Hydraulic Diameter Calculator
Calculate hydraulic diameter for circular pipes, rectangular ducts, annular passages, and custom flow geometries using cross-sectional area and wetted perimeter.
Hydraulic diameter is a characteristic length used in selected internal-flow calculations. It is especially useful for non-circular passages.
Use the wetted perimeter—the boundary actually in contact with the fluid—not automatically the total geometric perimeter.
Calculation Results
What Is Hydraulic Diameter?
Hydraulic diameter is a characteristic length used in internal-flow calculations, especially for non-circular passages. It is defined from the cross-sectional flow area and the wetted perimeter:
Hydraulic diameter helps extend selected circular-pipe relationships to non-circular flow passages, but it does not make every non-circular flow problem physically identical to a circular pipe.
What Is Wetted Perimeter?
Wetted perimeter is the portion of the flow boundary actually in contact with the fluid. For a fully filled closed duct, it normally includes the entire internal perimeter. For open-channel flow, the free surface is normally excluded.
Hydraulic Diameter of a Circular Pipe
For a fully wetted circular pipe, hydraulic diameter equals the inside diameter. This is a useful sanity check for the general formula.
Hydraulic Diameter of a Rectangular Duct
This follows from A = WH and P = 2(W + H). When width equals height, the passage becomes square and Dh equals the side length.
Hydraulic Diameter of a Square Duct
For a fully wetted square duct, hydraulic diameter equals the side length.
Hydraulic Diameter of an Annulus
This simplified result applies to a concentric, fully wetted annulus.
Hydraulic Diameter for Open Channels
Custom mode can be used for open channels when the supplied area and wetted perimeter represent the actual flow section. The free surface is normally not counted as wetted perimeter because it is not a solid boundary in contact with the fluid.
Why Hydraulic Diameter Exists
Many classical internal-flow relationships were developed using circular pipes. Hydraulic diameter provides a characteristic length that can be used in selected Reynolds-number, friction, and duct-resistance calculations for non-circular passages.
Geometry-specific effects still matter, particularly in laminar non-circular flow and in applications where corner behavior or detailed velocity profiles are important.
Hydraulic Diameter and Reynolds Number
Hydraulic diameter can serve as the characteristic length in many internal-flow Reynolds-number calculations for non-circular passages. Velocity and fluid properties are still required.
Hydraulic Diameter and Darcy-Weisbach
For applicable non-circular internal-flow calculations, Darcy-Weisbach relationships can use hydraulic diameter as the characteristic length. Hydraulic diameter is only one parameter; pressure loss can also depend on length, velocity, density, friction factor, roughness, Reynolds number, fittings, valves, and geometry.
For friction-loss work, see the Darcy-Weisbach Calculator.
Hydraulic Diameter and Flow Velocity
Hydraulic diameter does not calculate flow velocity by itself. Average velocity still comes from volumetric flow rate and flow area:
Hydraulic diameter is Dh = 4A/P, so the two quantities should not be confused. For Q/A calculations, see the Flow Velocity Calculator.
Hydraulic Diameter in Duct Design
ASHRAE duct-design guidance uses hydraulic diameter in selected friction calculations for non-circular ducts. Duct pressure loss still requires airflow, geometry, length, friction information, and system details.
Hydraulic Diameter vs Equivalent Diameter
Hydraulic diameter and equivalent diameter are related engineering concepts but should not automatically be treated as interchangeable in every application. This calculator additionally shows an area-equivalent circular diameter—the diameter of a circle with the same cross-sectional area—only as a geometry reference. It is not presented as a friction-equivalent duct diameter.
Dimensional Check
Hydraulic diameter is a length dimension, so its output may be expressed in inches, feet, millimetres, centimetres, or metres.
2026 Engineering Reference
Updated for 2026. The hydraulic-diameter equation is an established fluid-mechanics relationship. The 2026 update refers to the current engineering and unit references used by this page rather than a new annual version of the hydraulic-diameter formula.
Engineering References
Current HVAC&R engineering reference context.
ASHRAE HandbookReference context for hydraulic diameter in non-circular duct friction calculations.
ASHRAE Duct DesignSI units and general conversion reference.
NIST Special Publication 811Exact engineering unit-conversion factors including inches and feet to metres.
NIST Appendix B.9Current 2026 measurement and unit-reference context; not the source of the hydraulic-diameter equation.
NIST Handbook 44 — 2026Limitations
Hydraulic diameter is an engineering characteristic length. It does not make all non-circular flow behavior identical to circular-pipe behavior. Detailed work may require geometry-specific correlations, measured roughness, fluid properties, Reynolds number, friction factors, and qualified engineering judgment.
