Viscosity: fluids that stick
Pour honey and water side by side and honey lags far behind. The difference is viscosity — a fluid's internal friction, its resistance to being sheared. Neighbouring layers of a real fluid drag on one another, and — a fact that surprises people — the layer touching a solid wall does not slip at all; it sticks. That “no-slip” condition means flow in a pipe is fastest in the middle and zero at the walls, dragged back by viscosity all the way across.
Viscosity has dramatic consequences. For smooth (laminar) flow through a pipe, the flow rate scales as the fourth power of the radius, Q \propto r^4 \,\Delta P / (\eta L) — Poiseuille's result. Halve a pipe's radius and, for the same pressure, the flow drops by a factor of sixteen. This is why a slightly narrowed artery is so dangerous, and why forcing fluid through a fine needle takes surprising pressure. Viscosity is measured in pascal-seconds (Pa·s); water is about 0.001\text{ Pa·s}, honey thousands of times more.
Laminar, turbulent, and the Reynolds number
Watch smoke rise from a stick of incense: for a few centimetres it climbs in smooth, glassy ribbons, then abruptly dissolves into swirling chaos. The first regime is laminar flow — orderly layers gliding past one another; the second is turbulence — a churning tangle of eddies within eddies. Turbulence mixes ferociously and dissipates far more energy, and it is one of the great unsolved problems of classical physics.
Which one you get is predicted by a single dimensionless number — the Reynolds number, the ratio of a flow's inertia to its viscosity. Small \mathrm{Re} means viscosity dominates and smooths everything into laminar flow; large \mathrm{Re} lets inertia win and the flow tumbles into turbulence (in a pipe, the switch comes near \mathrm{Re} \approx 2300).
The Reynolds number compares inertial to viscous effects (ρ density, v speed, D a size scale, η viscosity). It is dimensionless — a pure number that sets the flow's character.
Drag, terminal velocity, and surface tension
Drop an object through a fluid and it does not fall forever faster. The fluid resists with a drag force that grows with speed, until drag plus buoyancy exactly balances gravity; from then on the object coasts at a steady terminal velocity. It is why a skydiver settles near 55\text{ m/s}, a raindrop lands gently instead of lethally, and a coffee filter flutters down almost at once. Drag and buoyancy are the fluid's two upward votes against a falling object's weight.
At the surface of a liquid a different force rules. Molecules in the bulk are pulled equally on all sides, but a molecule at the surface is pulled only inward and sideways, so the surface behaves like a taut elastic skin. This surface tension lets a water strider walk on a pond, pulls small droplets into spheres, and drives water up a narrow tube against gravity (capillary action). It even sets a pressure: the tighter you curve a surface, the harder it squeezes.
The Laplace pressure inside a spherical droplet of radius r and surface tension γ: smaller drops carry a higher internal pressure (a soap bubble, with two surfaces, gets 4γ/r).
Capstone: a draining tank
Let us pull the track together on one problem, using pressure, continuity and Bernoulli at once, and staying honest about the idealisations.
Where fluid physics leads next
You now hold the whole beginner's arc: density and pressure, hydrostatics and Pascal, buoyancy and Archimedes, continuity and Bernoulli, and the real-fluid corrections of viscosity and turbulence. Assembled fully, these ideas become the Navier–Stokes equations, the master equations of fluid motion. They govern weather and climate, the flow of blood and the design of aircraft and ships, ocean currents and the plasma in stars — and their turbulent solutions are so hard that one of mathematics' million-dollar Millennium Prize problems asks merely whether smooth solutions always exist.