Trying To Figure Out A Hydrostatic Pressue Problem
Trying To Figure Out A Hydrostatic Pressue Problem
(OP)
I have attached a picture of a problem I am trying to understand. Basically I have a Piston attached to the ground, and a container of water "free standing" above most of the Piston.... meaning, the container of water could collapse onto the Piston if the Physics say it will (and thus displace water up into the small pipe).
I'm trying to figure out what values I need to know to figure out if the container of water will collapse onto the Piston, or if the container of water will just stay where it is.
If I'm trying to push a Piston upwards into a container of water, I understand that I need to overcome the PSI of the water. However, in this problem there is not only PSI but the weight of the container itself.... and I'm not sure what to do.
Any advice would be appreciated.
I'm trying to figure out what values I need to know to figure out if the container of water will collapse onto the Piston, or if the container of water will just stay where it is.
If I'm trying to push a Piston upwards into a container of water, I understand that I need to overcome the PSI of the water. However, in this problem there is not only PSI but the weight of the container itself.... and I'm not sure what to do.
Any advice would be appreciated.





RE: Trying To Figure Out A Hydrostatic Pressue Problem
If the outlet is open, water is free to flow and the container will settle to the ground or the piston touches the inside of the container.
If the outlet is closed and the small pipe is full of water, the container will stay in place since no water displacement can occur.
Ted
RE: Trying To Figure Out A Hydrostatic Pressue Problem
it sounds like you have a container of liquid sitting on top of a piston. if you raise the piston, won't the container of water rise with it ? what's restraining the container ??
if the upper surface of the container is attached to ground, then raising the piston will cause the liquid to displace. if the outlet is closed it'll cause the gas (trapped above the liquid) to compress.
You could consider work/energy ... work done by the piston = work done by the liquid and the gas in the container.
you could consider volumes ... volume due to the piston changing it's postion = volume change in the gas.
RE: Trying To Figure Out A Hydrostatic Pressue Problem
I should also note that the small pipe can extend upwards. I am not suggesting the water expel from the container... but would stay in the container... only moved to a greater elevation in the container.
RE: Trying To Figure Out A Hydrostatic Pressue Problem
RE: Trying To Figure Out A Hydrostatic Pressue Problem
RE: Trying To Figure Out A Hydrostatic Pressue Problem
Under what circumstances will the container fall and displace the water into the upper chamber?
One person told me that, as long as the surface area surrounding the Piston is larger than the area of the Piston, the container would collapse.
RE: Trying To Figure Out A Hydrostatic Pressue Problem
RE: Trying To Figure Out A Hydrostatic Pressue Problem
is this like a balloon (flexible container) with maybe a straw sticking out of it sitting on top of a piston, perhaps balanced by the hand of a nearby experimenter. if th epoison is bigger than the container then i'd expect the container would spread out over the piston untill maybe the strain in the membrane restricts further spreading ... if the piston is bigger than this then the contianer should sit happily onto of the piston. if smaller, then the flexible container will spread over the edge and i'd expect it to collapse. sounds like a reasonable experiment to try ... somewhere you don't mind getting wet ...
RE: Trying To Figure Out A Hydrostatic Pressue Problem
Even if the Piston WERE the bottom surface of the container, there would be an extremely small gap between the side of the Piston and the wall of the container... which is where the seal would occur. So technically, the Piston has to be smaller than the surface of the container.
In my example, I clearly made the smaller than the full surface area of the bottom of the container.
This is basically the difference between hammering a nail into someone's back, and securing a nail to the ground and asking someone to lay on it. My example is a bit more complex than that, but it is the same in flipping the problem around to the other side.
The confusion I have is that there are two different ways to look at the forces in play here.
First you have the water pressure at the bottom of the container, which is acting on the bottom of the container (which INCLUDES the surface of the Piston). That is what is happening inside due to the Hydrostatic Pressure, right?
But then if you step back and look at the whole picture, you see the entire weight of the water in the whole container, and the weight of the container itself.
What I am trying to find out, mainly, is what is the "breaking point" where the container will collapse around the Piston vs. where the container will stay as it is originally illustrated.
One person told me "if the area of the surface of the container is larger than the surface area of the piston, the container will collapse". I believe said that because there will be more total PSI pressure on a larger area of the container floor, than on the Piston surface.... therefore the container wall will want to go lower.
RE: Trying To Figure Out A Hydrostatic Pressue Problem
"In my example, I clearly made the Piston area smaller than the full surface area of the bottom of the container."
RE: Trying To Figure Out A Hydrostatic Pressue Problem
Out of curiosity, do you have an engineering background?
Patricia Lougheed
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RE: Trying To Figure Out A Hydrostatic Pressue Problem
if the balloon sides are very thin, it could break before it reaches this stable state.
now put the balloon on a smaller surface ... it spread over this surface and spill over the side. maybe this is "collapse". maybe there's another surface 1/16" below the original one, so the balloon will probably keep spreading.
RE: Trying To Figure Out A Hydrostatic Pressue Problem
The problem with the balloon example is that the pliability of the balloon walls may be able to prevent any water from being displaced up into the straw. It is not similar enough to my liking.
.... however, you do seem to be agreeing with that "someone" who told me the Piston surface area (relative to the area of the entire container floor) plays a big factor in if the container would fall around the Piston.
RE: Trying To Figure Out A Hydrostatic Pressue Problem
Assuming you have a rigid container sliding over a fixed piston then you will be able to create head pressure based on the buoyancy of the container. The effects of water pressure on the surface of the container alone will not create a pressure differential that would allow you to pump water.
