How to Model the Volume of Water in a Graduated Cylinder with a Hole?

[RagincajunLA]

Hey guys, its my first time posting and i really need some help with a problem.
I have an experiment of a graduated cylinder with a hole at the bottom of it. I basically need to model a differential equation to give the volume of water in the cylinder at any given time. I am not allowed to directly use torriciellis law or bernoullis principal, but i can show the derivation of them for the answer.

A few key measurements that are needed are:
Initial Volume = 1000cm^3 = .001m^3
radius of outlet=.0018m
radius of cylinder = .031m
Initial height of water = .36m

All help would be appreciated, I am really stuck and have been at this for hours :/

 

[Sakha]

I can't think of anything not involving Bernoulli's. What have you been learning in class?

 

[RagincajunLA]

well the thing is, we can't explicitly use bernoullis/torricielli's but if we show the derivation, then that's ok. I was on the track of using conservation of energy to find the velocity of the water leaving the cylinder. but when i do everything out and find the equation for volume, I am very far off from the first data point which is t=3.4s and volume=950cm^3=9.5e-4