[Intro Fluids] Trying to figure out the rate at which oil will fall out of a tank in a car.

I have a tank of oil that has a hemispherical shape of R, the tank has an opening of area A at the bottom which the oil leaks out. If the depth of oil is measured from the lowest point at the bottom of the tank which is at a point z, and the depth decreases as oil drops out of the tank. If I make the assumption that the surface of the oil remains flat show that: [; \frac{dz}{dt} = -\sqrt { \frac { 2gzA^2 }{ \pi^2r^4 - A^2 } } ;]

where R is the radius of the hemisphere, and r is the local radius of a position of the fluid surface equivalent to a spherical co-ordinate.

The problem that I am having is that I am not sure which law I would need to use. i.e conservation of mass, conservation of momentum, or Bernoulli's equation. I feel like I would have to you a mixture of both conservation of momentum and Bernoulli's equation but i'm not 100% sure. Any guidance would be greatly appreciated to get me started. Cheers