A rectangular block of height L and horizontal

Chapter 3, Problem 3.34

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A rectangular block of height L and horizontal cross-sectional area A floats at the interface between two immiscible liquids, as shown below. Fluid 1 p,(glem3) Fluid 2 piglem3) Block ",,(glem3) HEAD Equipment Encyclopedia reactors (a) Derive a formula for the block density, Ph, in terms of the fluid densities p, and Pl., the heights ho, hI, and h" and the cross-sectional area A. (It is not necessary that all of these variables appear in the final result.) (b) Force balances on the block can be calculated in two ways: (i) in terms of the weight of the block and the hydrostatic forces on the upper and lower block surfaces; and (ii) in terms of the weight of the block and the buoyant force on the block as expressed by Archimedes' principle. Prove that these two approaches are equivalent.

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