Select a section, enter dimensions, get radius fast. See area and wetted perimeter calculations clearly. Download tables and share outputs with your team easily.
Hydraulic radius is the ratio of flow area to wetted perimeter: R = A / P. A is the cross‑sectional area of water, and P is the length of boundary in contact with water.
A = b·y, P = b + 2yA = y(b + z·y), P = b + 2y√(1+z²)A = z·y², P = 2y√(1+z²)θ = 2·acos((r−y)/r),
A = (r²/2)(θ − sinθ), P = r·θ, where r = D/2A and P directly.z as horizontal per 1 vertical.| Example | Area A (m²) | Wetted Perimeter P (m) | Hydraulic Radius R (m) |
|---|---|---|---|
| Rectangular (b=3.0, y=1.2) | 3.60000 | 5.40000 | 0.66667 |
| Trapezoidal (b=2.5, y=1.0, z=1.5) | 4.00000 | 6.10555 | 0.65514 |
| Triangular (y=0.9, z=1.0) | 0.81000 | 2.54558 | 0.31820 |
| Circular segment (D=1.2, y=0.6) | 0.56549 | 1.88496 | 0.30000 |
Hydraulic radius summarizes how efficiently a canal conveys flow for a given boundary contact. A larger radius usually means less relative frictional influence, which can reduce required slope for the same discharge. Designers use it to compare alternative shapes, linings, and operating depths. It is also a key geometric input for resistance equations and for checking whether a section will remain stable under expected velocities and debris conditions.
Start by selecting the section that matches field geometry: rectangular, trapezoidal, triangular, circular segment, or custom. Enter dimensions at the normal operating water depth, not the full excavation depth. For trapezoids and V-shapes, the side slope z is the horizontal-to-vertical ratio per side. Consistent units matter because area and perimeter scale differently and directly affect computed radius. If measured in the field, record stations and offsets for auditability.
Wetted perimeter is the portion of the boundary in contact with water. Rougher linings increase resistance, so two canals with the same radius can behave differently if their surfaces differ. Radius should be evaluated together with lining condition, vegetation, and sediment deposits that reduce effective area. If the canal is partially full or has freeboard variations, rerun the calculation at several depths to capture sensitivity across seasons.
After calculating radius, many workflows continue with Manning’s equation by combining radius, area, roughness n, and slope. Use the computed area to estimate velocity from discharge, then confirm that velocity remains within permissible limits for the soil or lining to avoid erosion. For circular segments, verify depth constraints and consider transitions and air entrainment. Radius values are most useful when paired with realistic operating scenarios in practice.
Document assumptions: section type, measurement method, and the depth used for evaluation. Compare results against typical section drawings or survey cross sections to confirm inputs. Use derived geometry like top width as a quick reasonableness check. Exporting CSV supports spreadsheet review, while PDF outputs provide a clean record for design packages, QA logs, and stakeholder communication across teams and agencies.
Hydraulic radius is the flow area divided by the wetted perimeter. It reflects how much water area is supported by each unit of boundary contact, influencing resistance and velocity.
Wetted perimeter is only the boundary touching water: bed plus side slopes, or the submerged arc in circular channels. The free water surface is never included.
Enter z as horizontal to one vertical on each side. For example, a 1.5H:1V bank uses z = 1.5. Use the same convention as your drawings.
Yes. Keep all length inputs in one unit system. The calculator outputs area in squared units and radius in length units. Convert to inches only after exporting results.
Hydraulic diameter equals four times hydraulic radius. It is commonly used when comparing open-channel sections to closed conduits or when applying friction concepts across different flow models.
Yes. Hydraulic radius changes with depth, especially for trapezoids and circular segments. Running several depths helps capture operating ranges, seasonal flow variation, and sediment or vegetation impacts.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.