- #1
FreezingFire
- 12
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Homework Statement
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"Derive a relation between the static pressure P at a point and its depth y from the free surface of the liquid. Given the surface density of liquid is ρο, and compressibility of the liquid is k."
Homework Equations
##ρ(P) = ρ_οe^{kP}##
##dP = ρg dy##
The Attempt at a Solution
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I have already found that:
##ρ(P) = ρ_οe^{kP}##
Then, from the relation:
##dP = ρg dy##
and using ##ρ(P) = ρ_οe^{kP}##, we get:
##e^{-kP} dP = ρ_ο g dy##
Integrating L.H.S. from 0 to P and R.H.S. from 0 to y, we get:
$$P = \frac {-1}{k} \ln(1 - kρ_ο gy)$$
Are my limits correct? Is the answer correct? I ask this because the answer looks like it could easily become undefined (if ##kρ_ο gy## became greater than 1). If it is wrong, then why? If it is correct, then how does it not become undefined?
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