Hydraulic Diameter

Hydraulic diameter of ducts and tubes

Hydraulic diameter - dh - is used to calculate the dimensionless Reynolds Number used 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 for the flow in the Reynolds equation is based on the actual cross section area of the duct or pipe.

The hydraulic diameter is also used to calculate pressure loss in ducts or pipes.

The hydraulic diameter is not the same as the geometrical equivalent diameter of a non-circular duct or pipe. 

Hydraulic diameter 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

circular tubes pipes hydraulic diameter

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

circular tubes pipes hydraulic diameter

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

rectangular tubes pipes hydraulic diameter

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.

Length side a - (m, ft)

Length side - b - (m, ft)

rectangular ducts tubes pipes hydraulic diameter

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.

Related Topics

  • Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time
  • Fluid Flow and Pressure Drop - Pipe lines - fluid flow and pressure loss - water, sewer, steel pipes, pvc pipes, copper tubes and more
  • Ventilation - Systems for ventilation and air handling - air change rates, ducts and pressure drops, charts and diagrams and more

Related Documents

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