If you can provide more info into what exactly you are trying to determine then somebody here may be able to help. However, if this is for a real world problem, you should get an engineer to work on it. Nobody here is going to design it for free for you, and without an engineering background it will be difficult for you to come up with a workable design.
Use of product voids warranty.
RE: Trying To Figure Out A Hydrostatic Pressue Problem
A1= piston area
A2= container area
A3= pipe area
H1= height of container
H2= height of water level in pipe (the large reservoir at the top of the pipe adds a complication which I don't think was intended. It will behave the same as a uniform diameter container with no pipe).
I'm not going to work out any equations as there are too many undefined factors.
The key factors are:
1. The weight of water outside the piston diameter ((A2-A1)H1) will push the container down and displace water up the pipe.
2. The head of water in the pipe above the container will push the container up by acting on an area A1-A3.
RE: Trying To Figure Out A Hydrostatic Pressue Problem
RE: Trying To Figure Out A Hydrostatic Pressue Problem
A1=piston area
A3=upper container area
s=container displacement
h=level change in upper container
H=initial distance of level in upper container to piston top
ρ=liquid density
Mc=container mass
Now:
A1s=A3h
Change in potential energy of liquid
ΔUl=ρA1s(h/2+H-s/2)
Change in potential energy of container
ΔUc=Mcs
By equating the changes in potential energy one can easily calculate s.
Limit cases:
-if H=Mc/ρA1 the container won't move, if H is larger the container will go upwards
-if A1>>A3 like in the first sketch, container movements will be small (the container behaves rigidly when you try to displace it)
prex
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RE: Trying To Figure Out A Hydrostatic Pressue Problem
Let A be the area of the piston head.
Let V be the total volume of water.
Let w be the unit weight of water.
Let H be the vertical distance from the piston head to the free water surface.
Let W be the weight of the (empty) container.
Consider the movement of water when the container moves down a small amount d.
This can be viewed as the entire "shape" of water (whose volume is V) moving downwards by a distance d, on top of which is "superimposed" the upwards movement of a volume Ad by a distance H.
Problem solved. The net effect of these two movement components is an increase of
(HA-V)dw
in the potential energy of the water. The potential energy of the container has decreased by
Wd
The container will be in equilibrium if these two quantities are equal. (I think this is a stable equilibrium, but do not have time to verify my feeling.)
It will tend to move up if
H > (Vw+W)/(Aw)
This is NOT the same result derived above by Prex. I think Prex has omitted the mass of the overall body of water.
RE: Trying To Figure Out A Hydrostatic Pressue Problem
Let me try again.
When the container goes down by s, the net effect on the water mass is that the volume A1s goes up by H-s/2+A1s/2A3=H+(A1/A3-1)s/2 , and the rest of the water goes down with the container.
So the energy balance gives, after some rearrangement (V= total volume of water):
Mc+ρ(V-A1H)=ρA1(A1/A3+1)s/2
At equilibrium H is as per Denial's solution, and again, s will tend to be smaller when A1>>A3.
prex
http://www.xcalcs.com : Online engineering calculations
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http://www.levitans.com : Air bearing pads
RE: Trying To Figure Out A Hydrostatic Pressue Problem
The annulus of water + containment are always in equilibrium since no matter, the configuration the differential pressure top and bottom x the annulus area is the weight of the water in the annulus.
So we are left with a piston the same diameter of the remaining "containment" whose outside diameter is equal to the diameter of the piston. Now, the vertical forces on the "containment" are always net upward and will continue until all of the water is inside the lower vessel. If there is excess water beyond this, shown in the neck section then ,it will lift above the piston.
My conclusion is, there is no possibility of collapse, but only upward motion of the container, so long as the neck section still holds water; otherwise, static equilibrium will be achieved
at the moment there is no water left in the neck.
RE: Trying To Figure Out A Hydrostatic Pressue Problem
RE: Trying To Figure Out A Hydrostatic Pressue Problem
The forces on the annulus of water are
1)downward pressure from the top of the container*A, A= annulus area
2) upward pressure from the bottom of the container*A
3) weight of the water h*rho*A, --h=height
but h*rho=pottom-ptop
in any configuration
which proves that that mass of water is always in equilibrium.
RE: Trying To Figure Out A Hydrostatic Pressue Problem
I agree that it is always the same.
You seem to be stating that pressure at the top of the annulus plus the pressure due to the mass of water in the annulus is the pressure at the bottom of the annulus. This is true. But then you say its all in equilibrium. This is not true. The mass of water in the annulus results in a downward force. The only thing that can resist this is water pressure acting on the top of the container over the piston area (A1-A3 in my earlier post).
You say: "You forgot the pressure from the top of the container pushing down on the annulus of water".
Pressure created by the column of water in the pipe has no net effect in the annulus area. It pushes up and down by the same amount.
RE: Trying To Figure Out A Hydrostatic Pressue Problem
Ted
RE: Trying To Figure Out A Hydrostatic Pressue Problem
Looked at this again and am now in agreement with the force of the annulus water pushes down on the container,and while if there is water in the pipe, then there is an upward force on the container due to the height of water in the pipe. Depending on the initial height of water in the pipe and the areas projected by the piston-pipe area, the container will move up or down.
For the case where there is no level in the pipe at first, then the container will move downward as Compositro says, raising the water level in the pipe and increasing the upward force on the container, and eventually, if there is sufficient pipe height, will reach equilibrium at which time
annulus water weight= rho *h*(piston area-pipe area)
h= height in pipe
rho water density