Hydraulic Diameter formula and calculation

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).

1. Calculation of hydraulic diameter

What is meant by hydraulic diameter ?

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

Calculation Hydraulic Diameter

DH=Hydraulic Diameter

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

2. Hydraulic diameter for rectangular duct

Hydraulic Diameter flow in rectangular pipe

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

Calculation of hydraulic diameter for rectangular flow

e=Height of the flow section (m)
l=Width of the flow section (m)

3. Hydraulic diameter for annular flow

Hydraulic Diameter flow in annular pipe

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

Calculation of hydraulic diameter for annular flow

R=Outside diameter of the tube (m)
Rinside=Inside diameter of the tube (m)

4. Hydraulic Diameter Excel Calculator

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