# Buoyancy forces on a tube exposes to Atmosphere at both ends that passes through a container filled with liquid

I'm trying to get an understanding of a free body diagram for the following situation. A container, such as Styrofoam cup has a straw pushed through the bottom of it and the cup is filled with water. The hole in the cup is very slightly larger than the straw so has no frictional forces and does not restrain the straw. The straw has an o-ring to seal the straw hole interface. What are the forces on the straw? My thoughts are that the straw is similar to the container wall, so sees side loading forces and no upward force. But then I think if a straw had a sealed bottom and was pushed to the bottom of the container in the same orientation, it would have buoyancy and would try to float up. Can someone explain? Thanks

• All hydrostatic forces on the straw will act perpendicular to the surface of the straw. Nov 11, 2022 at 1:54

For buoyancy to apply, the straw needs to have some sort of "bottom" in contact with the fluid. Even a regular straw at the bottom of a cup typically has buoyancy.

Buoyancy occurs due to hydrostatic pressure. The pressure is higher the lower you are, therefore as long as the horizontal parts of the object are in contact with the fluid, the force on the lower horizontal surface will be higher, so net force acts upwards.

In the situation where the straw goes through the cup, that analysis no longer applies. All that pushes the straw up is the air on the bottom, which will have essentially the same force as the air at the top of the straw (since air is not heavy).

• Thanks for your answer. I also just read a pretty good article on an experiment where a block of wood, that has a good seal on the bottom with no water under it, did not float in a glass tank of water for the reasons you gave. I think it would be a pretty good experiment for any physics teachers/professors out there to make the point that hydro static forces must be acting from underneath for Archimedes principle to apply. researchgate.net/publication/… Thanks again for your response!
– Bar
Nov 10, 2022 at 20:58
• @Bar This concept is one I really found makes a lot of sense when you see it all laid out, but Archimedes principle often isnt explained in these terms, so the assumption that buoyancy works without fluid below is very common (and a huge pet peeve of mine). I think this is a great question to be asking in terms of understanding buoyancy.
– JMac
Nov 10, 2022 at 21:30
• Re, "...since air is not heavy." There actually are situations in which one must take the buoyancy due to Earth's atmosphere into account. Weighing low density materials with extreme precision is one such. Hot-air ballooning is another, I think. [P.S., I estimate there's about 30kg of air in the home office where I am sitting, typing this comment.] Nov 10, 2022 at 22:16
• @SolomonSlow Obviously it's all relative. I think it's pretty apparent that the effect of buoyancy on a straw is very minimal in the atmosphere though.
– JMac
Nov 11, 2022 at 0:08
• @JMac, I just didn't want the newbie to get the wrong message. There's a huge difference between "the effect is too small to be significant in this example" and "there is no such effect." Nov 11, 2022 at 12:54