What is the coefficient of discharge and why use it as z?

[werson tan]

Homework Statement

why the author consider the coefficient of discharge as the z here ? what is exactly coefficient of discharge?

Homework Equations

The Attempt at a Solution

 

[BvU]

1. He doesn't . $\Delta z$ happens to be 0.61 m here. You can check: it has a dimension. C has not. (*
)
2. Didn't google work ? Plenty links when I try !(*) the author is rather sloppy with dimensions. $\rho_0$ has a dimension too.