# Water pressure under shelf

1. Sep 19, 2010

### jackrabbit

I understand that water pressure is solely a function of the weight of the water column (plus atmospheric pressure) above a given point in the body of water. Ignoring atmospheric pressure, assume that a water column above a given point at the bottom of a tank of water is 10 pounds. Assume that, half way up the side of the tank, a rigid shelf is attached to the wall that extends a foot or so horizontally out into the water. (Assume that the tank is several feet wide, so that the shelf only extends part way across). Is the water pressure at the bottom of the tank under the shelf only 5 pounds? And as soon as you step out from under the shelf, is the pressure back to 10 pounds? Or is the calculation more complicated than that, and if so, why?

Stated differently, if you swim into a cave at the bottom of the ocean, is the water pressure dramatically different than outside the cave?

2. Sep 19, 2010

### Studiot

Definitely not. It would be dangerous to find out the hard way.

The water pressure under your shelf is identical to the water pressure at the same depth, but not under the shelf.

3. Sep 19, 2010

### jackrabbit

Thanks. Why is that the case? Why wouldn't the shelf (or the cave) carry the pressure of the water above it (and if it were strong enough, not transfer the pressure to the water below it)?

4. Sep 19, 2010

### jackrabbit

To further elaborate on the question, if the shelf extended all the way across, so that it effectively cut the water tank in half, presumably the pressure at the bottom of the tank would be cut in half as well, right? Or not? But if I leave any space between the shelf and and the side, then the pressure at the top and bottom equalizes for some reason?

That sounds right intuitively, but I'm wondering about the math. Why does that happen if pressure is solely a function of the water weight above a given point?

5. Sep 19, 2010

### jackrabbit

Water pressure in triangular container

I'm trying to figure out whether water pressure is uniform across the bottom of a container shaped like a right triangle. Imagine that one of the shorter sides is the base, so there is a 90 degree angle on one side of the base and an acute angle on the other. Is the water pressure less in the corner with the acute angle than in the corner that is 90 degrees? The height of the water above the 90 degree corner is much greater than in the other corner, so is the water pressure greater in the 90 degree corner as a result? Or is there some principle that requires uniformity across the base?

6. Sep 19, 2010

### Staff: Mentor

If water pressure were differrent at two points right next to each other, the water would have to flow from the high to the low pressure, wouldn't it?

Consider your house: is the air pressure much different inside than outside?

Last edited: Sep 19, 2010
7. Sep 19, 2010

### jackrabbit

Thanks Russ Watters.

Yes, I suppose it should flow from the high pressure to the low pressure zone, but if the water is in a closed container, there is nowhere for the water to flow. So, I assume the pressure just builds in the corner until equilibrium is reached. Is that the way it works? So that, in fact, water pressure is not simply a function of the weight of the water column above a given point? And, in the triangular container example, the water pressure would be the same across the entire base?

I thought about the air pressure in the house example as well. Does gas behave exactly the same way as fluid on this point?

8. Sep 19, 2010

### Drakkith

Staff Emeritus
Water is a fluid, and will transfer the pressure along with the water no matter if it has to go around corners or under shelves.

If i extend your shelf all the way across the tank and put a small hole in it, then the force of the pressure will "transfer" through that hole into the rest of the tank i believe. If i simply extended your shelf all the way across to cut the tank in half, and if the shelf were strong enough to take the water pressure above it without transferring it into the water below it, then at the bottom of the tank the pressure would be half of the normal pressure, since the shelf absorbs the weight of the water above it.

Edit: Also, remember that water pressure is putting pressure on something from all sides, not just from above or below or to the side. So standing underneath a shelf underwater wouldnt do you any good for the reasons i've mentioned above.

9. Sep 19, 2010

### Staff: Mentor

If it flows a few nanometers it will adjust the pressure distribution enough to equilize the pressure.
Well if a container is closed and applies its own pressure to the water, you just add the pressure added by the container.
Yes.
Gas is a fluid, so yes.

10. Sep 19, 2010

### rcgldr

Depth related pressure is a function of density times height (assuming constant gravity force and density). The shape of a container and the actual amount of water or the weight of the water doesn't matter, only the height and density of the water. The pressure at the bottom of a 30 foot deep cylindrical tank is the same regardless if the tank has a radius of 1 inch or 1 mile.