Filling a tube with water

On 23 Aug 2004 21:37:37 -0500, Jim Smith
wrote:

Maybe it would help if you imagined the tire half filled with water
and half filled with air. We will do the experiment on earth so that
gravity will ensure the air is in the top half of the tube, the water
at the bottom. Now, put the valve stem at the top of the tire, load
the bike, and add enough air to make the contact patch the same size
as in a tire completely filled with water. At equilibrium the
pressure is the same in the air as in the water[1], and since the
bottom of the tire has know way of knowing what is going on in the top
of the tire, this is the same pressure as in a tire completely filled
with water.


Right. When you load the bike, the air at the top compresses as the
water (ok, pedant, RELATIVELY incompresssible water displaces some of
the air). You must pressurize the air in order to prevent the tire
from flatting in this case.

Now, remove ALL the air. Pump in water under just enough pressure to
expand the innertube firmly against the tire casing. What happens with
nearly zero water pressure?

larry

Larry Schuldt wrote:

On 23 Aug 2004 21:37:37 -0500, Jim Smith
wrote:


Maybe it would help if you imagined the tire half filled with water
and half filled with air. We will do the experiment on earth so that
gravity will ensure the air is in the top half of the tube, the water
at the bottom. Now, put the valve stem at the top of the tire, load
the bike, and add enough air to make the contact patch the same size
as in a tire completely filled with water. At equilibrium the
pressure is the same in the air as in the water[1], and since the
bottom of the tire has know way of knowing what is going on in the top
of the tire, this is the same pressure as in a tire completely filled
with water.



Right. When you load the bike, the air at the top compresses as the
water (ok, pedant, RELATIVELY incompresssible water displaces some of
the air). You must pressurize the air in order to prevent the tire
from flatting in this case.

Now, remove ALL the air. Pump in water under just enough pressure to
expand the innertube firmly against the tire casing. What happens with
nearly zero water pressure?

That's where the "relatively incompressible" nature of water becomes
important. That property means that it takes only a small change in
volume to cause a very large change in pressure, unlike the case with
air or other gasses where the two properties are inversely proportional
and change by about the same amount (i.e. for gasses, half the volume =
twice the pressure). So you start with the water at roughly ambient air
pressure and now you reduce the volume slightly by putting a load on the
tire and flattening the bottom portion of it. That reduction in volume
results in a very large pressure increase in the water which is why the
water-filled tire can support quite a load even if it had little
pressure when unloaded.

If you put a load of 100 lbs on the tire and it deforms to create a
contact patch of two square inches, then the outer rubber surface at the
bottom of the tire must be exerting an average pressure of 50 psi on the
ground to support the load. The tire has very little rigidity itself,
so if it's exerting that pressure on the ground, it must be feeling the
same pressure from the water inside the tire, so the water pressure must
also be 50 psi *when the tire has that load and contact patch*.

On 23 Aug 2004 21:37:37 -0500, Jim Smith wrote:

Larry Schuldt writes:

On 22 Aug 2004 07:40:15 -0500, Jim Smith
wrote:

It is easy to verify that the pressure in the tire can not be close to
zero as you say: just fill the tile with 0.0 psi of air and watch
how the tires behave. The tires have no way of "knowing" if the
pressure inside comes from air, water, blood, or some other fluid.
Your clue to this is that none of the fluids properties appear in
the equations which describe the tire at equilibrium.

Not true. Air at 0 psi (relative to atmospheric) is readily
compressible and the weight of the frame will cause the tire to deform
(flat). Water is not compressible.

I do not think you quite understand what it means for a fluid to be
"compressible."

Maybe it would help if you imagined the tire half filled with water
and half filled with air. We will do the experiment on earth so that
gravity will ensure the air is in the top half of the tube, the water
at the bottom. Now, put the valve stem at the top of the tire, load
the bike, and add enough air to make the contact patch the same size
as in a tire completely filled with water. At equilibrium the
pressure is the same in the air as in the water[1], and since the
bottom of the tire has know way of knowing what is going on in the top
of the tire, this is the same pressure as in a tire completely filled
with water.

Not at all. Your half air/water tire is a very different thing from one filled
completely with water.

Ride your tire over a bump and the air will be compressed. Ride one completely
filled with water and the only give will be the rubber and carcass stretching.

Ron

RonSonic writes:

On 23 Aug 2004 21:37:37 -0500, Jim Smith wrote:

Larry Schuldt writes:

On 22 Aug 2004 07:40:15 -0500, Jim Smith
wrote:

It is easy to verify that the pressure in the tire can not be close to
zero as you say: just fill the tile with 0.0 psi of air and watch
how the tires behave. The tires have no way of "knowing" if the
pressure inside comes from air, water, blood, or some other fluid.
Your clue to this is that none of the fluids properties appear in
the equations which describe the tire at equilibrium.

Not true. Air at 0 psi (relative to atmospheric) is readily
compressible and the weight of the frame will cause the tire to deform
(flat). Water is not compressible.

I do not think you quite understand what it means for a fluid to be
"compressible."

Maybe it would help if you imagined the tire half filled with water
and half filled with air. We will do the experiment on earth so that
gravity will ensure the air is in the top half of the tube, the water
at the bottom. Now, put the valve stem at the top of the tire, load
the bike, and add enough air to make the contact patch the same size
as in a tire completely filled with water. At equilibrium the
pressure is the same in the air as in the water[1], and since the
bottom of the tire has know way of knowing what is going on in the top
of the tire, this is the same pressure as in a tire completely filled
with water.

Not at all. Your half air/water tire is a very different thing from one filled
completely with water.

Ride your tire over a bump and the air will be compressed. Ride one completely
filled with water and the only give will be the rubber and carcass stretching.

I was speaking of a tire at rest. I should have been more clear and
said "at equilibrium and at rest" instead of just saying "at
equilibrium." So, we have the tire at rest, loaded, half filled with
water, and at equilibrium (steady state). Adjust the air pressure to
obtain a contact patch which is identical to that of a tire completely
filled with water. The pressure in the two tires will be the same.
Picture a hydraulic lift or jack. The pressure required to lift a
given weight is independent of the fluid used. Does not matter if it
is oil, water, air, maple syrup, blood... makes no difference.

Yep, for a tire filled with an incompressible fluid the compliance
(dV/dP) of the tire is going to determine the pressure inside. The
smaller the compliance the higher the pressure is going to be for a
given load. That is why I suspect the water filled tire will have even
higher pressure than the air filled tire.

Of course, it will be possible to adjust the pressure in the water
filled tires any value desired within reason, but expect the pressure to
behave quite differently under changing loads than the air filled tire.