What counts as a fluid?
Look around and most of the world is not rigid. The air you breathe, the water in a glass, honey, blood, molten lava, the whole ocean and atmosphere — none of them holds a shape of its own. Tip the glass and the water pours; open a window and the air moves in. Anything that flows and takes the shape of its container is a fluid, and — this surprises many beginners — that includes both liquids and gases.
The deep reason is that a fluid cannot resist a sideways (shear) push the way a solid can. Push the top of a brick sideways and it stays a brick; push the top layer of water sideways and it just keeps sliding forever. A solid deforms a fixed amount and stops; a fluid deforms continuously under any shear, however small. That single property is the seed of the entire field.
Density: how much matter in how much space
Why does a small lead fishing weight sink instantly while a gigantic steel ship floats? The answer is not weight alone but how tightly the matter is packed. We measure that packing with density: the amount of mass contained in each unit of volume.
Density (the Greek letter rho) is mass divided by volume. Its SI unit is the kilogram per cubic metre, kg/m³.
Water sets the scale: \rho_{\text{water}} \approx 1000\text{ kg/m}^3 (the same as 1\text{ g/cm}^3). Air is about 1.2\text{ kg/m}^3 at room conditions — nearly a thousand times thinner. Lead is 11{,}300\text{ kg/m}^3; gold, 19{,}300. Density is an intensive property: a drop of water and a bathtub of water have exactly the same density. It is a fingerprint of the material, not of the amount.
Pressure: force spread over an area
Press your palm flat against a table and nothing happens. Press a thumbtack with the very same push and it drives into the wood. The force is identical; what changed is the area it acts over. Concentrate a force onto a tiny area and its effect explodes; spread it out — as snowshoes spread your weight over soft snow — and it barely dents the surface. That force-per-area is pressure.
Pressure equals the force pushing perpendicular to a surface, divided by the area of that surface. Its SI unit is the pascal: 1 Pa = 1 N/m².
A pascal is a small unit — one newton (about the weight of an apple) spread over a whole square metre. So real pressures reach big numbers: the atmosphere presses on you at about 101{,}000\text{ Pa} \approx 100\text{ kPa}, a car tyre holds roughly 200\text{ kPa} above that, and the deep ocean reaches hundreds of times atmospheric. We simply do not notice the air's crush because it pushes equally from every side, inside and out.
Pressure pushes in every direction
Here is the property that makes fluids behave so differently from solids. At any point inside a fluid at rest, the pressure pushes equally in all directions — up, down, and sideways. Pressure itself is a single number (a scalar) with no direction of its own; but wherever the fluid meets a surface, it pushes on that surface at right angles, with a strength set by the pressure there.
This all-directions push explains why a balloon inflates into a smooth sphere and why a submerged object is squeezed from every side. It is also the hinge for everything ahead: because pressure acts everywhere at once, we can ask how it grows with depth (Guide 2), why it lifts submerged objects (Guide 3), and what happens when the fluid finally starts to move (Guides 4–5).