Given a design flow rate and assigned certain geometric characteristics: width, freeboard, and chute slope, the application allows calculating the spillway height by exploiting the law governing the discharge over a broad-crested weir.
To size the spillway of a check dam, it is necessary to study the flow of the current in the transient phase, before the upstream section is filled with transported and retained material.
Under these conditions, the hydraulic behavior of the spillway is that of a broad-crested weir and, assuming a trapezoidal shape, the relationship that establishes the critical depth is the following:
Figure 1 – Spillway geometry
Q=9.810.5⋅(B0 ⋅k+tanα⋅k2 )1.5/(B0+2⋅tanα⋅k)0.5 (1)
Where:
B0 [m]= bottom width of the spillway
k [m]= critical depth
α [°]= slope of the chutes
Q [m3/s]= design flow rate
The app iterates relation (1) by varying the value of the critical depth k until it reaches the value of the design flow rate Q.
The height of the spillway H [m] is assumed equal to the total head ek, corresponding to the critical hydraulic state, to which a freeboard f (about 25-30 cm) must be added:
H=ek+f = k+{Q2/[19.62⋅(B0⋅k+tanα⋅k2 )2 ]}+f (2)