calculatorbrowser-only

Hydraulic Diameter Calculator

Compute hydraulic diameter, cross-sectional area, wetted perimeter, and geometry interpretation for internal CFD passages.

Hydraulic Diameter inputs

Result section

warningRectangular duct

Hydraulic diameter

0.133333 m

Secondary results

Cross-sectional area: 0.02 m^2
Wetted perimeter: 0.6 m
Aspect ratio: 2

Unit conversion summary

Unit-normalization summary: 0.133333 m; 0.02 m^2; 0.6 m

Warnings

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.
Fluid presets are starter values only; verify properties at the actual operating condition.

Assumptions

Wetted perimeter includes only wall boundaries in contact with the fluid.
Hydraulic diameter supports correlation use but does not make shapes physically identical.

Calculation steps

Resolve geometryD_h = 2ab / (a + b)
Apply hydraulic-diameter relationship0.133333 m

Hydraulic diameter formula

D_h = 4A / P_w

D_h = 2ab / (a + b)

D_h = 4(0.02 m^2) / 0.6 m

Technical visual

Technical sketch for hydraulic diameter calculator. Values are illustrative; calculated values appear in the result section.

Engineering interpretation

Use hydraulic diameter as the characteristic internal-flow length for Reynolds number and Darcy-Weisbach correlations when the correlation supports the selected geometry.

What is hydraulic diameter and how does this Hydraulic Diameter Calculator work?

Hydraulic diameter is a characteristic length for internal flow, defined as four times flow area divided by wetted perimeter. It lets many pipe-flow correlations be applied cautiously to rectangular ducts, annuli, and other non-circular passages while preserving the effect of cross-sectional area and wall contact.

Hydraulic Diameter Calculator applies this concept to its defined inputs and workflow. It resolves circular, rectangular, square, annular, custom area-perimeter, and custom hydraulic-diameter geometries for internal-flow correlations. Its governing relationship or workflow is stated as follows: Hydraulic diameter equals four times cross-sectional area divided by wetted perimeter.

The calculator evaluates Geometry mode, Flow input mode, Viscosity mode, and Number format and returns Hydraulic Diameter, base-unit normalization, formula substitution, and calculation steps using the stated method. The selected units and sign or reference conventions must describe one consistent physical case. Users should interpret the output within the assumptions shown on the page and repeat the check with trusted reference values when the result affects engineering or research decisions. Hydraulic diameter does not make non-circular passages physically identical to circular pipes.

How to use the hydraulic diameter calculator

Select the calculation mode that matches the data you already have.
Enter values with units; the calculator normalizes inputs to SI internally.
Review derived values, warnings, formulas, and assumptions before using the result in another CFD step.
Use the transfer link when the resulting hydraulic diameter should feed the Reynolds Number Calculator.

Input explanations

Circular pipes use D_h = D.
Rectangular ducts use D_h = 2ab/(a+b).
Annuli use D_h = D_o - D_i when both walls are wetted.
Custom sections use D_h = 4A/P_w and require a wetted perimeter.

Notation

Formula notation
Symbol	Meaning	Unit
D_h	Hydraulic diameter	m
A	Cross-sectional area	m^2
P_w	Wetted perimeter	m
a, b	Rectangular duct side lengths	m
D_o, D_i	Annulus outer and inner diameters	m

Worked examples

Circular pipe: D = 0.1 m gives D_h = 0.1 m.

Rectangular duct: a = 0.2 m and b = 0.1 m gives D_h = 0.133333 m.

Annulus: D_o = 0.10 m and D_i = 0.06 m gives D_h = 0.04 m.

Cross-tool workflow

The Hydraulic Diameter Calculator resolves circular, rectangular, square, annular, custom area-perimeter, and custom hydraulic-diameter geometries for internal-flow correlations.

Use hydraulic diameter in Reynolds Number Calculator

Common mistakes

Including boundaries that are not wetted in the wetted perimeter.
Treating hydraulic diameter as proof that a duct behaves exactly like a circular pipe.
Using outer annulus diameter alone instead of D_o - D_i.
Mixing area and perimeter units without normalization.

Limitations

Hydraulic diameter does not make non-circular passages physically identical to circular pipes.
Correlation validity must be checked for aspect ratio, roughness, and entrance effects.
Open-channel hydraulic radius needs careful wetted-perimeter treatment and is not solved as a separate mode.

References

White Fluid Mechanics: White, F. M., Fluid Mechanics, McGraw-Hill.
Fox and McDonald Fluid Mechanics: Fox, McDonald, and Pritchard, Introduction to Fluid Mechanics, Wiley.
Versteeg and Malalasekera CFD: Versteeg, H. K. and Malalasekera, W., An Introduction to Computational Fluid Dynamics, Pearson.
Pope Turbulent Flows: Pope, S. B., Turbulent Flows, Cambridge University Press.
NASA Turbulence Modeling Resource: NASA Langley Research Center, Turbulence Modeling Resource.

