# Does the force on the bottom piece of a hummingbird feeder depend on the height of the water in the reservoir?

Intuitively I would think that the more nectar you put into the reservoir the more weight it will put on the bottom piece (the tray that holds the open pool of nectar that the birds can feed out of). While I was trying to think about this I thought about doing some free body diagrams. The reservoir would have a force acting upwards on it from the hanger, and a downwards force from the sheer from the stored nectar. The bottom piece would have an upwards force from where it threads onto the reservoir and I can't really figure out how to do the downwards force. I'm thinking if I could calculate the pressure all along the interface between the pan and the nectar that would do it..

• Make sure that your FBD includes the air pressure pushing the column from above. Commented Jul 26, 2016 at 20:50
• Short answer : Yes. (re BowlOfRed's comment : if the column of nectar is not open to the atmosphere, the pressure pushing it from above will be less than the surrounding air pressure.) Commented Jul 26, 2016 at 22:48
• As the humming birds feed the level in the tray drops till there is air flowing up into the reservoir and liquid flowing out. But then the liquid pulling down tries to make a "Torricellian vacuum" (I got that term from here en.wikipedia.org/wiki/Barometer while trying to do some more research on this). If you assume there is no air in there to begin with (they filled it 100%) that pressure is zero and you effectively have a vacuum (ignore the vapors coming off the liquid), and as the birds feed the pressure would slowly go to atmospheric. Commented Jul 26, 2016 at 23:38

## 1 Answer

The force the fluid does on the bottom piece does not depend on the height of the water column of the reservoir. It does depend on the height $h$ of the water column in the plate.

This can be easily seen by the fact the water is static so the pressure at any horizontal plane is the same. The pressures in $a$ and $b$ are the same. The force of the water on the plate is $F=pA=\rho g h A$, where $\rho$ is the water density and $A$ is the area of the plate.

It is definitely counterintuitive so I had to go get an empty bottle of wine and a plate to check it. As long as the bottle does not touch the plate, the latter weights the same no matter if the bottle is full or almost empty.

• The description of your experiment gave me another way to think about it! If you are holding the wine bottle up and you feel the weight of the entire column of liquid in the bottle, then the plate probably doesn't feel that weight other wise the weight would get counted twice, and probably screw up some conservation law. So to get an intuition pull a glass out of the sink upside down and if it feels like it's as heavy as the water it is pulling up... Commented Jul 27, 2016 at 16:30