Although liquids, in general, are hard to compress, the compressibility effect (variation in the density) may become unavoidable at the great depths in the oceans due to enormous pressure increase. At a certain depth the pressure is reported to be
(a) Taking the liquid density at the free surface to be
(b) Use Eq. 2-13 to estimate the density for the specified pressure and compare your result with that of part (a).
(a)
The density of water at the specified depth.
Answer to Problem 118P
The density of water at the specified depth is
Explanation of Solution
Given information:
The pressure at a certain depth is
Write the expression for density at a depth.
Here, the partial derivative of density is
Write the expression for ratio of partial derivative of density with respect to pressure.
Here, the pressure at the specified depth is
Substitute
Substitute,
Conclusion:
The density of water at the specified depth is
(b)
The density of water at the specified depth and its comparison with part (a).
Answer to Problem 118P
The density of water at the specified depth is
Explanation of Solution
Write the expression for the density of water using Equation 2-13.
Write the expression for pressure change.
Write the expression for change in density.
Substitute
Here, the coefficient of compressibility is
Substitute,
The value of density obtained in part (a) that is
Conclusion:
The density of water at the specified depth is
The density calculated in part (b) is more exact as the isothermal compressibility of water in part (a) is an approximate value.
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Chapter 2 Solutions
Fluid Mechanics: Fundamentals and Applications
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