Sinking Can Boat: Debating the Rate of Water Flow

[tosse]

Assume you have a can (representing a boat) with a hole in the bottom floating in a tank filled with water. The "boat" will start to sink.

Now to my question..
My teacher told me that the speed of which water is runnig through the hole of the can is constant. But i can't seem to understand that, since (i think) the speed depends on the pressure which constantly increases as the boat is sinking - wouldn't that mean the speed increases aswell!??

 

[tiny-tim]

Welcome to PF!

Hi tosse! Welcome to PF!

Couldn't you argue that the more water in the boat, the less is the difference in pressure?

Test it by calculating what the pressure is if you put a plug in (to keep the boat afloat) when the water inside the boat is height h above the bottom

 

[nlightner]

Thank you for your question. I can understand your confusion about the relationship between water flow and pressure in this scenario.

Firstly, it is important to understand that the speed of water flow through the hole in the can is not constant, but rather it is determined by the pressure difference between the water inside the can and the surrounding water in the tank. As the boat sinks, the pressure inside the can increases, causing the water to flow out of the hole at a faster rate. This is because the higher pressure inside the can creates a greater force pushing the water out through the hole.

However, it is also important to consider the rate at which the water level in the tank is rising. As the boat sinks, the water level in the tank will increase, which means that the pressure at the bottom of the tank will also increase. This will create a back pressure on the water flowing out of the hole, slowing down the rate of flow.

So, although the pressure inside the can is increasing, the back pressure from the rising water level in the tank will counteract this and the overall rate of water flow will remain relatively constant. This is why your teacher may have said that the speed of water flow is constant.

I hope this explanation helps to clarify the relationship between water flow and pressure in this scenario. Keep asking questions and exploring scientific concepts – it's a great way to learn and understand the world around us.