Fluid Flow  Hydraulic Diameter
Calculate hydraulic diameter for pipes and ducts.
Hydraulic diameter  d_{h}  is the "characteristic length" 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 in the Reynolds equation is based on actual cross section area of duct or pipe.
The hydraulic diameter is used the DarcyWeisbach equation to calculate pressure loss in ducts or pipes.
Note!  the hydraulic diameter is not the same as the geometrical equivalent diameter of noncircular ducts or pipes.
Hydraulic diameter 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 or pipe (m^{2}, ft^{2})
p = "wetted" perimeter of the duct or pipe (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 r^{2}/2 π r
= 2 r
= d (2)
where
r = pipe or duct inside radius (m, ft)
d = pipe or duct inside diameter (m, ft)
As we could expect the hydraulic diameter of a standard circular tube or duct is the inner diameter or two times the inner radius.
Hydraulic Diameter of Circular Tube with Circular Tube on the Inside
The flow is in the volume between the inside and outside pipe.
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_{o}^{2} π r_{i}^{2}) / (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)
Related Mobile Apps from The EngineeringToolBox
 free apps for offline use on mobile devices.
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.
Equivalent diameter
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.
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