# Is it possible to limit water flow this way and how is this effect called?

I needed to propose a mechanism to store water and keep water flow at the same level with 100% passive equipment.

Here's what I came up with. If you turn a water reservoir upside down and put in another one, with its end under water, the water doesn't run down, because air can't get inside, and water column is held by low air pressure.

Now, if I add a small hole in the bottom reservoir, h will be low, hence water velocity will be low too.

Flow rate will be the same until the upper reservoir empties, and water level starts decreasing.

Am I right? How is this mechanism called? It seems similar but different to medical drip chamber, but can't google out any confirmaiton, nobody discusses its physics.

ADDED Tested this in real life with plastic and washing liquid bottles. Indeed, the flow rate was gradually decreasing, but the device did keep water from bursting out. The upper bottle just gradually kept letting bubbles of air in.

• Constant flow rate has been a requirement of water clocks for... ages. A simple all passive feedback mechanism can be implemented by using a float valve: water from an upper container is allowed to flow in the lower container through a pipe. When the water reaches the right level, a float closes the output of the pipe by rising with the level. When you drain some water from the bottom reservoir, the level lowers and so does the float, leaving more water in. This will keep the level and thus the flow out of the bottom container - constant. Sep 14 '14 at 21:50
• There's a bit of an error in the diagram that you've made. The height of the external water would not be simply stay at the bottom of the tube. The height difference between the two will depend on the difference between the internal and external air pressure s.t. $\Delta P = \rho_{water} g \Delta h$. That'll change the pressure at the outlet, resulting in a different flow rate. This looks like a good problem for an intro fluids exam.... Sep 15 '14 at 6:24
• @Peltio the one in the question is even more simple and even more passive Sep 15 at 12:03

As @user3823992 points, this does not work: the (excess) pressure of water at the level of the hole is equal to $\rho g h$, where $h$ is the altitude difference between the hole and the free surface in contact with atmosphere. As water flows out, $h$ decreases and thus the pressure and flow rate too.

In the tube now, the pressure in the water column is less than the atmospheric pressure, and as the reservoir empties, will get lower and lower, making it harder and harder to maintain the tube in position. Eventually, the water level $h$ will be lower than the tube inlet, and air will flow into the tube, then you'll get a sudden burst in the outflow.

• You were right on the flow rate. But there was no burst. I tested it on a real life plastic bottles. Instead of a burst of outflow it just kept sucking air bubbles all the way. Try this at home, you need two plastic bottles, scissors and an electric drill. Sep 19 '14 at 16:55
• Good point about the burst, at least for small enough setups (low enough Reynolds): if you have a sufficiently large lower reservoir compared to the typical size of the air bubble that form (which will depend, it seems to me, on the fluid and on the geometry), then the time period when the upper reservoir is emptying is the time when you have the most regular outflow rate, as the pressure is maintained to the water height difference between the hole and the lower part of the upper reservoir plus or minus bubble volume divided by lower reservoir excess area.
– Joce
Sep 22 '14 at 7:18

I would say that it depends what your requirements are. If you just need approximately a constant flow rate your design is not bad. You can separate the functions of maintaining the level water level and supplying air. You could even totally separate reservoir from the basin and connect it by tubes.

If you need a simple and cheap design, give it some more thoughts!

• Is there a way to change the size of the image? the Help does not "help"...
– dani
Sep 19 '14 at 17:36
• No idea how to change its size. I don't need this device anymore, but that was an interesting test. Sep 19 '14 at 18:38