Equivalent Hydraulic Diameter

The hydraulic diameter - d_h - is used to calculate the dimensionless Reynolds Number to determine if a flow is turbulent or laminar. A flow is

• laminar if Re < 2300
• transient for 2300 < Re < 4000
• turbulent if Re > 4000

The hydraulic diameter is also used to calculate the pressure loss in a ducts or pipe.

The hydraulic diameter is not the same as the geometrical diameter in a non-circular duct or pipe and can be calculated with the generic equation

d_h = 4 A / p (1)

where

d_h = hydraulic diameter (m, ft)

A = area section of the duct (m², ft²)

p = wetted perimeter of the duct (m, ft)

Note! Inches are commonly used in the Imperial unit system.

Hydraulic Diameter of a Circular Tube or Duct

Based on equation (1) the hydraulic diameter of a circular duct can be expressed as:

d_h = 4 π r² / 2 π r

= 2 r (2)

where

r = pipe or duct radius (m, ft)

As we could expect the hydraulic diameter of a standard circular tube or duct is two times the radius.

Hydraulic Diameter of a Circular Tube with an inside Circular Tube

Based on equation (1) the hydraulic diameter of a circular duct or tube with an inside duct or tube can be expressed as

d_h = 4 (π r_o² - π r_i²) / (2 π r_o + 2 π r_i)

= 2 (r_o - r_i) (3)

where

r_o = inside radius of the outside tube (m, ft)

r_i = outside radius of the inside tube (m, ft)

Hydraulic Diameter of Rectangular Tubes or Ducts

Based on equation (1) the hydraulic diameter of a rectangular duct or pipe can be calculated as

d_h = 4 a b / (2 (a + b))

= 2 a b / (a + b) (4)

where

a = width/height of the duct (m, ft)

b = height/width of the duct (m, ft)