Turn on a shower and the curtain sometimes billows inward, clinging against your legs, as though something were pulling it toward you rather than pushing it away — which feels backwards, given that the shower is blasting water and disturbing air right where the curtain is. The everyday explanation for this, and for a great deal of practical fluid mechanics besides, comes down to a single relationship between a fluid's speed and the pressure it exerts: Bernoulli's principle.
Faster flow, lower pressure
Bernoulli's principle, derived from the conservation of energy applied to a moving fluid, states that within a flow, an increase in the fluid's speed occurs together with a decrease in its pressure. Intuitively, energy in a smoothly flowing fluid can be thought of as split between its motion and its pressure; where the fluid speeds up, more of that available energy is going into motion, leaving less to show up as pressure pushing outward. The shower stream drags a column of air along with it as it falls, creating a region of relatively fast-moving air inside the curtain. The still air on the other side of the curtain, in the rest of the bathroom, is moving far more slowly and so sits at relatively higher pressure. That pressure difference pushes the curtain from the higher-pressure side toward the lower-pressure side — inward, against the bather, not outward as the water spray itself might suggest.
The same relationship, doing much bigger jobs
The shower curtain effect is a small, everyday demonstration of a relationship that also does far more consequential work. An aircraft wing is shaped so air travelling over its curved top surface moves faster than air travelling along its flatter underside, which by Bernoulli's principle means lower pressure above the wing than below it — and that pressure difference is a major contributor to the lift that keeps an aircraft airborne, alongside the reaction forces from air being deflected downward by the wing's angle. The same underlying relationship between fluid speed and pressure shows up across engineering: in the design of pipes, pumps, carburettors, and the venturi tubes used to measure flow rate, all of which rely on predictable changes in pressure as a fluid speeds up or slows down through a constriction.
What we're still unsure about
Bernoulli's principle itself is a settled, precisely derivable consequence of energy conservation for smooth, steady flow, and it isn't in dispute. Where explanation gets genuinely contested is exactly how much of an aircraft wing's lift Bernoulli's principle alone accounts for, versus the separate contribution from Newton's third law — air being pushed downward by the wing, producing an equal and opposite upward reaction. Physicists and aerodynamicists broadly agree both effects are real and connected rather than competing explanations, but popularised, simplified accounts of "how wings work" have long been criticised within the field for overstating Bernoulli's role in isolation, and a fully rigorous account requires the more complete equations of fluid dynamics rather than either simplified story on its own.
This sits inside Fluid Mechanics, one of eight topics in Mechanical Engineering, one of four domains in Engineering, one of seventeen subjects the app can quiz you on.