In a lecture about meteorology I learned that so called geostrophic wind follows lines of constant pressure. Since both pressure and Coriolis force are perpendicular to the direction of motion (Coriolis by definition and pressure force, because we are moving on a line with constant pressure with pressure gradient perpendicular to motion) the air parcel must have constant magnitude of speed, since all forces on it are perpendicular to its motion. On the other hand, speed of geostrophic wind is given by the balance of pressure gradient and Coriolis force - so in equilibrium, speed is proportional to the gradient of p or to the density of lines of constant p. Typically this gradient changes spatially - therefore wind speed changes too and increases at points, where the pressure gradient is higher. But how can it change at all, if all forces are always perpendicular to its momentary direction of motion? I cannot resolve this discrepancy.