Fluid MechanicsLast fall, researchers using a manned submarine discovered coral reefs at unprecedented ocean depths of 1/2 mile, of the coast of South Carolina. Find the hydrostatic pressure at that depth. Find the fractional changes in density (drho/rho) and in volume (dV/V) for the seawater at that depth. The density of seawater at the surface of the ocean is 1025kg/m3, and the bulk modulus of elasticity of seawater is 2.34*109 Pa.

Question
Asked Sep 3, 2019

Fluid Mechanics

Last fall, researchers using a manned submarine discovered coral reefs at unprecedented ocean depths of 1/2 mile, of the coast of South Carolina. Find the hydrostatic pressure at that depth. Find the fractional changes in density (drho/rho) and in volume (dV/V) for the seawater at that depth. The density of seawater at the surface of the ocean is 1025kg/m3, and the bulk modulus of elasticity of seawater is 2.34*109 Pa.

check_circleExpert Solution
Step 1

The general equation for the hydrostatic pressure is given as follows:

dP
dZ
dP
-Pg
dZ
dP
-g dZ.
.1
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dP dZ dP -Pg dZ dP -g dZ. .1

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Step 2

The equation for the bulk modulus of elasticity is as follows:

dp
dp K
Here, density p' is a function of pressure P
P
dp
p
Po
PK[p
P=K ln
Po
P
In
K
Po
eq (2)
p = Poe
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dp dp K Here, density p' is a function of pressure P P dp p Po PK[p P=K ln Po P In K Po eq (2) p = Poe

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Step 3
Putting the value of pin equation 1
dP
-gdZ
dP
=-gdZ
P
PoeR
KdP -PogdZ, integrating both sides
e
dPPodz
e
1- Pogh
K
P=-K ln
..3
help_outline

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Putting the value of pin equation 1 dP -gdZ dP =-gdZ P PoeR KdP -PogdZ, integrating both sides e dPPodz e 1- Pogh K P=-K ln ..3

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