Q.Two sheets of paper are held vertically, a small distance apart and parallel to each other, and air is blown steadily through the narrow gap between them. Explain, using Bernoulli's theorem, why the two sheets move towards each other instead of moving apart.

When air is blown steadily through the narrow gap between the two vertical sheets, the air in that gap is moving comparatively fast. By Bernoulli's theorem, applied at the same height (so the $\rho gh$ terms are the same on both sides), a region of faster-moving air corresponds to a region of lower pressure: the pressure energy term $P$ must decrease to compensate for the increase in the kinetic energy term $\tfrac12\rho v^2$, so that the sum $P + \tfrac12\rho v^2$ stays the same as it was in the still air before it entered the gap. …

Identify that the air in the gap is moving faster than the still air outside the sheets, apply Bernoulli's theorem (constant height) to conclude the gap is at lower pressur …

• Assuming that blowing air "into" the gap should push the sheets apart, by analogy with blowing air directly at a single object -- the relevant effect here is the pressure drop in the fast-moving air, not a direct push from the air stream itself. …