# Rate of water flow into an immersed container

Hi,
I am wondering how I may calculate the rate of water flow into a container(say, a empty box) with a hole in it, and with the whole box immersed in water. Does it have something to do with the force of water pushing against the container, and calculating how fast water can flow through the hole as a result of that force? Or do you assume the hole is a pipe of small width, and use the equation of continuity from there?

Thanks!

Baluncore
Welcome to PF.
You could consider the differential pressure available across the hole and compute the acceleration of the water needed to get it through the hole. Don't forget the rising internal pressure due to air that may be inside the empty box. It is escape of that air that may regulate the filling of the box.

My physics knowledge is quite limited, so I'm still unsure as to how could I find the differential pressure. Will I need to use a measurement instrument and physically measure the difference in pressure outside and inside of the box, and/or is it possible to find theoretically? I am also unsure of the equations and relationships that link the acceleration of the water to the pressure. I've tried to find some resources on this, but I've only seen posts about leakages from a container, not into one. Are there any search terms/ that I should be using for this?

Baluncore
There is no one equation that will answer such a hypothetical situation.
We need a better description of the system you are trying to analyse. Is it a submarine or a glass bottle?
You will need to identify the initial condition, is the box really empty or does it contain air at atmospheric pressure?
What are the dimensions and orientation, of the box and the hole?
How thick is the wall of the box at the hole?
How deep is the hole in the box below the surface? Is it submerged in sea water of fresh water?

The pressure difference is the hydrostatic pressure due to water depth at the hole, less the rising pressure inside the box as it fills.
It is easier to calculate pressures than to measure.

Unless you can better describe the problem here, the only answer will be to suggest you study computational fluid dynamics.

SonfusedCoul