You have basically the following image. We know the height at all the points, so we just need to know a velocity and pressure at some more points to determine the velocity at $C$. Where do we know the pressure? At point $A$ and $C$! Why? We know that if a surface is exposed to air, it must be atmospheric pressure. If it wasn't, there would be pressure difference and a force, so the system would not be in equilibrium$^\dagger$. It is hard to say whether point $C$ is in equilibrium because water is spilling out, so I tried to draw it this way to make it a little more clear.
Since the velocity at the point $A$ is zero, we have enough information to solve the system. Define the height at point $A$ as zero, then
\begin{align}
P_A+\tfrac 1 2\rho v_A^2+\rho gh_A&=P_C+\tfrac 1 2\rho v_C^2+\rho gh_C\\
\implies P_0+0+0&=P_0+\tfrac 1 2\rho v_C^2-\rho g d_{AC}
\end{align}
where $P_0$ is atmospheric pressure and $\rho$ is the density of the water.
$\dagger$ With 'in equilibrium' I mean that the problem does not change in time. This problem is an example of hydrostatics, which only deals with 'static' configurations of fluid. This might seem confusing because the water is moving, but we define a fluid as static when all important variables such as velocity, pressure etc. do not change in time. The water level is dropping, but it is dropping slowly enough that we can neglect this.
