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Formula
4 × (width × height) ÷ (2 × (width + height)) × 1000
Result unit: mm

Dh = 4A/P. For rectangular duct: A = W×H, P = 2(W+H). ×1000 converts m to mm.

Introduction

Hydraulic diameter (Dh = 4A/P) allows using pipe flow equations (Reynolds number, Darcy-Weisbach) for non-circular ducts. For a circular pipe, Dh equals the actual inner diameter.

How This Calculator Works

Dh = 4A/P. For rectangular duct: A = W×H, P = 2(W+H). ×1000 converts m to mm.

Step-by-step process:

  1. Enter your input values in the calculator above
  2. The engine converts all inputs to SI base units (meters, kg, Pa)
  3. The formula is evaluated: 4 * (width * height) / (2 * (width + height)) * 1000
  4. Result is formatted with the appropriate unit and precision

Calculation Example

400×200mm rectangular duct: Dh = 267mm, allowing pipe flow equations to be used.

Inputs: width=400, height=200
Result: 266.7 mm

Unit Conversion for Hydraulic Diameter

**Length units**

- 1 m = 1000 mm = 3.28084 ft

- 1 inch = 25.4 mm

**Area units**

- 1 m² = 10.764 ft²

- 1 mm² = 1×10⁻⁶ m²

**Perimeter units**

- Same length unit as the diameter result

D_h = 4A/P is dimensionally consistent: if area is in m² and wetted perimeter in m, D_h is in m. Convert all inputs to the same unit system before computing.

Engineering Applications

  • •HVAC duct design
  • •Shell-and-tube exchangers
  • •Rectangular channels
  • •Annular flow

Frequently Asked Questions

Why use hydraulic diameter?

Dh lets engineers apply circular pipe correlations (Re, f, Nu) to non-circular geometries like rectangular ducts and annuli.

What about annular flow?

For an annulus between outer diameter D_o and inner D_i: Dh = D_o − D_i. This calculator handles rectangular ducts.

What units should I use for hydraulic diameter?

Any consistent length unit works because D_h = 4A/P is a ratio of area to perimeter. Use m with m² and m, or mm with mm² and mm — the result is in the same length unit as the inputs.

Related Calculators

Reynolds Number CalculatorDarcy-Weisbach Pressure Drop CalculatorPipe Flow CalculatorFlow Rate CalculatorPipe Velocity CalculatorPipe Diameter CalculatorPipe Volume CalculatorWater Velocity CalculatorPressure Drop Calculator (Darcy-Weisbach)Friction Loss CalculatorHead Loss CalculatorPressure Loss CalculatorNPSH Calculator - Net Positive Suction HeadOrifice Plate Flow CalculatorFlow Unit Conversion Calculator

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Engineering Disclaimer: Calculations are for reference and educational purposes only. Always verify results independently for engineering design. See full disclaimer.
Reviewed by: Industrial Engineering Team
References: ASME B31.3, ASTM A36, Perry's Chemical Engineers' Handbook