Stepped Spillway Discharge Coefficient

As water is transported to a dam downstream, it generates high volumes of kinetic energy. This can damage parts of structures within a dam or levee that are not designed to convey water. In such cases, a stepped weir or spillway is used to lower the kinetic energy of flow travelling downstream. In stepped spillways, the design of the steps has a significant impact on how much of the flow’s kinetic energy is transferred downstream. Currently, pooled designs are more commonly used in stepped spillways as these are better at dissipating kinetic energy. In addition, increasing the number of steps in a spillway increases the energy dissipation rate. However, an increase in discharge leads to an increase in the discharge coefficient and thus decreases the energy dissipation rate.

What is a Stepped Spillway?

A stepped spillway is a structure that provides controlled release of water downstream from a dam or levee. It is also used to measure the discharge and depth of rising water in irrigation channels. Stepped spillways have steps on their faces running from close to the crest to the toe. These steps accelerate the rate of energy dissipation from the weir surface. Using a stepped spillway can also reduce the cavitation risk by boosting self-aerated flow compared to smooth weirs.

Energy Dissipation

The energy between the inlet section and the approach channel of the spillway can be used to calculate and measure the energy dissipation E₀ and any area of intriguing phase E.

Similarly, the energy at the outlet section of the spillway E₁ can be measure as follows:
Thus, the energy loss ΔE is the difference between the energy at the inlet section E₀ and the energy at the outlet section E₁.

The dissipation of energy is a dimensionless parameter used to research the energy dissipation characteristics of a stepped spillway and can be formulated as ΔE/ E₀.

Discharge Coefficient

The discharge coefficient (C_d) is directly dependent on the upstream head to crest length ratio (y₀/L_c) such that an increase in y₀/L_c results in an increase in the discharge coefficient.

In addition, the rate of the discharge leads to an increase in the discharge coefficient, which results in a decrease in the rate of energy dissipation.

The relationship between discharge and energy dissipation can be expressed with the help of the following equation:

Where, Q = Discharge over weir,

L = Length of the weir crest

H = Distance between water surface and the crest

C_d = Discharge coefficient

Thus, to calculate the value of C_d, the above formula can be rearranged as follows: