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Chapter 1: Q11-31E (page 1)

The bulk modulus for bone is 15 GPa. (a) If a diver-in-training is put into a pressurized suit, by how much would the pressure have to be raised (in atmospheres) above atmospheric pressure to compress her bones by 0.10% of their original volume? (b) Given that the pressure in the ocean increases by 1.0 * 104Pa for every meter of depth below the surface, how deep would this diver have to go for her bones to compress by 0.10% ? Does it seem that bone compression is a problem she needs to be concerned with when diving?

Short Answer

Expert verified

(a) 150 atm

(b) 1.5 Km

Step by step solution

01

Given information:

Bulk modulus β=15Gpa,ΔVV0=-0.0010

02

Concept/Formula used:

Bulk modulus is given by the ratio of pressure applied to the corresponding relative decrease in the volume of the material.

Mathematically, it is represented as follows:

β=ΔpΔVV0

Where, is Bulk modulus

ΔpIs change of the pressure or force applied per unit area on the material

ΔVis Change of the volume of the material due to the compression

V0 is Initial volume of the material

03

Raised in pressure

(a)

Δp=-βΔVV0=-15×109Pa-0.0010=1.5×107Pa=150atm

04

Depth increases due to pressure variation

∵Δp=1.5×107Pa1atm=1.01×105Pa

So depth increases is 1.5 Km

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