Open Channel Geometry: circular
Hydraulic geometry section properties for standard open channel cross-sections — rectangular, trapezoidal, triangular, parabolic, and circular (partial flow y/D = 0.05–1.0). Provides symbolic formulas and pre-computed normalized coefficients for area (A/D²), wetted perimeter (P/D), hydraulic radius (R/D), and top width (T/D) as functions of depth ratio.
| channel shape | record id | area formula | area normalized (dimensionless) | critical depth formula | depth ratio y over D (dimensionless) | hydraulic depth formula | hydraulic radius formula | hydraulic radius normalized (dimensionless) | normal depth note | top width formula | top width normalized (dimensionless) | wetted perimeter formula | wetted perimeter normalized (dimensionless) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| circular | yD0.05 | A = 0.014681*D^2 | 0.014681 | Trial via specific energy diagram | 0.05 | D_h = A/T | R = 0.032551*D | 0.032551 | Partial flow — theta = 2*arccos(1-2*y/D) | T = 0.435890*D | 0.43589 | P = 0.451027*D | 0.451027 |
| circular | yD0.10 | A = 0.040875*D^2 | 0.040875 | Trial | 0.1 | D_h = A/T | R = 0.063520*D | 0.06352 | Partial flow | T = 0.600000*D | 0.6 | P = 0.643501*D | 0.643501 |
| circular | yD0.15 | A = 0.073875*D^2 | 0.073875 | Trial | 0.15 | D_h = A/T | R = 0.092878*D | 0.092878 | Partial flow | T = 0.714143*D | 0.714143 | P = 0.795399*D | 0.795399 |
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