A container that is 1.2 meters under the sea near the shore is full of water of density 1,020 kilograms per cubic meter. The container is suspended above the seabed on a pole. The container is 3.5 meters in height. Water can enter and leave the container through three holes in its walls and one hole in its base, as shown in the diagram. Water pressure is increased gradually at one of the holes in the walls until the pressure there is 7,500 pascals. Is the pressure 𝑃 one greater than, less than, or equal to 7,500 pascals?
Here is our container that we’re told is entirely submerged in water. The container has four openings in it: one on this end, one on this side, one on this end, and one on the bottom. So these are all places where water can move into or out of the container. This first part of our question is about the pressure, labeled 𝑃 one. And that’s the outward pressure exerted by the water at this opening in the container. We want to know how 𝑃 one compares to 7,500 pascals, the pressure pushing in on the container at this opening.
If we were to look at a side-on view of our container, it might look like this. From this perspective, we have our 7,500-pascal pressure acting in from this end. And as we’re seeing it, the pressure 𝑃 one points into the screen. The key to answering this first part of our question is to realize that the opening through which pressure 𝑃 one acts and the opening through which there’s this pressure of 7,500 pascals are both at the same depth below the surface of the water above the container. In other words, these two distances indicated by the pink arrows are the same. Because these two openings in the container have the same depth, that means they also have the same pressure. This must be the case because both openings have the same amount of water pushing down on them. In answer to our question then, we write that the pressure 𝑃 one is exactly equal to 7,500 pascals.
The next part of our question asks, is the pressure 𝑃 two greater than, less than, or equal to 7,500 pascals?
Looking back at our side-on view of our container, we see that the pressure 𝑃 two acts through this opening. This opening is the same depth below the surface of the water as the other two in the container sides. That’s the determining bit of information in comparing the pressure 𝑃 two to 7,500 pascals. Because these two pressures act at the same depth, they’re equal. The pressure 𝑃 two is equal to 7,500 pascals.
Let’s now look at the last part of our question.
Is the pressure 𝑃 three greater than, less than, or equal to 7,500 pascals?
𝑃 three is the pressure that acts through the opening in the bottom of our container. In terms of this opening’s depth below the surface of the water, we see that it’s at a greater depth than the other openings. This means that there’s effectively all this water contributing to additional pressure through this opening. In our problem statement, we’re told the height of our container as well as the density of the water in it. We could calculate the difference between the pressure here in the side of the container and the pressure 𝑃 three. But for this question, we just need to know if 𝑃 three is greater than, less than, or equal to 7,500 pascals. Because the opening at which the pressure 𝑃 three acts is at a greater depth than the opening that has a pressure of 7,500 pascals, the pressure 𝑃 three is greater than 7,500 pascals.