Part 2:
Now, let’s modify our drawing slightly. Suppose we’ve welded the piston to the left side of the container. There is no air at all between the piston head and the left wall; they are mechanically joined.
We can redraw the perpendicular forces, and unsurprisingly, there are no net forces acting on the piston. The perpendicular forces (drawn in blue) cancel each other out exactly, just as they did before. However, the difference this time is that there are no forces acting on the piston head, as no air is present between the wall and the piston head to exert any pressure.
You may notice a slight change in the forces acting around the O-ring. The forces acting on the O-ring would certainly push it outward. These forces were present in the previous illustration as well, but I omitted them for clarity. But remember, it is the O-ring getting pushed, not the piston. There is not force that can push the piston towards the right, as they all act perpendicular to it.
Now, let’s revisit the balanced piston, but this time with a piston that is free to move and not fixed to the walls of the container.
You’ll notice there is virtually no difference from the previous illustration. How could there be? The high pressure is still unable to pass between the piston head (now forming the orifice) and the wall of the container (now occupied by the seat). The perpendicular forces act on the walls of the piston, cancelling each other out. From this, it’s clear that no matter the supply pressure, whether 10bar or 100bar, as long as the piston is closed and touching the seat, there are no net forces acting on the piston from the high-pressure side. All forces are perpendicular to the piston, and none of these perpendicular forces point in a direction the piston could move.
The above is an idealistic view of how the piston is balanced. In reality, the edge of the piston (the orifice) cannot be machined perfectly flat and sealed; this is mechanically impossible. There must be an edge machined into it, and no matter how sharp I make it, this edge will always be slightly thinner than the rest of the piston and, more importantly, the inner sealing diameter of the piston O-ring. The illustration below is greatly exaggerated, but the principle holds true in real-world scenarios.
Notice how the purple forces are still perpendicular to the edge (orifice) of the piston. However, they are no longer perpendicular to the shaft of the piston. As a result, these forces impart a tiny force pushing the piston toward the lower-pressure side. This tiny vector of forces pushes the piston to the right, which is why this design is not truly fully balanced. Supply pressure does play a role in opening and closing this mechanism and will change with changes in supply pressure.
Engineers have become increasingly clever and worked around this limitation as well. By increasing the orifice of the piston, we give the high pressure a larger area to act against, pushing the piston toward the closed position. This means I need a lower intermediate pressure to close the piston, as part of the work is done by the high pressure.
The opposite is also possible: by effectively making the orifice smaller than the piston shaft, I can use the high pressure to assist in opening the piston.
However, in reality, the engineer doesn’t want the high-pressure supply to play any role in opening or closing the piston. Therefore, they slightly widen the orifice or, more precisely, thin the diameter of the stem. They ensure that the orifice diameter after having a edge machined into it matches the stem diameter, or more accurately, the inner sealing diameter of the stem O-ring exactly.
The one thing I usually omit is how the O-ring on the piston shaft interacts with things. In the above I have dismissed it, which is not entirely correct. There is an ever so slight downward force onto the piston from the O-ring dragging on it. In an ideal world the friction would be zero, but even with the best lubricant there is still some tiny friction left.
In the end I find this fascinating from an engineering point of view. From a practical standout I find it all but irrelevant. Those tiny drops of not being fully balanced don't make any difference in the real world, it is a gimmick, nothing else.