What is hydraulic diameter?

Hydraulic diameter is D_h = 4A/P_w, a characteristic length used in many internal-flow correlations.

Is hydraulic diameter equal to pipe diameter?

For a full circular pipe, yes. For non-circular passages it is derived from area and wetted perimeter.

How is rectangular-duct hydraulic diameter calculated?

For width a and height b, D_h = 2ab/(a+b).

What is wetted perimeter?

It is the length of boundary in contact with the fluid, excluding walls or surfaces not wetted by the flow.

Can hydraulic diameter be used for any shape?

It can be calculated for many shapes, but correlation validity must still be checked.

Does hydraulic diameter replace CFD validation?

No. It is an input to correlations and estimates, not validation of a CFD model.

Why include a custom area-perimeter mode?

It lets users apply D_h = 4A/P_w to sections not covered by the built-in geometries.

Professional support from ScholarEase Consultancy Services LLP

Professional CFD, simulation setup, engineering calculations, technical documentation, and research support are available through the connected services website. These calculators remain free to use without purchasing services.

Visit ScholarEase

Engineering disclaimer

This tool is intended for educational, estimation, and preliminary CFD setup support. Always verify critical engineering calculations with applicable standards, validated software, solver documentation, and qualified professional judgment.

Need Professional Support?

ScholarTool is powered by ScholarEase Consultancy Services LLP. Professional engineering, simulation, research, and technical documentation support is available through the connected services website.

Visit ScholarEase

Loading ScholarTool content...

Result section

warningRectangular duct

Hydraulic diameter

0.133333 m

Secondary results

Cross-sectional area: 0.02 m^2
Wetted perimeter: 0.6 m
Aspect ratio: 2

Unit conversion summary

Unit-normalization summary: 0.133333 m; 0.02 m^2; 0.6 m

Warnings

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.
Fluid presets are starter values only; verify properties at the actual operating condition.

Assumptions

Wetted perimeter includes only wall boundaries in contact with the fluid.
Hydraulic diameter supports correlation use but does not make shapes physically identical.

Calculation steps

Resolve geometryD_h = 2ab / (a + b)
Apply hydraulic-diameter relationship0.133333 m

Hydraulic diameter formula

D_h = 4A / P_w

D_h = 2ab / (a + b)

D_h = 4(0.02 m^2) / 0.6 m

What is hydraulic diameter and how does this Hydraulic Diameter Calculator work?

How to use the hydraulic diameter calculator

Select the calculation mode that matches the data you already have.
Enter values with units; the calculator normalizes inputs to SI internally.
Review derived values, warnings, formulas, and assumptions before using the result in another CFD step.
Use the transfer link when the resulting hydraulic diameter should feed the Reynolds Number Calculator.

Symbol

Meaning

Unit

D_h

Hydraulic diameter

Cross-sectional area

m^2

P_w

Wetted perimeter

a, b

Rectangular duct side lengths

D_o, D_i

Annulus outer and inner diameters

References

White Fluid Mechanics: White, F. M., Fluid Mechanics, McGraw-Hill.

Fox and McDonald Fluid Mechanics: Fox, McDonald, and Pritchard, Introduction to Fluid Mechanics, Wiley.

Versteeg and Malalasekera CFD: Versteeg, H. K. and Malalasekera, W., An Introduction to Computational Fluid Dynamics, Pearson.

Pope Turbulent Flows: Pope, S. B., Turbulent Flows, Cambridge University Press.

NASA Turbulence Modeling Resource: NASA Langley Research Center, Turbulence Modeling Resource.

Hydraulic Diameter inputs

Geometry

Result section

Secondary results

Unit conversion summary

Warnings

Assumptions

Calculation steps

Hydraulic diameter formula

Technical visual

Engineering interpretation

What is hydraulic diameter and how does this Hydraulic Diameter Calculator work?

How to use the hydraulic diameter calculator

Input explanations

Notation

Worked examples

Cross-tool workflow

Common mistakes

Limitations

References

Related tools

Professional support from ScholarEase Consultancy Services LLP

Print summary

Engineering disclaimer

Need Professional Support?

Hydraulic Diameter inputs

Geometry

Result section

Secondary results

Unit conversion summary

Warnings

Assumptions

Calculation steps

Hydraulic diameter formula

Technical visual

Engineering interpretation

What is hydraulic diameter and how does this Hydraulic Diameter Calculator work?

How to use the hydraulic diameter calculator

Input explanations

Notation

Worked examples

Cross-tool workflow

Common mistakes

Limitations

References

Related tools

Professional support from ScholarEase Consultancy Services LLP

Print summary

Engineering disclaimer

Need Professional Support?