## Theory of calculation

The calculation formulas of the discharge of overflow weir which are shown in 'The Collection of Hydraulic Formulas (JSCE)' are indicated below:

Flow type | Equation of discharge calculation | Condition of $h' / h$ |
---|---|---|

Complete free overflow | $Q=C B h^{3/2}$ $C=1.24+ 1.64 \cdot (h/W)$ |
$\sim 0.25$ |

Incomplete free overflow | $Q=(\alpha\cdot h'/h +\beta)\cdot C B h^{3/2}$ $\alpha=-0.124, \beta=1.032$ |
$0.25 \sim 0.8$ |

Submerged overflow | $Q=\gamma\cdot C B h' (h-h')^{1/2}$ $\gamma=2.6$ |
$0.8\sim$ |

Model of Trapezoidal Weir | Conditions |
---|---|

$m_1=0\sim 1/3$ $m_2=2/3$ (approximately) |

## Programs and Script

Program name | Description |
---|---|

py_spline.py | Program for cubic spline interpolation |

py_ps_weir1.py | Program for calculation of the water depth |

py_ps_figHQ.py | Drawing program of H-Q curve |

a_py.txt | Script for data making and execution of programs |

### Process of calculation

- Preparation of Discharge - Water level relationship at downstream of the weir
- Interpolation of Discharge - Water level relationship using cubic spline interpolation method
- Calculation of the upstream water depth of the weir using the fomulas shown above. In this case, since the upstream water depth of the weir is unknown, Brent's method is used to solve the non-linear equations of the upstream water depth.
- The cubit spline interpolation method and Brent's method are modules included in Scipy of Python library.