Supplied continuously-Tank Draining Problem

[nj_sk]

Homework Statement

OK, here is my problem.
There's a tank, continuously filled by water from top, at 5 L/minute flow rate. The tank has a hole on bottom (at h=0) of it, so water also come out through it. The Area of hole is 1 cm² and Area of tank is 0.25 m².
The height of the tank supposed to be very high so water can't out.

The question is about equation h(t), that is height of water in the tank versus time.

Homework Equations

My teacher told us to start from Bernoulli's Law, but I'm stuck now...the problem just confused me because there is continuously water supply...

The Attempt at a Solution

I realized that water flow at the hole is dependent on height of the water, and height is also dependent on time.

Any idea? Please help me. Thanks in advance.

 

[merryjman]

This sounds like a classic problem in differential equations. Like you said, the rate of water flow out the bottom depends on height, and the height depends on the overall water flow which is a combination of the drain and the continuous supply. So write a differential equation that includes all this.

Intuitively, since the tank is very tall, you can imagine that there will be a point where the inflow and outflow rates become equal: the height - and therefore water pressure - becomes large enough so that the outflow approaches 5 L/min, and the tank stops filling. So I would think you're looking for some sort of exponential decay.

 

[nj_sk]

Yes, I also think it's a differential problem, but my teacher wasn't. I don't know why he said that we don't need to use differential equation...he's a professor in quantum physic, expert one, so I still confuse about that...is it true that we don't need it? Is it possible?

Still, I can't make a differential equation too...(I am new here, also not so smart in physic, this is not my field actually...)

 

[nj_sk]

OK. I have figured it out.

I build a differential equation, solve it using finite difference.

dh/dt = ((2-A2*sqrt(2g*h))/A1

 

[hikaru1221]

You should check your equation. It's wrong, at least, in the dimensions; but the form looks fine.
Maybe your professor meant, computing a direct integral is not solving a differential equation?