Flow of Overflow Weir

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 typeEquation of discharge calculationCondition 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 $Q=\gamma\cdot C B h' (h-h')^{1/2}$


Model of Trapezoidal WeirConditions
png $m_1=0\sim 1/3$

$m_2=2/3$ (approximately)

Programs and Script

Program nameDescription
py_spline.pyProgram for cubic spline interpolation
py_ps_weir1.pyProgram for calculation of the water depth
py_ps_figHQ.pyDrawing program of H-Q curve
a_py.txtScript 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.

Result of calculation


inserted by FC2 system