Bernoulli's theorem

Bernoulli's theorem states that the pressure in a fluid decreases as its velocity increases. In the diagram below the same amount of fluid has to pass through the constriction during any given time as passes through the wider parts of the river, so the fluid velocity v2 in the constriction is larger than the velocity v1 outside it. (This phenomenon is easy to observe in any creek or river.) As a consequence the pressure P2 is smaller than the pressure P1.

The same principle operates in the second diagram. During any given time interval the same volume has to pass through the narrow section A1 of the pipe with diameter 2h1 as through the wide section A2 (V1 = V2). Therefore the velocity v1 is larger than the velocity v2, and the pressure in the narrow part is smaller than in the wider part.

If the fluid flow is visualized by streamlines (as in the first diagram) it is seen that the pressure is large where the streamlines are far apart and small where they are close together. The third diagram applies this principle to a cross-section through the wing of an aircraft. Below the wind the air streams past undisturbed. Above the wing the streamlines are compressed. As a result the air pressure is larger underneath the wing than above it, giving rise to a lifting force.