Equivalent Diameter

Convert rectangular and oval duct geometry to a equivalent circular diameter - online calculator with imperial and SI-units

The equivalent diameter is the diameter of a circular duct or pipe that gives the same pressure loss or resistance as an equivalent rectangular duct or pipe.

The equivalent diameter of a rectangular tube or duct can be calculated as (Huebscher)

de = 1.30 (a b)0.625 / (a + b)0.25                         (1)

where

de = equivalent diameter (mm, inches)

a = length of major or minor side (mm, inches)

b = length of minor or major side (mm, inches)

Example - Equivalent Diameter

The equivalent diameter of a 300 mm x 500 mm rectangular duct can be calculated as

de = 1.30 ((300 mm) (500 mm))0.625 / ((300 mm) + (500 mm))0.25

= 420 mm

Rectangular to Equivalent Circular Duct Calculator

The calculator below is based on formula (1). The formula is generic and any unit can be used.

Length side a - (mm, inches)

Length side - b - (mm, inches)

Equivalent diameters for some common mm rectangular duct dimensions:

Circular equivalent diameter - de (mm)
Duct
side
- a -
(mm)
Duct side - b (mm)
100 150 200 250 300 400 500 600 800 1000 1200 1400 1600 1800 2000
100 109 133 152 168 183 207 227
150 133 164 189 210 229 261 287 310
200 152 189 219 244 266 305 337 365
250 168 210 246 273 299 343 381 414 470
300 183 229 266 299 328 378 420 457 520 574
400 207 260 305 343 378 437 488 531 609 674 731
500 227 287 337 381 420 488 547 598 687 762 827 886
600 310 365 414 457 531 598 656 755 840 914 980 1041
800 414 470 520 609 687 755 875 976 1066 1146 1219 1286
1000 517 574 674 762 840 976 1093 1196 1289 1373 1451 1523
1200 620 731 827 914 1066 1196 1312 1416 1511 1598 1680
1400 781 886 980 1146 1289 1416 1530 1635 1732 1822
1600 939 1041 1219 1373 1511 1635 1749 1854 1952
1800 1096 1286 1451 1598 1732 1854 1968 2073
2000 1523 1680 1822 1952 2073 2186

Equivalent diameters of some common inches rectangular ducts:

Circular equivalent diameter (inches)
Length
- b -
(inches)
Length - a - (inches)
4 5 6 8 10 12 16
4 4.4 4.9 5.3 6.1
5 4.9 5.5 6 6.9 7.6
6 5.3 6 6.6 7.6 8.4 9.1
8 6.1 6.9 7.6 8.6 9.8 10.7 12.2
10 7.6 8.4 9.8 10.9 12 13.7
12 9.1 10.7 12 13.1 15.1
16 12.2 13.7 15.1 17.5

Oval Equivalent Diameter (Ellipse)

The equivalent diameter of a oval duct or tube (ellipse) can be calculated as (Heyt & Diaz)

de = 1.55 A0.625 / P0.25                           (2)

where

A = cross-sectional area oval duct (m2, in2)

P = perimeter oval duct (m, inches)

The cross-sectional area of an oval duct can be expressed as

A = π a b / 4

where

a = major dimension of the flat oval duct (m, in)

b = minor dimension of the flat oval duct (m, in)

The perimeter of an oval duct (ellipse) can be approximated to

P ≈ 2 π (1/2 ((a / 2)2 + (b / 2)2))1/2                          (2b)

Oblong Ducts

Equivalent diameters of oblong ducts or pipes can be expressed as

de = 1.55 (π b2 / 4 + a b - b2)0.625/(π b + 2 a - 2 b)0.25                              (3)

Hydraulic Diameter

Note! - equivalent diameter is not the same as hydraulic diameter. The hydraulic diameter express the rate between the area section of the duct or tube, and the wetted perimeter of the duct or tube. Hydraulic diameter is used to determine if the flow is laminar or turbulent and to calculate the pressure loss.

Related Topics

• Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time
• Ventilation - Systems for ventilation and air handling - air change rates, ducts and pressure drops, charts and diagrams and more

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