Your quest for a "mechanism" is almost sure to fail as you are talking about how an Avogadro number of molecules interact with each other. That is precisely why instead of macroscopic quantities like energy and density (in the continuity equation) are used.

However, we can still try to get some intuition more than just saying energy is conserved (I will still use it though) for the case of ideal gas. 

The point is pressure come from force per unit area from random motion of molecules. When the fluid **has to** (continuity equation) pass through a narrow tube, it has to increase its velocity in a certain direction (i.e. the tube direction) and then since energy **has to** be conserved, assuming 'thermalization' happens at time scales much faster than it takes to pass through the tube, the fraction of energy available for 'random' kinetic energy and thus pressure, is less.

If you prefer mathematical expressions, for $N \gg 1$ molecules of unit mass, the total energy (ignoring potential energies from bound states and walls of container) is 

$$
2 E = \sum_{i=1}^N v_i^2 = \sum_{i=1}^N (v- \langle v \rangle +\langle v \rangle)^2 \\
=\sum_{i=1}^N (v- \langle v \rangle)^2 + \sum_{i=1}^N\langle  v \rangle^2 
$$
where $\langle v \rangle$ is the mean velocity and the cross terms vanish because the 'random flucatuations' about the mean are isotropic. The first part contributes to pressure and the second is the velocity through the tube. You can clearly see the effect you mentioned.