Example preset
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Inputs
Forward (calculate V,Q)
Results
| Cross-sectional area A [m²] | — |
|---|---|
| Wetted perimeter P [m] | — |
| Hydraulic radius R [m] | — |
| Hydraulic depth Dm=A/T [m] | — |
| Froude number Fr [-] | — |
| Flow regime | — |
| Estimated water depth y [m] | — |
| Iteration details | — |
Cross-sectional view (outline)
Displays the cross-sectional shape according to the input value.
Graph
Display a graph with valid input.
Calculation formula and procedure
R = A / P
V = (1/n) × R^(2/3) × S^(1/2)
Q = A × V
Flow area A, wetted perimeter P, and top width T are calculated for rectangular, trapezoidal, and partially full circular sections. Depth is solved with bracketed bisection; slope is solved analytically.
At the full-depth boundary y=D, Q and V can be evaluated from Manning's equation, but hydraulic depth and a free-surface Froude number are not defined.
FAQ
What does the Froude number Fr indicate?
Fr compares inertial and gravitational effects. Fr<1 is subcritical flow, Fr≈1 is critical flow, and Fr>1 is supercritical flow.
What does slope S mean?
S is the energy gradient in Manning's equation. For this educational estimate, the channel-bed slope is used as an approximation when uniform flow is assumed.
Which Manning roughness coefficient n should I use?
Choose n from a source appropriate to the channel material, vegetation, irregularity, alignment, and maintenance condition. The presets are reference examples, not design values.
Can I use the circular-section result for a pressurized pipe?
No. This calculator models open-channel flow with a free surface. It does not model a pressurized full pipe.
Why can a partially full circular section have two depths for one discharge?
Circular-section Manning discharge reaches a maximum before the section is completely full and then decreases slightly toward y=D. Between the full-depth discharge and the maximum discharge, one target Q has a shallow and a deeper mathematical depth. The calculator selects the shallow depth and also reports the deeper alternative.
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