Pressure in fluids

Fluids push in every direction, not just down. A solid resting under gravity only presses downward on its support. A fluid is different: because its particles are free to move and settle against every surface they touch, a liquid or gas presses on the base and the walls of its container, and on every face of an object immersed in it — top, bottom and sides alike. This is why a balloon held underwater feels squeezed from all around, not just pushed downward.

Pressure increases with depth. Imagine slicing a tank of water into thin horizontal layers. A point near the surface has only a shallow layer of water above it, so little weight presses down. A point near the bottom has the entire column of water above it pressing down, so the pressure there is much greater. In words, without introducing density or a numerical formula:

where: the "depth" is measured straight down from the free surface of the fluid to the point in question, and the proportionality captures the qualitative fact tested at this level — go deeper, feel more pressure. (The full relation, $P = h\rho g$, brings in the fluid's density $\rho$ and is developed only from Class 10 onward; Class 9 uses the proportionality idea alone.)

At a fixed depth, pressure is the same in every direction. A submerged object at one particular depth feels equal push from above, below and the sides at that depth, because the fluid around it has the same weight of fluid above every point at that depth. This is a distinct fact from "pressure increases with depth" — one compares different depths, the other compares different directions at the same depth.

Air is a fluid too. The atmosphere presses on everything at the Earth's surface exactly the way a liquid presses on a submerged object, and for the same reason: it is greater at sea level, where a taller column of air sits overhead, and smaller on a mountaintop, where less air remains above.

Pressure in a fluid comes from the weight of the fluid itself pressing down through every layer beneath it, combined with the fluid's ability to transmit that push sideways and outward because its particles are not locked in place the way a solid's are.

Why deeper means more pressure. Picture the fluid as a stack of thin horizontal slabs. Each slab has to support the weight of every slab above it, plus pass that weight on to the slab below. A point near the bottom of the tank is beneath the entire stack, so it experiences the combined weight of every slab above — far more than a point just below the surface, which has only a thin slab of fluid overhead. This is exactly why a dam is built thicker at its base: the water pressure at the bottom of a dam, where the water column above is tallest, is much greater than near the top, and the structure must be strong enough to resist that greater thrust.

Why the push is not just downward. A solid resting on a table only presses down because gravity pulls straight down and the solid's shape holds it rigid. A fluid's particles, by contrast, are free to slide past one another and settle against any surface, so the weight of fluid above a point gets redirected sideways and even upward against any surface at that depth — this is why a submerged wall feels a sideways push, and why a submerged object is squeezed from every side rather than just pressed downward. At a single depth, this redirected push is equally strong in every direction, since the same weight of fluid sits above every point at that level.

Why this sets up buoyancy. Because the pressure pushing up on the bottom of a submerged object is at a greater depth than the pressure pushing down on its top, the upward push is slightly larger than the downward push. That small difference in pressure between the bottom and top faces is precisely what produces the net upward buoyant force explored in the next article — it is a direct consequence of "pressure increases with depth" applied to two faces of the same object.

Question: A diver swims from the surface of a lake down to a depth of 10 m, and notices the squeezing sensation on the eardrums becomes uncomfortable. Two identical balloons are then held underwater, one at 2 m and one at 8 m depth. Using only the qualitative facts about fluid pressure, (a) explain the diver's discomfort, and (b) state which balloon feels the greater water pressure and in how many directions the water pushes on each.

Step 1. Explain the diver's discomfort. At the surface, only a thin layer of water (plus the atmosphere) presses on the diver. As the diver descends to 10 m, an increasingly tall column of water lies above at every deeper point, so the water pressure on the diver's body rises steadily with depth. By 10 m, this larger pressure pushes inward on the eardrum, producing the squeezing sensation — a direct consequence of pressure increasing with depth.

Step 2. Compare the two balloons' depths. The balloon at 8 m has a taller, heavier column of water above it than the balloon at 2 m. Since pressure increases with depth, the balloon at 8 m experiences the greater water pressure.

Step 3. State the number of directions at each depth. At its own depth, each balloon is pushed on by water from every direction — top, bottom and sides — equally, because a fluid exerts pressure in all directions on any surface it touches at a given depth, not only downward.

Step 4. Combine the two facts. Answer: the diver's ears hurt more at 10 m because water pressure increases with depth; the balloon at 8 m feels the greater pressure than the one at 2 m, but at their own depths, both balloons are pushed on equally from all directions (top, bottom and sides).

• Thinking fluids only push downward, the way a solid resting under gravity does — fluids also push sideways and upward on every surface they touch.
• Assuming pressure is the same at every depth in a fluid — it increases with depth, which is why dams are thicker at the base and divers feel more pressure lower down.
• Treating atmospheric pressure as negligible because air feels weightless — air is a fluid too and presses substantially on everything at the Earth's surface, more so at sea level than on a mountain.
• Trying to compute pressure using $P = h\rho g$ with numbers for density at this stage — Class 9 keeps the idea qualitative; the density-based formula belongs to Class 10 and 11.

Ask the tutor: want to see how this pressure-increases-with-depth idea turns into the buoyant force and Archimedes' Principle in the next article?