Hydraulic Radius Calculator — R = A/P
Compute hydraulic radius R = A/P (wetted cross-sectional area divided by wetted perimeter) for 6 channel shapes. Inverse mode finds flow depth from a target R, plus a hydraulic-depth bonus. Dh = A/T.
1. Choose mode & channel shape
2. Enter dimensions
3. Results
Formulas per channel shape
| Bentuk | Luas A | Keliling basah P | Surface width T |
|---|---|---|---|
| Persegi (b, y) | b·y | b + 2y | b |
| Trapesium (b, y, m) | (b + m·y)·y | b + 2y·√(1+m²) | b + 2·m·y |
| Segitiga (m, y) | m·y² | 2y·√(1+m²) | 2·m·y |
| Lingkaran penuh (D) | πD²/4 | πD | — (no free surface) |
| Lingkaran sebagian (D, y) | D²/8·(θ − sin θ) | D·θ/2 | D·sin(θ/2) |
| Setengah lingkaran (D) | πD²/8 | πD/2 | D |
θ = 2·acos(1 − 2y/D) is the central angle (radians) for partially filled circles.
Batasan vs Open Channel Flow Calculator
R = A/P from channel dimensions, finds depth y from a target R, and gives a hydraulic-depth bonus Dh = A/T. Ia does not compute discharge, slope, or Manning roughness. For the full Manning equation (discharge Q, normal depth, slope S, roughness n, Froude number), use Open Channel Flow Calculator — there R appears only as an intermediate result.Verified examples
Rectangular channel with base width b = 2 m and depth y = 1 m:
- Luas basah A = 2 × 1 = 2.00 m²
- Keliling basah P = 2 + 2×1 = 4.00 m
- Jari-jari hidraulik R = 2 / 4 = 0.50 m
- Kedalaman hidraulik Dh = 2 / 2 = 1.00 m
Note: R (0.50 m) ≠ Dh (1.00 m) — two different quantities, don’t confuse them.
Pertanyaan umum
What is the hydraulic radius?
The hydraulic radius R is the wetted cross-sectional area A divided by the wetted perimeter P (R = A/P). It measures how efficiently a cross-section conveys flow: larger R means less relative friction for the discharge passing through.
What is the difference between hydraulic radius (R) and hydraulic depth (Dh)?
Hydraulic radius R = A/P (area divided by wetted perimeter) is used for friction calculations and enters the Manning equation. Hydraulic depth Dh = A/T (area divided by free-surface width) is the average depth and is used in the Froude number. The two are equal only in very wide rectangular channels.
How does hydraulic radius relate to the Manning equation?
The Manning equation Q = (1/n) x A x R^(2/3) x S^(1/2) uses R to the two-thirds power. Larger R means larger discharge capacity for the same area, roughness, and slope. This calculator computes the R; for full discharge use the Open Channel Flow calculator.
What is the hydraulic radius of a full-flowing circular pipe?
R = D/4. For a full circle A = pi x D^2 / 4 and wetted perimeter P = pi x D, so R = A/P = D/4. Example: a D = 1 m pipe running full has R = 0.25 m.
How do you compute R for a partially filled circular pipe?
Use the central angle theta = 2 x acos(1 - 2y/D). Wetted area A = D^2/8 x (theta - sin theta) and wetted perimeter P = D x theta / 2, then R = A/P. At y = D/2 (half full), R = D/4 just like a full pipe.
What is the wetted perimeter?
The wetted perimeter P is the length of channel cross-section in direct contact with water. The free water surface (exposed to air) is not counted as wetted perimeter.
What is the hydraulic depth Dh = A/T?
Hydraulic depth is the wetted cross-sectional area A divided by free-surface width T. It represents the average flow depth and is used in the Froude number Fr = V / sqrt(g x Dh) to determine subcritical or supercritical flow.
When should I use the Depth-from-R mode?
Inverse mode is for design: you set a desired hydraulic radius R target, then the calculator finds the flow depth y producing it. For trapezoids and partially filled circles the bisection method is used because R cannot be isolated algebraically.
What units does this calculator use?
Two options: SI (meters) and US (feet). Hydraulic radius R, hydraulic depth Dh, and wetted perimeter P follow the input length unit, while area A is in squared length units.
How is this different from the Open Channel Flow Calculator?
This calculator is a pure geometry solver: it computes R = A/P from channel dimensions, plus inverse depth-from-R mode and a hydraulic-depth bonus. The Open Channel Flow Calculator is a Manning-equation solver for discharge, normal depth, slope, and roughness n, with R only as an intermediate result.
See also
Open Channel Flow Calculator — Manning equation: discharge, normal depth, slope, roughness n, and Froude number.
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