Problem #$1$

consider an oil spill which is contained $($kept near the coast$)$ by a belt $($red$),$ curved as a semi$-$cylinder. Note that the water $($blue$)$ and oil $($black$)$ do not mix. Oil $($as the lighter fluid$)$ stays in a layer of height $"h_1+h_2"$ on top of the water below the water surface and $h_2$ above the water surface$).$

Known: The total volume of oil spilled $V,$ the density of water ${}_w$ the density of oil ${}_0$ and radius $R$ of the semi$-$cylinder formed by the belt. Determine: $h_1,h_2$ and the net pressure force $\frac{F}{}L$ on the belt at a segment of length $L.$ Note that the oil applies a force outward and the water applies a force inward on the semi$-$cylinder formed by the belt.