Frequently Asked Questions
1. What is the hydraulic diameter formula?
The general definition is D_h = 4A/P, where A is cross-sectional flow area and P is wetted perimeter. It is commonly used as a characteristic length for selected internal-flow calculations involving non-circular passages.
2. How do you calculate hydraulic diameter?
Calculate the effective cross-sectional flow area, determine the wetted perimeter that is actually in contact with the fluid, and divide four times the area by that perimeter. Keep all units consistent.
3. What is the hydraulic diameter of a rectangular duct?
For a fully wetted rectangular duct, D_h = 2WH/(W+H). This comes directly from A = WH and P = 2(W+H).
4. What is the hydraulic diameter of a square duct?
For a fully wetted square duct with side a, the area is a² and the perimeter is 4a, so D_h = a. The hydraulic diameter equals the side length.
5. What is the hydraulic diameter of a circular pipe?
For a fully wetted circular pipe, hydraulic diameter equals the actual inside pipe diameter. The general 4A/P formula reduces exactly to D.
6. What is the hydraulic diameter of an annulus?
For a concentric fully wetted annulus, D_h = D_o − D_i. This follows from the annular flow area and the sum of the inner and outer wetted circumferences.
7. Is hydraulic diameter the same as pipe diameter?
Only for a fully wetted circular pipe. For non-circular passages, hydraulic diameter is a characteristic length calculated from area and wetted perimeter rather than a physical circular diameter.
8. What is a wetted perimeter?
Wetted perimeter is the portion of the passage boundary actually in contact with the fluid. In a full closed pipe it is normally the entire internal perimeter; in open-channel flow it excludes the free surface.
9. Does wetted perimeter include the free surface?
Normally no for open-channel flow. Wetted perimeter refers to solid boundary in contact with the fluid, so the free liquid surface is not normally counted.
10. Why is hydraulic diameter used for rectangular ducts?
It provides a characteristic length that can be used in selected internal-flow and duct-friction relationships originally developed around circular pipes, while still preserving the actual rectangular flow area and perimeter in its definition.
11. Can hydraulic diameter be used for HVAC ducts?
Yes, hydraulic diameter is used in selected HVAC duct friction and Reynolds-number calculations for non-circular ducts. It is not enough by itself to determine duct pressure drop or fan requirements.
12. How is hydraulic diameter used in Reynolds number?
For many non-circular internal flows, hydraulic diameter can be used as the characteristic length in Re = ρVD_h/μ or Re = VD_h/ν, together with velocity and fluid properties.
13. How is hydraulic diameter used in Darcy-Weisbach?
For applicable non-circular internal-flow calculations, D_h can replace circular pipe diameter as the characteristic length. Friction factor, length, velocity, roughness, and fluid properties still matter.
14. Can hydraulic diameter be used for open channel flow?
It can be calculated with D_h = 4A/P when A is the flow area and P is the wetted solid boundary. The free surface should normally be excluded from the wetted perimeter.
15. What happens to hydraulic diameter when a rectangular duct becomes wider?
The result depends on both width and height. Increasing width while holding height fixed changes both area and wetted perimeter, so D_h approaches a limiting value rather than increasing exactly in proportion to width.
16. Does hydraulic diameter have units?
Yes. Because it is area divided by perimeter, hydraulic diameter has dimensions of length. It can be expressed in inches, feet, millimetres, centimetres, or metres.
17. Can I calculate hydraulic diameter from area and perimeter?
Yes. That is the most general mode: enter cross-sectional flow area and wetted perimeter, then use D_h = 4A/P. This is useful for irregular or measured passages.
18. Is hydraulic diameter the same as equivalent diameter?
Not necessarily. Hydraulic diameter is defined by 4A/P. Other “equivalent diameter” definitions may preserve area, friction behavior, or another property. Always confirm which definition an engineering method requires.
19. Can hydraulic diameter be used for irregular flow passages?
Yes as a characteristic length when the chosen engineering correlation permits it. Use measured or calculated flow area and the actual wetted perimeter. Geometry-specific behavior may still require additional treatment.
20. Does hydraulic diameter make a rectangular duct equivalent to a round pipe?
No. It gives a characteristic length useful in selected correlations, but it does not make every velocity profile, laminar-flow characteristic, friction behavior, or geometric effect identical to a circular pipe.
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Engineering Disclaimer
This calculator provides hydraulic diameter based on the user-supplied flow geometry, cross-sectional area, and wetted perimeter. Hydraulic diameter is a characteristic length used in selected internal-flow correlations and does not make every non-circular flow problem physically identical to a circular pipe. For detailed engineering design, use the appropriate fluid-mechanics method, applicable standards, measured geometry, fluid properties, and qualified engineering review.