Detailed analysis of the hydrostatic balance machine.
The inventor has designed this machine cleverly, to mislead the reader into thinking it might work. The flaws can be exposed on several levels of physics. I shall tease the reader by analyzing this slowly, gradually revealing the essential flaws that prevent this from working. That makes this document grotesquely long, for these two figures supplied by the inventor have subtle details, and he will not be satisfied until we address every one of them.
Force and torque analysis 1.
Let's analyze the system of Fig. 2., which is an allegedly perpetually turning machine. The assembly of buoyant can (56) and its curved rigid tail (60, shown in dotted outline) has four little wheels that keep this assembly stabilized. As usual we begin by assuming zero friction. The wheels are located so that three of them provide only horizontal forces to the tube, and therefore cannot affect the scale readings. The lowermost wheel (62) provides only an upward force, but since the line of action of that force passes through the pulley axles, it can't provide a torque that would unbalance the system.
When the buoyant can is put into the liquid, the water levels rise on both sides, as the diagrams correctly show.
The only thing that can cause the spring balance readings to change would be a change in upward force components on the flexible tube. The pressure on the vertical portions of the tube walls exerts strictly horizontal force and can't affect the spring balance readings. The only place where vertical components of force act on the tube are on the U-shaped section at the bottom. These forces are larger when the buoyant can assembly is in place, but they are balanced left and right, for the pressures on the walls of the tube in the U shaped section are strictly dependent on height. These pressures and these forces all increase in size when the can assembly is put in (and the water level rises in both tubes). But these forces remain in balance, and their net torque is zero in any case. So there's no reason to expect the system to turn.
Force and torque analysis 2.
What is the purpose of the little wheel (54) on the top left side of the can? Obviously it is needed to keep the can in position within the liquid, for without it the can would move to the left and directly contact the tube wall. In either case, that contact with the wall provides horizontal force at the point of contact. If we consider torques on the can, about the axle of the lower pulley, this force has a clockwise torque that will adjust in size to exactly counterbalance the torque due to buoyant force of the liquid on the can. The net torque on the can and its stabilizing assembly is zero. (The other three wheels give zero torque, since their forces pass through our chosen center of torques.)
But isn't the left side heavier? The inventor suggests that the left side of the apparatus is heavier since the water levels are the same, and part of the water on the right is displaced by the can. Then the inventor supposes that this extra weight would make the entire apparatus rotate in the direction of the arrows. This does not follow. This museum has many examples of wheels that are continually heavier on one side of the axle, yet do not initiate or sustain motion.
The liquid in the tube exerts force due to pressure, and those forces are always perpendicular to the tube walls. They cannot exert force parallel to the walls, and therefore cannot produce any force to cause the tube to initiate or sustain rotation in either direction. The only things that can exert force parallel to the tube walls are the four little wheels. Even if they indent the flexible tube walls somewhat, the only force they can exert would be in a direction to oppose motion of the tube.
Loose ends. Oh, yes. What about that counter-clockwise torque that the can assembly (56, 60) exerts on the tube? It is exactly opposed by a couple made up of horizontal forces supplied by the upper and lower pulleys (if the system has both pulleys), or by flexing of the tube where the little wheels press on it. There is no net torque on the flexible tube.
Finally, there's the ultimate "gotcha" to frustrate the inventor. If you intend to extract any energy from this machine, you'll need friction between at least one pulley and the tube, otherwise the tube would simply slide over the pulley. And we all know what friction does to a machine's performance.
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