# Effect of water pressure on sinking objects

As I understand, water pressure increases as we go towards bottom of the ocean. So if an object* is thrown into water and it starts sinking with some speed, does the sinking object's acceleration increase with increasing pressure?

Also does water solidify under very high pressure and if so is that high pressure achieved at the ocean bottom? If so, would a sinking object stop sinking and rest on the "solidified" water, if we have a deep enough ocean?

• e.g. black box of a submerged plane

Edit: I have accepted best current answer, if you think you can write a better answer, please do so.

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Because water is one of the few substances whose liquid phase is more dense than the solid phase (ice floats), you can never solidify water by only increasing the pressure. –  Jim Mar 21 at 14:32
If the increasing pressure crushes the object, its size will decrease (possibly less hydrodynamic drag) and it will be denser (less buoyancy), both of which could make it speed up somewhat. Leakage of water into the object will also make it denser. –  Phil Perry Mar 21 at 16:51

That is right, deeper the pressure is stronger. But the pressure is not just in one direction it is in every direction. So the velocity will decrease in most cases. But also you have to be aware of the density of the object. You could read this classical description of diving objects "Thrust" on wikipedia. This is a classical effect, in real cases the relation between deepness and pressure is not always linear.

Here is an example of the every direction pressure.

And answering the other question. That is possible under some specific conditions. You could have solid water. But I don't know exactly if our planet is capable of have that rare condition. In addition I have found information of a exoplanet that matches those conditions NatGeo.

Regards.

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Why isn't the pressure force downwards given that there is pressure because of water on top? –  user13107 Mar 21 at 14:05
Yes. But the pressure comes in all directions. It isn't just downwards. –  tcassanelli Mar 21 at 14:07
Sorry I'm not able to visualize it.. anyway, if pressure is from all the directions, it should not cause any decrease in speed right? (as u said in 3rd sentence) –  user13107 Mar 21 at 14:12
It does decrease speed unless the object has a huge density. –  tcassanelli Mar 21 at 14:14
@user13107 pressure comes in all directions but not equally. The pressure from the water below is slightly greater than the pressure from the water above because it is more compressed. An object will sink until the volume of water it displaces has a mass equal to its own; it floats at about that point. As the object descends, the water becomes denser, which means the same volume displaces more mass. Naturally, the object will lose speed until the point of buoyancy. –  Jim Mar 21 at 14:37

If You make a simplified force balance of a sinking box, You can identify two main forces: Force associated with box's weight $F_g$ acting downwards and buoyancy force $F_b$ acting upwards. The formulas are as follows:

$F_g=mg$,

$F_b=-\rho g V$,

where $m$ is the mass of the box, $g$ is the gravitational acceleration, $\rho$ is the density of water, $V$ is the volume of the box.

The buoyancy force is a result of superposition of two forces associated with pressure: force acting on the bottom of the box and force acting on the top of the box:

$F_b=p_tS-p_bS=\rho g HS-\rho g (H+h)S=-\rho g h S=-\rho g V$,

where $p_t$ is the pressure on top of the box, $p_b$ is the pressure on the bottom of the box, $H$ is the distance from the water surface to the top side of the box and $h$ is the box's height. I assume that the top and bottom side of the box has the same area $S$.

Now the balance is:

$F_t=F_g-F_b$

assuming that the axis goes downwards.

$F_t=mg-\rho gV$

When the depth ($H$) increses, the density of water also increases and therefore the total force draging the box down should decrease if we assume that $V$ is constant. So it looks like the acceleration should decrease in this case. If You consider viscosity forces, dynamic viscosity of water increases with pressure, so it should further slow down the box, but I don't know to what extent.

When it comes to Your second question, the melting point of water decreases with increasing pressure, as it is shown here:

As You can see, the water at the bottom of an ocean should have the temperature much below 0 Celsius degree to solidify, so this isn't really probable. According to wikipedia the temperature of deep ocean water varies from 0 °C to 3 °C.

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I don't think your Fh is correct. The net hydrostatic force should be approximately zero, since you have pressure on the surface area on the bottom pushing upward as well. In fact, it should be very slightly upward for tall objects, since the pressure at the bottom of the object will be slightly higher than the pressure at the top. –  Doresoom Mar 21 at 18:24
@Doresoom I see Your point, how would You change the force balance? –  Wojciech Mar 21 at 18:32
It should be m*g-rho*g*V-Fdrag. rho will change with water temperature, so the buoyant force should increase as the depth increases. –  Doresoom Mar 21 at 18:54
@Doresoom I guess now I got it right, seems like friday's not my best day. Thanks for Your remarks! –  Wojciech Mar 21 at 20:37