Hydraulic Radius Calculator

What is Hydraulic Radius?

The hydraulic radius (R) is a geometric property of channels and pipes that characterises how efficiently the flow cross-section conveys fluid. It's defined as the cross-sectional area of flow divided by the wetted perimeter (the length of boundary in contact with fluid).

The Formula

R = A / P

Where:

• A = cross-sectional area of flow (m²)
• P = wetted perimeter (m)

For a full circular pipe: R = D/4 (not D/2 — a common mistake) For a very wide, shallow channel: R ≈ y (flow depth)

Hydraulic Diameter

For non-circular cross-sections, the hydraulic diameter is: D_h = 4 × R = 4A / P

Used in the Reynolds number and Darcy-Weisbach equations when the cross-section is non-circular.

Practical Examples

Example 1 — Full circular pipe, 200mm diameter: A = π × 0.1² = 0.0314 m²; P = π × 0.2 = 0.628m; R = 0.0314/0.628 = 0.05m = D/4. ✓

Example 2 — Rectangular channel, 3m wide, 1.2m deep: A = 3 × 1.2 = 3.6m²; P = 3 + 2(1.2) = 5.4m; R = 3.6/5.4 = 0.667m.

Example 3 — Trapezoidal canal, bottom width 2m, side slopes 1:1, depth 1.5m: A = (2 + 1.5) × 1.5/2 + 2 × 1.5 = wait, correctly: A = (b + z×y) × y = (2 + 1×1.5)×1.5 = 5.25m² P = 2 + 2×(1.5×√2) = 2 + 4.24 = 6.24m; R = 5.25/6.24 = 0.841m.