A rectangular block of height Land horizontal cross-sectional area A floats at the interface between two immiscible liquids, as shown below. Fluid 1 Pi(g/em³) Fluid 2 Block P:(g/cm³) Po(g/cm³) (a) Derive a formula for the block density, Pp, in terms of the fluid densities p, and p2, the heights họ. h1, and h2, 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.
A rectangular block of height Land horizontal cross-sectional area A floats at the interface between two immiscible liquids, as shown below. Fluid 1 Pi(g/em³) Fluid 2 Block P:(g/cm³) Po(g/cm³) (a) Derive a formula for the block density, Pp, in terms of the fluid densities p, and p2, the heights họ. h1, and h2, 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.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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
Transcribed Image Text:A rectangular block of height Land horizontal cross-sectional area A floats at the interface between two
immiscible liquids, as shown below.
Fluid 1
Pi(g/em³)
Fluid 2
Block
P:(g/cm³)
Po(g/cm³)
(a) Derive a formula for the block density, Pp, in terms of the fluid densities p, and p2, the heights
họ. h1, and h2, 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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