# Relationship between critical depth and discharge coefficient for free overflow on dam spillway

In general, the discharge for free overflow on dam spillway can be expressed as follow:

On the other hand, a critical depth of rectangular cross section channel can be expressed as follow:

When it is assumed the water depth at the overflow crest of the dam is equal to the critical depth, the design head including approach velocity head can be expressed as follow:

Considering a unit length of overflow crest which means ,

From above, can be expressed as follow:

Therefore, discharge coefficient becomes a constant and it can be expressed as follow:

That is all.