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 1.0×104Pa for every meter below the surface

A) 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?

B) How deep must a diver go so that each drop of blood compresses to third its volume at the surface?

C) Is the ocean deep enough to have this effect on the diver?

Answer 1

A)
Y=(pressure increasesperunit length)/(change in length/initial length)

2.20*10^-9 Pa = -(1.0*10^4 Pa/m)/(change in volume/33m).

Change in volume = -(1.0*10^4 Pa/m)*(33m)/(2.20*10^9 Pa)

Change in volume = -1.5*10^-4 cm^3

B)
Y=(F/A)/(deltaL/L)

2.20*10^9 = -(1.0*10^4 Pa/ m)/(-0.5/L)

L = -(-0.5)(2.20*10^9)/(1.0*10^4) = 1.1*10^5 meters = 1.1*10^2 km.

L = 1.1*10^2 km

C)
10,994 meters = 10.994 km.

10.994 km < 110 km => NO, the ocean isn t deep enough.