In this note we unify two physical situations treatable with hydrostatics: an object floating on a denser fluid and an open U-shaped tube with two immiscible fluids. We begin by reviewing the problem of a partially floating uniform, rectangular prism of horizontal area A immersed in a denser fluid, with respective densities ρ1 < ρh for the prism and fluid (the subscripts stand for light and heavy): see Fig. 1. We define three horizontal levels within the solid, y0, y1, and y2, corresponding to the bottom, flotation line, and top of the prism. The buoyant force is ρh (y1 − y0)gA upwards, and the weight of the prism is ρ1 (y2 − y0)gA downwards. By Newton's second law, these two forces balance at equilibrium. After dividing by the common horizontal area, one obtains A detailed derivation can be found for example in Ref. 1, Section 13-7.
(1)
References
1
D. C.
Giancoli
, Physics for Scientists & Engineers with Modern Physics
, 4th ed. (Prentice Hall
, 2009
).2.
D. H.
Sharp
, “An overview of Rayleigh-Taylor instability
,” Physica D
12
(1
), 3
–18
(1984
). 3
http://uw.physics.wisc.edu/~djchung/phys207/207final_S08_solns.pdf, accessed Sept. 12, 2015.
© 2016 American Association of Physics Teachers.
2016
American Association of Physics Teachers
AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.