# Hydraulic Diameter

## Hydraulic diameter of ducts and tubes

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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

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

d_{h}= 4 A / p(1)

where

d_{h}= hydraulic diameter (m, ft)

A= area section of the duct (m^{2}, ft^{2})

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 r^{2}/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_{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 Engineering ToolBox

- 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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