The bulk modulus for bone is 15.0 GPa If a diver-in-training is put into a press

Question

The bulk modulus for bone is 15.0 GPa

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 0.120 % of their original volume?

Given that the pressure in the ocean increases by 1.0 x 10^4 Pa for every meter of depth below the surface, how deep would this diver have to go for her bones to compress by 0.120 % ?

Does it seem that bone compression is a problem she needs to be concerned with when diving?

Explanation / Answer

The bulk modulus for bone B= 15.0 GPa
                                          = 15 x 10 9 Pa
Compression dV = 0.12 % of V
Volume strain dV / V = 0.12 %
                              = 0.0012
Pressure P = B x volume strain
                = 18 x 10 6 Pa
                = [18 x 10 6]/[101.3 x 10 3 ] atm

                = 177.69 atm

Required pressure = P - 1atm

                           = 176.69 atm

(b).Gauge pressure = 176.69 atm

                  gh = 176.69 x 101.3 x 10 3 Pa

Where = density of water

              = 1020 kg / m3

So, h = 1790.58 m

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