# Terminal velocity in water? **URL:** \ **Category:** Factual Questions\ **Created:** [July 24, 2003, 9:28pm UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722 "2003-07-24T21:28:50Z")\ **Posts on this page:** 13\ **Page:** 1
**Author:** ![whatami](https://avatars.discourse-cdn.com/v4/letter/w/85f322/32.png) [@whatami](https://boards.straightdope.com/u/whatami)\ **Post date:** [July 24, 2003, 9:28pm UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/1 "2003-07-24T21:28:50Z")
I was talking with a friend about skydiving today (not for me thanks!), when the subject of terminal velocity came up. I then got to thinking about water and that there must be some type of limit there as well. Is there a formula I can use to figure that speed for a given weight, water density, etc…? ---
**Author:** ![kanicbird](https://avatars.discourse-cdn.com/v4/letter/k/5f8ce5/32.png) [@kanicbird](https://boards.straightdope.com/u/kanicbird)\ **Post date:** [July 24, 2003, 9:40pm UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/2 "2003-07-24T21:40:56Z")
What’s the terminan velocity of a hot air baloon in air? Boyancy becomes much too big a factor to be ignored. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [July 24, 2003, 9:54pm UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/3 "2003-07-24T21:54:15Z")
Terminal velocity depends on the body and the fluid. A human body, a house fly and an M1 tank all have different terminal velocities in air… . . and in water. In water a human body will have a very small or zero terminal velocity. If it floats the speed is zero. ---
**Author:** ![whatami](https://avatars.discourse-cdn.com/v4/letter/w/85f322/32.png) [@whatami](https://boards.straightdope.com/u/whatami)\ **Post date:** [July 24, 2003, 10:07pm UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/4 "2003-07-24T22:07:05Z")
> [@](#): > > \*Originally posted by sailor \* > \*\*Terminal velocity depends on the body and the fluid. A human body, a house fly and an M1 tank all have different terminal velocities in air… . . and in water. In water a human body will have a very small or zero terminal velocity. If it floats the speed is zero. \*\* Well, that makes sense. Is there a way to figure the speed for, say a 100lb. block of lead? ---
**Author:** ![Rabid\_Squirrel](https://avatars.discourse-cdn.com/v4/letter/r/e0b2c6/32.png) [@Rabid\_Squirrel](https://boards.straightdope.com/u/Rabid_Squirrel)\ **Post date:** [July 24, 2003, 10:36pm UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/5 "2003-07-24T22:36:33Z")
What shape is the block? The fluid drag forces in water is much more higher than air (it’s ~1000X denser), so your shape is going to be critical. What you want to do is look up the drag force correlations for your shape, then relate them to the force of gravity (adjusting for bouyancy). Adjust the velocity value until the drag force equals the weight. I can’t find any correlations for external turbulent flow (all my books are for internal flow), and the only helpful correlation I’ve got on hand is for laminar flow over a sphere. Perhaps some Mech Eng Dopers can lend a hand? ---
**Author:** ![SkyBum](https://avatars.discourse-cdn.com/v4/letter/s/a88e57/32.png) [@SkyBum](https://boards.straightdope.com/u/SkyBum)\ **Post date:** [July 25, 2003, 12:41am UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/6 "2003-07-25T00:41:47Z")
If they ever perfect THIS technology, it would be pretty damn fast… [http://www.subsim.com/ssr/page33.html](http://www.subsim.com/ssr/page33.html) ---
**Author:** ![whatami](https://avatars.discourse-cdn.com/v4/letter/w/85f322/32.png) [@whatami](https://boards.straightdope.com/u/whatami)\ **Post date:** [July 25, 2003, 6:20am UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/7 "2003-07-25T06:20:45Z")
Wow… This is much more complicated than I had anticipated. Thanks for the answers, but I think this is more than I really want to get into! ---
**Author:** ![Thaidog](https://avatars.discourse-cdn.com/v4/letter/t/50afbb/32.png) [@Thaidog](https://boards.straightdope.com/u/Thaidog)\ **Post date:** [July 25, 2003, 10:42am UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/8 "2003-07-25T10:42:57Z")
> [@](#): > > \*Originally posted by sailor \* > \*\*Terminal velocity depends on the body and the fluid. A human body, a house fly and an M1 tank all have different terminal velocities in air… . . and in water. In water a human body will have a very small or zero terminal velocity. If it floats the speed is zero. \*\* yeah, that’s due to drag… in a vacum, they all have the same, however… ---
