You might associate high pressure in a fluid with high velocity. Everyday experience makes it clear that the pressure from a hose spraying a jet of water is much more intense than the pressure from a gentle stream, but this intuition can sometimes lead you astray.
In a bottleneck, high velocity doesn't mean high pressure.
The last challenge involving flow revealed how the flow velocity changes through a bottleneck. It turns out that keeping track of the velocity can tell us a lot about how the pressure changes. For example, with a steady flow of water through a bottleneck, the flow velocity is always the highest at the narrowest point.
When the water is flowing from a wide pipe to a narrow pipe, the flow speeds up as it goes through the bottleneck. This is just another way of saying that the water is accelerating. According to Newton's laws, acceleration can only be caused by an unbalanced force. Forward acceleration means that the net force on the water must be pushing in the forward direction.
The force exerted by a fluid is usually referred to as pressure. Any unbalanced force accelerating the water must be explained by unbalanced pressures on the wide and narrow sides of the pipe.
If the water is speeding up through the bottleneck, we can conclude that the pressure behind the water must be greater than the pressure in front of it.