It is reasonable to assume that the bulk modulus of blood is about the same as t

Question

It is reasonable to assume that the bulk modulus of blood is about the same as that of water (2.20 GPa). As one goes deeper and deeper in the ocean, the pressure increases by 1.0 times 10^4 Pa for every meter below the surface If a diver goes down 33.0 m (a bit over 100 ft) in the ocean, by how much does each cubic centimeter of her blood change in volume? How deep must a diver go so that each drop of blood compresses to fourth its volume at the surface? Is the ocean deep enough to have this effect on the diver?

Explanation / Answer

from the volume expansion

delV= -P/ B *Vo = -( 1.0* 10^4 Pa) /2.2* 10^9 Pa * 33 m = -1.5 * 10^-4 cm^3

one cubic centimeter of blood dicreses in volum by 1.5 * 10^-4 cm^3

(b)

del V/ V0 = 1/4

so del P = B/4 = 2.2* 10^9 Pa/ 4 = 0.55 * 10^9 Pa

d= delP/del P = 0.55 * 10^9 Pa/1.0 * 10^4 Pa/m = 0.55 * 10^5 m = 55 km

the ocean is not this dep the greatest depth in hte ocean is an order of magnitude less than this about 55 km

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