Salt water is kept in a cylindrical column of cross-sectional area 31 cm2 and height 63 cm. The salt is allowed to settle, and when the salinity of the water is measured, it reduces linearly from s0 = 99 gNaCl/kgH2O (grams of salt per kilogram of water) at the bottom to sH = 27 gNaCl/kgH2O at the top. Assume that the density of water molecules remains constant throughout the water column and the density of ?H2O = 1 g/cc. The additional weight of the salt water is accounted for by the density of the salt in the water at that point (a) Find the density of the salt water at the top of the column. ?(63 cm) = (b) Find the density of the salt water at the bottom of the column. ?(0 cm) = (c) What is the function for the total density of the water as a function of height z? ?(z) = + z
Salt water is kept in a cylindrical column of cross-sectional area 31 cm2 and height 63 cm. The salt is allowed to settle, and when the salinity of the water is measured, it reduces linearly from s0 = 99 gNaCl/kgH2O (grams of salt per kilogram of water) at the bottom to sH = 27 gNaCl/kgH2O at the top.
Assume that the density of water molecules remains constant throughout the water column and the density of ?H2O = 1 g/cc. The additional weight of the salt water is accounted for by the density of the salt in the water at that point
(a) Find the density of the salt water at the top of the column.
?(63 cm) =
(b) Find the density of the salt water at the bottom of the column.
?(0 cm) =
(c) What is the function for the total density of the water as a function of height z?
?(z) = + z
(d) Integrate this density to find the total mass of the water in the column.
M =
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