# 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. – BowlOfRed Jul 26 '16 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.) – sammy gerbil Jul 26 '16 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. – user273872 Jul 26 '16 at 23:38

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.