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Docs Open channels

Every step of the calculation

Each equation of the open channel calculation, with its terms: normal flow, the flow regime and the capacity of the section.

The same steps, in the same order, as the calculation report.

1Normal flow

Water surface elevation
$Q(y_n) = \Sigma_j \frac{1}{n_j} A_j R_j^{2/3} S^{1/2} = Q \quad \text{(normal depth, the section divided where } n \text{ changes)}$
where $Q$ discharge (m³/s)
Normal depth
$y_n = WSE - z_{bed}$
Flow area
$A = \int (WSE - z) \, dx$
Wetted perimeter
$P = \Sigma P_i$
Hydraulic radius
$R = A / P$
where $A$ flow area (m²); $P$ wetted perimeter (m)
Mean velocity
$V = Q / A$
where $Q$ discharge (m³/s); $A$ flow area (m²)

2Flow regime

Top width
$T$
Froude number
$Fr = \frac{V}{\sqrt{g A / T}}$
where $V$ mean velocity (m/s); $A$ flow area (m²); $T$ top width (m)
Critical depth
$\frac{Q^2 T_c}{g A_c^3} = 1$
where $Q$ discharge (m³/s)
Specific energy
$E = y + \frac{V^2}{2g}$
where $y$ normal depth (m); $V$ mean velocity (m/s)

3Capacity of the section

Bank-full capacity
$Q_{bank} = \Sigma_j \frac{1}{n_j} A_j R_j^{2/3} S^{1/2} \quad (y = y_{bank})$
where $y_{bank}$ depth to the lower bank (m); $S$ longitudinal slope (m/m)
Bank-full capacity
$Q \le Q_{bank}$