**Author:** ![av8rmike](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@av8rmike](https://boards.straightdope.com/u/av8rmike)\ **Post date:** [July 25, 2003, 1:56pm UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/9 "2003-07-25T13:56:29Z")
> [@](#): > > \*Originally posted by whatami \* > \*\*Is there a formula I can use to figure that speed for a given weight, water density, etc…? \*\* (Mech Eng. Doper) Unfortunately, it’s not a single, simple formula. As **Rabid\_Squirrel** alluded to, drag force (and terminal velocity, therefore) are proportional to fluid density, object shape, and speed. In air, weight is not usually a factor because the buoyant force is negligibly small, but you can’t make the same assumption for water. Also, since the drag coefficient (a proportionality constant) is usually unknown, it has to be an iterative calculation. It’s not all bad news, though. My text has a comparative study on terminal velocity of a 50-mm plastic sphere falling in air and water. They determined the velocity in air to be 41 m/s (over 90 mi/hr!), while in water the same sphere would fall at 0.63 m/s (1.4 mi/hr). I just don’t feel like doing the math now for your 100-lb block of lead. Maybe later… 🙂 ---
**Author:** ![micco](https://avatars.discourse-cdn.com/v4/letter/m/5f8ce5/32.png) [@micco](https://boards.straightdope.com/u/micco)\ **Post date:** [July 25, 2003, 1:58pm UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/10 "2003-07-25T13:58:48Z")
> [@](#): > > \*Originally posted by Thaidog \* > \*\*yeah, that’s due to drag… in a vacum, they all have the same, however… \*\* In a vacuum, there is no terminal velocity. Terminal velocity is defined as the point at which the acceleration due to drag exactly counters the acceleration due to gravity. In a vacuum where this is no drag or other forces on the body except gravity, the body continues to accelerate without limit. ---
**Author:** ![whatami](https://avatars.discourse-cdn.com/v4/letter/w/85f322/32.png) [@whatami](https://boards.straightdope.com/u/whatami)\ **Post date:** [July 25, 2003, 2:30pm UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/11 "2003-07-25T14:30:51Z")
> [@](#): > > \*Originally posted by av8rmike \* > [B I just don’t feel like doing the math now for your 100-lb block of lead. Maybe later… 🙂 \*\* Please don’t! That was just something I threw out there to get a rough idea of the difference. Like I said, it was just something that crossed my mind and I thought there might be some simple answer. Alas, I think I’d be better off asking about the meaning of life! Thanks again, whatami ---
**Author:** ![Ale](https://avatars.discourse-cdn.com/v4/letter/a/f19dbf/32.png) [@Ale](https://boards.straightdope.com/u/Ale)\ **Post date:** [July 25, 2003, 9:27pm UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/12 "2003-07-25T21:27:11Z")
As far as I remember, water produces 600 times more drag than air; you can begin there. Boyancy is a big issue too, specially for a human; in shallow water a body does usually have positive boyancy, but as you go down the water pressure compress your cavities (not only the ones in your teeth) so the body actually becomes more dense. Free divers deal with that all the time. ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [July 25, 2003, 9:57pm UTC](https://boards.straightdope.com/t/terminal-velocity-in-water/190722/13 "2003-07-25T21:57:24Z")
> [@](#): > > \*Originally posted by whatami \* > Please don’t! That was just something I threw out there to get a rough idea of the difference. Like I said, it was just something that crossed my mind and I thought there might be some simple answer. Alas, I think I’d be better off asking about the meaning of life! Sorry that you think it’s so hard. It’s actually a pretty simple concept to understand, but it’s difficult to get exact numbers. Hopefully somebody can correct me if I make any huge errors, but here’s how you get an approximate value. The formula for downward force is: F = (m - rho × Volume) × g (Note: rho is the density of the medium, in this case water.) The simple formula for drag force is: D = 1/2 × C[sub]D[/sub] × rho × V[sup]2[/sup] × Area This formula is not so good if you wanted to be precise, but from the sound of your OP you just want a general idea. Everything in there is a constant except for the speed V, and that’s what you want to solve for. For terminal speed, you set D = F, and get: V = sqrt(2(m - rho × Volume) × g / (C[sub]D[/sub] × rho × Area)) This simplifies to: **V = sqrt(2(rho[sub]OBJ[/sub]/rho - 1) × g × L / C[sub]D[/sub])** L is the characteristic size of your object (Volume / Area), and rho[sub]OBJ[/sub] is its density. Now, the only actually complicated part is C[sub]D[/sub]. Getting an exact value for this is tough, as it depends on the shape and everything. But the values [don’t vary all that much](http://www.insideracingtechnology.com/Resources/Shapes2.gif) if you’re dealing with unstreamlined slabs - it’s usually between 0.5 and 1. So say you’ve got a 0.13-meter slab of lead, which is 11 times denser than water. For C[sub]D[/sub] = 0.5 (spherical-ish), V is around 7 m/s.