# How fast does a human sink in h20?

1. May 3, 2007

### shintashi

assuming a human being with average body type and health, how fast does a human being fall through water from the surface? what is the terminal velocity and what is it reached at?

I've been trying to find answers everywhere but can't get a straight answer. These calculations would be useful as a comparison for gravity.

thanks.

2. May 3, 2007

### Danger

It varies with several factors, including the purity and temperature of the water. You won't sink at all, for instance, in the Dead Sea.

3. May 3, 2007

### Staff: Mentor

It also varies with depth. As you sink, your lungs and fat get compressed, making you less buoyant. So I guess you could say that there is no terminal velocity - you'll just keep accelerating (slowly) all the way to the bottom of the ocean.

Last edited by a moderator: May 3, 2007
4. May 3, 2007

### Integral

Staff Emeritus

Since this average person may not exist not much can be gained from this type of analysis. You would, at the least, have to consider the BMI (body mass index) as a variable.

What does "comparision to Gravity" mean?

5. May 3, 2007

### DyslexicHobo

I believed he meant "comparison of acceleration due to gravity between air and water". The force being applied to an object in water by gravity is equal to the force being applied to an object out of water by gravity. The difference is that water is producing more of a resisting force than air would (air resistance is much less than the drag that would be created by water).

6. May 4, 2007

### lpfr

A person, with air filled lungs does not sink. He floats slightly, but not always with his nose out of the water. Drowned people sink because they have partially filled their lungs with water and have lost buoyancy.

There is not really a terminal velocity because buoyancy decreases with deep as the air remaining in the lungs is compressed.

7. May 6, 2007

### dimensionless

The density of the human body is either higher or lower than that of water. The difference is determined by how much air they have in their lungs. People will generally float. If you are underwater, however, and you exhale enough of your air, you will sink.

8. May 6, 2007

### Astronuc

Staff Emeritus
Protein has density > 1 gm/cc, and fat has density < 1 gm/cc.

Even with air in my lungs, my neutral bouyancy point is below the water surface. On the other hand, my father floats quite easily at the surface, and so do most women I know.

One would sink until the water density equals ones body density.

9. May 6, 2007

### lpfr

I'm sure this is not what you wanted to say.

10. May 6, 2007

### Staff: Mentor

That is a common misconception, Astronuc: you don't have a neutral buoyancy point.

11. May 7, 2007

### dimensionless

Yes, but the body is mostly water. According to Wikipedia:
Also, after inhaling a large amount of air, as one is likely to do before jumping into water, the lungs will hold about 6 liters of air. Additional air is contained in the throat, mouth, and nasal cavities. Presumably some gas could also be found in the stomach and large intestine as well.

12. May 7, 2007

### lpfr

I'm curious to know how much de density of the water of the Atlantic ocean will change if you plunge in it.

13. May 8, 2007

### pmb_phy

The Dead Sea is full of salt (a very rich concentration from what I here) and it is the salt that gives the greatly increased bouancy. However the person inquired about h20 i.e. pure water, not salt water.

As stated several times above, one of the main determining factors is the persons mass density which is determined by several factors mentioned above. A person with a high fat content will float much easier while a person of very low fat content would tend to sink more easily. To know which one hold you'd have to give us some numbers for the fat content of a.

Pete

Last edited: May 8, 2007
14. May 9, 2007

### caslav.ilic

Well, quite obviously there has to exist a terminal velocity, due to water drag. Even neglecting boyancy force (eg. sinking iridium statue of a man :), the terminal velocity would not exceed 3 m/s. The "derivation": skydiver's terminal velocity, legs-down, is put at about 70 m/s; the density of water to density of air is about 800; 70 / sqrt(800) < 3.

--
Chusslove Illich (Часлав Илић)

15. May 12, 2007

### shintashi

thanks for not dodging the question. For the rest, an average body type can be found using military tables and BTM indexes such as those in in health magazines or ezines. One of the ways fat ratio can be measured is specifically with submersion in water.

16. May 12, 2007

### Staff: Mentor

No one dodged the question - caslav is just wrong. The change in buoyancy is why there is no terminal velocity. Since the buoyant force is always changing, the speed is always changing.

The velocity at which a person sinks may always be less than 3m/s, but that doesn't mean there must be a specific value to it.

Last edited: May 12, 2007
17. May 12, 2007

### caslav.ilic

Speaking of definitions, in practice the term "terminal velocity" is used more in an engineering (i.e. fuzzy) than strict mathematical sense.

Sure, density of the sinking body will increase as long as all the gas doesn't liquify (or, more realistically, escapes), and even than some as no fluid is perfectly incompressible, then there are environmental changes in the water that would affect viscosity, etc, etc. But, looking that way, there is no terminal velocity for skydivers either, as the density of air increases with decreasing altitude, which changes both drag and whatever little boyancy there is in air too. Yet, in skydiving they do talk about "terminal velocity".

So, by my "practical" definition, the terminal velocity would be the quasi-stationary velocity, observed when acting forces are nearly in balance at any given moment, and this balance changes very slowly. My previous post thus applies with this definition in mind.

--
Chusslove Illich (Часлав Илић)