1. General formula

2. Formula for rectangular duct

3. Formula for annular flow

What is the hydraulic diameter ? The hydraulic diameter, defined as
the ratio in between 4 times the flow section over the wetted
perimeter, allows, for non circular flows, to define an equivalent
diameter which allows to perform fluid dynamic calculation.

**The hydraulic diameter is especially useful when having to
calculate a Reynolds
number in order to determine the flow regimes (laminar,
intermediary, turbulent).**

What is meant by hydraulic diameter ?

The hydraulic diameter is used for non-circular flow and is
calculated thanks to the following general formula : D_{H}=4*(flow
section)/(wetted perimeter)

D_{H}=Hydraulic Diameter

The Hydraulic Diameter formula for 2 simple geometries : rectangular duct and annulus are given below.

The Hydraulic Diameter in
rectangular pipe is calculated thanks to the following formula : D_{H}=(2.e.l)/(l+e)

e=Height of the flow section (m)

l=Width of the flow section (m)

The Hydraulic Diameter in annular
flow is calculated thanks to the following equation : D_{H}=2.R.(1-K)

R=Outside diameter of the tube (m)

K=R

R

You can access here
an Excel Calculator to calculate the hydraulic diameter
defined above.

Mecanique et Rheologie des fluides en genie chimique, Noel Midoux, Lavoisier Tec et Doc, page 197