(Solved): Problem 1. The buoyant force in a density-stratified ocean/ What is the magnitude of the buoyant fo ...

Problem 1. The buoyant force in a density-stratified ocean/ What is the magnitude of the buoyant force on a cylinder submerged in an incompressible density stratified ocean, i.e. if $\rho =\rho (z)$. Find an explicit relationship for the buoyant force when $\rho ={\rho }_0-\alpha z$. Hint: Let's define a coordinate system with the $x$-axis on the mean free surface and $z$-axis positive upward. Note that the buoyant force is equal to the weight of the water displaced. Therefore, all we need to do is to calculate the weight of water that occupies the volume of the cylinder in the absence of the cylinder. Figure: A cylinder submerged in a stratified fluid.