## Discussion of Sinclair's Siphon

In order to lift the left column of liquid up to within the bulb, the pressure inside the bulb must be less than atmospheric pressure. The pressure at the mouth of the inverted V tube must be lower than atmospheric pressure also, by an amount r gh, where h is the height difference between the top of the left (straight) tube and the reservoir water level. r is the density of the liquid. The pressure at the bottom of the inverted V-tube must be atmospheric pressure, since the tube is open to the atmosphere there. So the pressure difference at the ends of the inverted V-tube is in the wrong direction to produce flow through it in the direction shown in the picture. The pressure is higher at the "outlet" than at the "inlet", therefore the water in the V-tube will empty back into the bulb. This admits outside air into the bulb, and the water in the left tube drains back into the reservoir.

Phil Stracchino submitted a more detailed look at the problem:

The easiest way to see why Sinclair's siphon does not work, I believe, is this (no math required!):

Since the upper end of both tubes is within the bulb and below the liquid surface, the same partial vacuum that draws liquid up the lower tube from the dish to the bulb will also act to draw liquid through the siphon towards the bulb. This force is counteracted in each tube by the weight of the hydraulic head of water in that tube. Although the siphon tube is higher than the straight lower tube, that portion of the siphon which is above the level of water in the bulb is balanced and in equilibrium, and does not contribute to the hydraulic head of the siphon. The hydraulic head in the siphon tube is based upon the height of the water column between the water level in the bulb and the higher of the water level in the dish or the end of the siphon tube, not from the total height of the siphon.

It is immaterial how deep within the liquid either end of either tube is, because so long as both tips of either tube are below the surface, hydraulic head in that tube acts between the surfaces of the two bodies of water, not between the ends of the tube. Any increase in the weight of water in either tube caused by extending the tube deeper into either body of liquid is exactly counterbalanced by the increased opposing hydrostatic pressure at the opening resulting from the greater depth of water above it. There is therefore nothing to be gained by putting the end of the siphon deeper into the dish; it changes nothing (or more to the point, the changes it creates cancel out). This is why you can't siphon water from a lower level to a higher, only from a higher to a lower.

Now, consider first the state in which the end of the siphon is below the liquid level in the dish. In that case, the siphon and the lower tube, although taking different paths, are actually equivalent closed routes between exactly the same two water reservoirs. The same pressure differential applies to both, and the system is in equilibrium. No water will flow because there is no net force favoring one path over the other.

Secondly consider the case in which the lower end of the siphon is raised out of the dish, as shown in the diagram. The siphon, in this case, now ends not at the pool of water in the dish, but some distance above it. The siphon, since it now ends above the water surface and thus above the effective end of the lower tube, now has less hydraulic head than the lower tube; thus, the weight of water in the lower tube exceeds the weight of unbalanced water in the siphon. Water will flow down the lower tube out of the bulb, causing water to be drawn up the siphon to replace, it until the siphon tube is empty. At that point, air enters the bulb through the siphon, collapsing the partial vacuum, and all remaining water in the bulb drains into the dish via the straight tube.

This is yet another example of how an incorrectly rendered picture can bias one's thinking. It also illustrates the important fact that it's not merely the height difference between the input and output of a siphon that matters. It's the pressure difference.