Open Channel Geometry: circular
yD0.55 to yD1.00
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 | standard | top width formula | top width normalized (dimensionless) | wetted perimeter formula | wetted perimeter normalized (dimensionless) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| circular | yD0.55 | A = 0.442616*D^2 | 0.442616 | Trial | 0.55 | D h = A/T | R = 0.264886*D | 0.264886 | Partial flow | Chow 1959 Table 2-2; Sturm 2001; FHWA HDS-4 | T = 0.994987*D | 0.994987 | P = 1.670964*D | 1.670964 |
| circular | yD0.60 | A = 0.492028*D^2 | 0.492028 | Trial | 0.6 | D h = A/T | R = 0.277644*D | 0.277644 | Partial flow | Chow 1959 Table 2-2; Sturm 2001; FHWA HDS-4 | T = 0.979796*D | 0.979796 | P = 1.772154*D | 1.772154 |
| circular | yD0.65 | A = 0.540418*D^2 | 0.540418 | Trial | 0.65 | D h = A/T | R = 0.288148*D | 0.288148 | Partial flow | Chow 1959 Table 2-2; Sturm 2001; FHWA HDS-4 | T = 0.953939*D | 0.953939 | P = 1.875489*D | 1.875489 |
| circular | yD0.70 | A = 0.587230*D^2 | 0.58723 | Trial | 0.7 | D h = A/T | R = 0.296235*D | 0.296235 | Partial flow | Chow 1959 Table 2-2; Sturm 2001; FHWA HDS-4 | T = 0.916515*D | 0.916515 | P = 1.982313*D | 1.982313 |
| circular | yD0.75 | A = 0.631852*D^2 | 0.631852 | Trial | 0.75 | D h = A/T | R = 0.301687*D | 0.301687 | R max near y/D=0.81 | Chow 1959 Table 2-2; Sturm 2001; FHWA HDS-4 | T = 0.866025*D | 0.866025 | P = 2.094395*D | 2.094395 |
| circular | yD0.80 | A = 0.673574*D^2 | 0.673574 | Trial | 0.8 | D h = A/T | R = 0.304193*D | 0.304193 | Near max hydraulic radius | Chow 1959 Table 2-2; Sturm 2001; FHWA HDS-4 | T = 0.800000*D | 0.8 | P = 2.214297*D | 2.214297 |
| circular | yD0.85 | A = 0.711523*D^2 | 0.711523 | Trial | 0.85 | D h = A/T | R = 0.303267*D | 0.303267 | Partial flow | Chow 1959 Table 2-2; Sturm 2001; FHWA HDS-4 | T = 0.714143*D | 0.714143 | P = 2.346194*D | 2.346194 |
| circular | yD0.90 | A = 0.744523*D^2 | 0.744523 | Trial | 0.9 | D h = A/T | R = 0.298037*D | 0.298037 | Partial flow | Chow 1959 Table 2-2; Sturm 2001; FHWA HDS-4 | T = 0.600000*D | 0.6 | P = 2.498092*D | 2.498092 |
| circular | yD0.95 | A = 0.770717*D^2 | 0.770717 | Trial | 0.95 | D h = A/T | R = 0.286452*D | 0.286452 | Near-full flow | Chow 1959 Table 2-2; Sturm 2001; FHWA HDS-4 | T = 0.435890*D | 0.43589 | P = 2.690566*D | 2.690566 |
| circular | yD1.00 | A = 0.785398*D^2 | 0.785398 | N/A full pipe | 1 | D h = N/A | R = 0.250000*D | 0.25 | Full pipe; Q max = 1.076*Q full at y/D=0.938 | Chow 1959 Table 2-2; Sturm 2001; FHWA HDS-4 | T = 0.000000*D | 0 | P = 3.141593*D | 3.141593 |
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