It is reasonable to assume that the bulk modulus of blood is about the same as that of water (2.20 m). As one goes deeper and deeper in the ocean, the pressure increases by 1.0*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?

(delta)V=(delta)P/BulkMod. * V ???

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

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

To find out how much each cubic centimeter of blood changes in volume when a diver goes down 33.0m in the ocean, we can use the formula:

(delta)V = (delta)P / Bulk Modulus * V

where:
- (delta)V is the change in volume
- (delta)P is the change in pressure
- Bulk Modulus is the bulk modulus of blood (assumed to be the same as that of water, which is 2.20 m)
- V is the initial volume

First, we need to calculate the change in pressure at 33.0m below the surface using the given information that the pressure increases by 1.0*10^4 Pa for every meter below the surface.

(delta)P = (1.0*10^4 Pa/m) * (33.0 m) = 3.3 * 10^5 Pa

Now we have all the values to calculate the change in volume:

(delta)V = (3.3 * 10^5 Pa) / (2.20 m) * V

The result will give you the change in volume per cubic centimeter of blood.

To find out how deep a diver must go so that each drop of blood compresses to half its volume at the surface, we can use the same formula but set the change in volume equal to half the initial volume:

(delta)V = (1/2) * V

Now, solve the equation for (delta)P:

(1/2) * V = (delta)P / Bulk Modulus * V

(1/2) = (delta)P / Bulk Modulus

(delta)P = (1/2) * Bulk Modulus

Substitute the value of the bulk modulus (2.20 m) and solve for (delta)P:

(delta)P = (1/2) * 2.20 m

(delta)P = 1.10 m

So, for each drop of blood to compress to half its volume at the surface, a diver must go down approximately 1.10 meters.

Now, given that the pressure increases by 1.0*10^4 Pa for every meter below the surface, we can calculate the depth required for this change in pressure:

1.10 m = (1.0*10^4 Pa/m) * Depth

Depth = 1.10 m / (1.0*10^4 Pa/m) = 0.00011 meters

Therefore, the diver would need to go about 0.00011 meters (or 0.11 millimeters) deep for each drop of blood to compress to half its volume at the surface.

As for whether the ocean is deep enough to have this effect on the diver, the answer is no. The change in pressure required is very small (0.11 millimeters) and cannot be achieved by diving in the ocean.

To calculate the change in volume, we can apply the formula you provided for the change in volume:

ΔV = ΔP/BulkMod. * V

Given that the pressure increases by 1.0 x 10^4 Pa for every meter below the surface, and the diver goes down 33.0 meters, we can substitute the values into the formula:

ΔP = 1.0 x 10^4 Pa/m * 33.0 m = 3.3 x 10^5 Pa

Assuming the bulk modulus of blood is approximately the same as water, which is 2.20 x 10^9 Pa, and the volume is 1 cm^3 or 1 cm^3 = 1 x 10^-6 m^3, we can now calculate the change in volume:

ΔV = (3.3 x 10^5 Pa) / (2.20 x 10^9 Pa) * (1 x 10^-6 m^3)

Simplifying the equation:

ΔV = 1.5 x 10^-4 m^3

Therefore, each cubic centimeter of the diver's blood changes in volume by approximately 1.5 x 10^-4 cubic centimeters.

To find how deep a diver must go so that each drop of blood compresses to half its volume at the surface (ΔV = -0.5), we can rearrange the formula:

ΔV = ΔP/BulkMod. * V

-0.5 = ΔP/BulkMod. * V

Since the change in volume will be negative, we can set -0.5 equal to the expression:

-0.5 = (1.0 x 10^4 Pa/m) * h / (2.20 x 10^9 Pa) * V

Simplifying further:

-0.5 = (1.0 x 10^4 Pa/m) * h / (2.20 x 10^9 Pa) * (1 x 10^-6 m^3)

Solving for h, the depth the diver must go:

h = (-0.5) * (2.20 x 10^9 Pa) * (1 x 10^-6 m^3) / (1.0 x 10^4 Pa/m)

h ≈ -1.1 x 10^-2 m

Since depth cannot be negative, it means there is no depth at which each drop of blood compresses to half its volume. Therefore, the ocean is not deep enough to have this effect on the diver.

The bulk modulus of water is 2.2*10^9 Pa. You omitted some terms. Use the formula which you wrote But with a minus sign) to solve for

(delta V/V). At 33 m depth, the delta P is 33*10^4 Pa

You will find that deltaV/V is a small fraction at this depth.

Then find that delta P needed to make
delta V/V = 1/2, and calculate the corresponing depth.

The deepest spot in the ocean has a depth of about 10,000 m.