Chapter 3, Problems #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.

(a) Derive a formula for the block density, p_{b}, in terms of the fluid densities p_{1} and p_{2}, the heights h_{0}, h_{1}, and h_{2}, 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 blocks 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.

3rd Edition

Authors: Richard M. Felder, Ronald W. Rousseau

ISBN: 978-0471720638