The deepest point known in any of the earth\'s oceans is in the Marianas Trench,

Question

The deepest point known in any of the earth's oceans is in the Marianas Trench, 10.92 km deep. Assuming water is incompressible, what is the pressure at this depth? Use the density of seawater. The actual pressure is 1.16 times 10^8 Pa; your calculated value will be less because the density actually varies with depth. Using the compressibility of water and the actual pressure, find the density of the water at the bottom of the Marianas Trench. What is the percent change in the density of the water?

Explanation / Answer

(1) We know that
pressure= pgh
where p is the density , g is the acceleration due to gravity and h is the height or depth
Pressure (P) = 1025*9.81*10.92*103 = 1.098*108 Pa
(2) We know that
compressibility = volumetric strain /Pressure = (dV/V) /P
dV = VS - VD
where VS is the volume at surface and VD is the volume at depth
Compressiblity = (VS - VD) /VS*P = (1-VD/VS) /P
(1-VD/VS) = Compressibility*Pressure
(1-ps /pD) = 45.8*10-11*(1.16*108 Pa)
ps = 1025 kg/m3
pD = 1082.511 kg/m3
(3)
percentage change in the density = (pD - ps / ps )*100 = ((1082.511 - 1025) / 1025)*100 = 5.61%

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