# Fluid Flow - Hydraulic Diameter

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 Darcy-Weisbach equation to calculate pressure loss in ducts or pipes.

Note! - the hydraulic diameter is not the same as the geometrical equivalent diameter of non-circular 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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