Hydraulic diameter of ducts and tubes
The hydraulic diameter - dh - 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
Note that the velocity of the flow in the Reynolds calculation is based on the actual cross section area of the duct or pipe.
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
dh = 4 A / p (1)
dh = 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:
dh = 4 π r2 / 2 π r
= 2 r (2)
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
dh = 4 (π ro2 - π ri2) / (2 π ro + 2 π ri)
= 2 (ro - ri) (3)
ro = inside radius of the outside tube (m, ft)
ri = 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
dh = 4 a b / (2 (a + b))
= 2 a b / (a + b) (4)
a = width/height of the duct (m, ft)
b = height/width of the duct (m, ft)
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Rectangular to Circulate Duct/Tube Hydraulic Diameter Calculator
The calculator below is based on formula (4) an can be used to calculate the hydraulic diameter of rectangular duct or tube. The formula is generic and any unit can be used.
Note! The hydraulic diameter is not the same as the equivalent diameter. The equivalent diameter is the diameter of a circular duct or pipe that gives the same pressure loss as a rectangular duct or pipe.