Hydraulic and Equivalent Diameter

The difference between hydraulic and equivalent diameter - with formulas

Hydraulic diameter

The hydraulic diameter - d_h - is used for calculating the dimensionless Reynolds Number to determine if the flow is turbulent or laminar. The flow is

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

d_h is also used when calculating the pressure loss in ducts and pipes.

The hydraulic diameter is not the same as the geometrical diameter in non-circular ducts or pipes and can be calculated from the generic equation:

d_h = 4 A / P (1)

where:
d_h = hydraulic diameter (m, in)
A = area section of the duct (m², in²)

P = wetted perimeter of the duct (m, in)

Example - Hydraulic Diameter of a Circular Tube or Duct

Based on equation (1):

d_h = 4 π r² / 2 π r = 2 r (2)

As we could expect the hydraulic diameter in a standard circular tube is 2 times the radius.

Example - Hydraulic Diameter of a Circular Tube with an inside Circular Tube

Based on equation (1):

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, in)

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

Hydraulic Diameter for Rectangular Tubes or Ducts

Based on equation (1), the hydraulic diameter for a rectangular duct or pipe can be calculated by means of the following expression:

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

where

a = width of the duct (m, in)

b = height of the duct (m, in)

Equivalent diameter

Equivalent diameter is used for estimating pressure loss or head loss in non circular duct or pipes with tables and nomogram made for circular ducts or pipes.

Equivalent Diameter for Circular Tubes or Ducts

For circular tubes equivalent diameter is the same as the hydraulic diameter which is the same as the standard diameter.

Equivalent Diameter for Rectangular Tubes or Ducts

Equivalent diameter for a rectangular tube or duct can be expressed as:

d_e = 1.3 (a b)^0.625 / (a + b)^0.25

where

a = width of the duct (m, in)

b = height of the duct (m, in)

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