Hydraulic Radius Calculator
Free Hydraulic radius Calculator for hydrology & water resources. Enter variables to compute results with formulas and detailed steps.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
R = A / P
The hydraulic radius formula R = A / P relates channel geometry to flow efficiency. A is the wetted cross-sectional area (m²) — the portion of the channel cross-section occupied by flowing water — and P is the wetted perimeter (m), the length of the channel boundary in contact with water. The result R (meters) represents the effective depth driving flow. A larger hydraulic radius indicates less frictional resistance per unit of flow area. R enters Manning's equation as R^(2/3), making it the key geometric variable for computing flow velocity and discharge.
Worked Examples
Example 1: Trapezoidal Irrigation Canal
Problem:Bottom width b = 3 m, flow depth y = 1.2 m, side slope z = 1.5 (H:V)
Solution:A = y(b + zy) = 1.2(3 + 1.5×1.2) = 1.2 × 4.8 = 5.76 m²; P = b + 2y√(1+z²) = 3 + 2×1.2×√3.25 = 3 + 4.33 = 7.33 m; R = A/P = 5.76/7.33 = 0.786 m
Result:Hydraulic radius R = 0.786 m — use with Manning\'s n to find flow velocity
Example 2: Full Circular Sewer Pipe
Problem:Pipe diameter D = 0.6 m, flowing full
Solution:A = πD²/4 = π×0.36/4 = 0.283 m²; P = πD = π×0.6 = 1.885 m; R = A/P = 0.283/1.885 = D/4 = 0.150 m
Result:R = 0.15 m (= D/4 — applies to any full circular pipe)
Frequently Asked Questions
What is hydraulic radius and why does it matter in open-channel flow?
Hydraulic radius (R) is the ratio of the cross-sectional flow area (A) to the wetted perimeter (P): R = A / P. It is the single most important geometric parameter in Manning\'s equation for predicting flow velocity and discharge in channels, pipes, and culverts. A larger hydraulic radius means less frictional resistance per unit of flow area.
What is the hydraulic radius of a full circular pipe?
A full circular pipe of diameter D has area A = π D²/4 and wetted perimeter P = π D, giving R = D/4. At approximately 94% full, a pipe achieves its maximum velocity (not at full flow) because the hydraulic radius peaks slightly below full capacity. This counter-intuitive result is critical for sewer design.
What are typical hydraulic radius values for natural streams?
Small upland streams with widths of 1–3 m and depths of 0.2–0.5 m typically have R values of 0.15–0.4 m. Large lowland rivers may have R of 2–5 m. Irrigation canals are often designed with R of 0.5–2 m. Very low R indicates a wide, shallow cross-section with high friction losses per unit discharge.
How does hydraulic radius affect Manning\'s equation results?
Manning\'s equation is V = (1/n) × R^(2/3) × S^(1/2). Hydraulic radius enters as R^(2/3), so it has a strong influence on velocity. Doubling R increases V by a factor of 2^(2/3) ≈ 1.59. Accurate R computation from channel geometry is therefore essential for reliable discharge estimates in flood routing and hydraulic design.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy