Liquid pressure

Every liquid has weight. At any point inside a liquid at rest, the pressure there comes from the weight of the liquid column pressing down from above — so the deeper the point, the more liquid is stacked above it, and the greater the pressure. This is the single most important fact about liquid pressure at this level, and it rests on the same definition of pressure you already know:

where: $P$ is pressure, $F$ is the force pressing on a surface, and $A$ is the area over which that force acts. For a liquid, the "force" at a given point comes from the weight of everything above it, so a greater depth means a greater weight bearing down, and hence a greater $F$ and a greater $P$, even though $A$ has not changed. Three properties describe liquid pressure completely at Class 8 level:

• Depth. Pressure increases as depth below the surface increases. A point near the bottom of a tank experiences far more pressure than a point just below the surface, because a taller column of liquid presses down on it.
• Density. At the same depth, a denser liquid exerts more pressure than a lighter one. Mercury is about 13.6 times denser than water, so at an equal depth mercury pushes back much harder.
• Direction. Pressure at a point acts equally in all directions — up, down, and sideways — not only downward. This is why a submerged ball feels pressure pushing in from every side, and why water sprays sideways from a hole in a bucket's side, not just from a hole in its base.

Notice what liquid pressure does not depend on: the shape of the container, and the total amount (volume) of liquid. Two containers of very different widths, filled to the same height with the same liquid, have exactly equal pressure at equal depths — a wide tank does not press harder than a narrow tube at the same depth.

Liquid pressure grows with depth and density because pressure at a point is caused entirely by the weight of the liquid above pushing down on it, spread over an area — the same $P = F/A$ idea you already use for solids, applied to a stack of liquid instead of a solid block.

Step 1. Imagine slicing the liquid in a tank into thin horizontal layers, like pages of a book stacked flat. Each layer has weight, and that weight presses down on every layer beneath it.

Step 2. A point near the surface has only a few thin layers above it, so the downward force pressing on it is small, and the pressure there is low. A point near the bottom has the entire stack above it — every layer's weight adds up — so the total downward force is much larger, and by $P = F/A$ the pressure is much larger too.

Step 3. Density enters the same way: a denser liquid packs more mass, and so more weight, into each thin layer. Stack layers of a denser liquid to the same height, and the total weight bearing down at a given depth is greater than for a lighter liquid, so the pressure there is greater.

Step 4. The sideways and upward push follows from the liquid's ability to flow. Unlike a rigid solid, a liquid transmits the push from the weight above it outward in every direction, not only straight down — which is why a submerged object feels squeezed from all sides at once, and why a hole anywhere on a container's wall lets liquid spray out.

Question: A large aquarium tank has glass walls. Explain why the glass near the bottom is made noticeably thicker than the glass near the top, and then explain what would change if the same tank were filled with mercury instead of water to the same height.

Step 1. Compare a point on the glass near the top of the tank (small depth) with a point near the bottom (large depth), both in the same water. Apply the depth rule: liquid pressure increases with depth, so the water pressure pushing outward on the glass near the bottom is far greater than near the top, because a much taller column of water presses down on and out toward that lower point.

Step 2. Connect pressure to the glass's job: it must withstand the outward push without cracking or bulging. Since the outward push is much stronger at the bottom, the glass there needs to be thicker and stronger than the glass near the top, which only has to resist a small pressure.

Step 3. Now change the liquid to mercury, which is much denser than water, filled to the same height. Apply the density rule at any matching depth: a denser liquid exerts greater pressure than a lighter one at that same depth, so mercury would push on the glass even harder than water did at every corresponding point.

The glass walls are thicker near the bottom because pressure rises with depth, and if the tank held mercury instead of water, every wall — top and bottom alike — would need to be thicker still, because pressure also rises with the liquid's density.

Competitive stretch

If a third tank held oil (less dense than water) filled to the same height, the pressure at any given depth would be lower than in the water tank — so its glass could safely be thinner than the water tank's glass at the same depth, though still thicker at the bottom than at its own top.

• Thinking a wider or larger container holds "more pressure" because it holds more liquid — pressure at a point depends only on depth and density, never on the container's shape or the total volume of liquid it holds.
• Assuming liquid pressure pushes only downward, like gravity — it actually pushes equally in every direction at a given point, including sideways and upward on a submerged surface.
• Mixing up depth and density as if they were the same factor — both raise pressure, but a shallow point in a dense liquid (like mercury) can have higher pressure than a deep point in a lighter liquid (like water); they must be reasoned about separately.
• Reaching for the formula $P = h\rho g$ on a Class 8 test — this exact relationship, and Pascal's Law, belong to Class 9; at this stage you are expected to reason in words, not calculate a numeric pressure.

Ask the tutor: Want to see how these same depth-and-density ideas turn into the exact formula $P = h\rho g$ next year, or work through a few more "which point has greater pressure" comparisons? Ask the AI tutor.