Okay so I watched this YouTube video of a guy doing applied differential equations and he was able to find the equation for the height of water as function of time in a cylinder and when it reaches zero. What I want to understand is how to find the volume flow rate as a function of time and not the height.

Isn't the best way to solve this is to find the derivative of the height function and that would give you change in volume over time? My logic behind this is that a small change in height of the water will give you the volume.

Video: https://youtu.be/sUroO7PXm5M