What is the hydraulic radius formula?

R_h = A / P, where A is the cross-sectional flow area (m²) and P is the wetted perimeter (m). For a circular pipe flowing full: R_h = D/4. The hydraulic diameter D_h = 4R_h = 4A/P is used in the Darcy-Weisbach equation and Reynolds number calculations for non-circular sections.

What is the hydraulic radius of a partially full circular pipe?

For a circular pipe of diameter D with flow depth y: A = (D²/8)(θ - sin θ) and P = Dθ/2, where θ = 2 arccos(1 - 2y/D) in radians. R_h = A/P. Maximum R_h occurs at y/D ≈ 0.813, not at full flow — which is why Manning's equation predicts maximum velocity at about 85% full for a circular sewer pipe.

Hydraulic Radius Calculator

Calculate hydraulic radius and hydraulic diameter for open channels and closed conduits flowing full or partially full.

2D stress state at a point. All stresses in MPa.

σx — Normal Stress X (MPa)

σy — Normal Stress Y (MPa)

τxy — Shear Stress (MPa)

⚙ Mechanical Note: Results are based on standard textbook formulas and ISO/AASHTO references. Always verify critical designs with applicable codes (ISO 898, AASHTO 1993, AISC, Eurocode 3) and a qualified engineer.

How to Use

Enter the values for the patient or scenario you are assessing. Calculate hydraulic radius and hydraulic diameter for open channels and closed conduits flowing full or partially full. Use the hydraulic radius result to inform your clinical assessment.

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Frequently Asked Questions

What is the hydraulic radius formula?

What is the hydraulic radius of a partially full circular pipe?