There are basically two ways to make fluid flow through a pipe.

1. Tilt the pipe and let gravity pull the fluid downhill.
2. Make the pressure higher at one end of the pipe than the other. A pressure difference is equivalent to a net force, accelerating the fluid toward lower-pressure regions.

In our tube of varying cross-section, where is the pressure greatest?

1. At the ends, where the tube is wide (9/31) (29%)
2. In the middle, where the tube is narrow (22/31) (71%)

The fluid speeds up as it enters the narrow section, and then slows down again as it emerges into the wide section. The pressure must therefore be largest at the ends, and smaller in the narrow section.

This might be counter-intuitive. Don't we feel a force when we stick our hand into a fast-flowing fluid? Yes, but that's not the fluid pressure we're sensing. We're changing the momentum of the flowing fluid, so it exerts a force on us.