Question

The bulk modulus for bone is 15.0 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 0.100 % of their original volume? b-Given that the pressure in the ocean increases by 1.0× 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 0.100 % ? c-Does it seem that bone compression is a problem she needs to be concerned with when diving?(yes,no)

Answer 1

Bulk Stress Equation -

Where 1 atm = 1.01 * 10⁵ Pa

a)

From the above mentioned bulk stress equation,

= - (15 * 10⁹ Pa)(-0.0010)

= 1.5 * 10⁷ Pa

= 150 atm

Therefore, the pressure has to be raised by 150 atm above atmospheric pressure to compress her bones by 0.100% of their original volume.

b)

As there is an increase of 10⁴ Pa for 1m depth,

From (a) solution, the depth for a pressure increase of 1.5 * 10⁷ Pa is

= 1.5 * 10³ m

= 1500m (or) 1.5 Km

Therefore, the diver has to go 1.5 Km for her bones to compress by 0.100%

c)

No.

As we can see from the above solutions, she need not be concerned about bone compression while diving unless going too deep (~ 10 Km and above) which is not possible in a normal dive condition.