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Old Jan 31st 2014, 08:05 AM   #1
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a sample problem

H!
we have a glass full of water we know that pressure in down of glass is most than the up but why the water dont flow in glass??
(Sorry for my bad English)
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Old Jan 31st 2014, 11:25 AM   #2
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Originally Posted by panda View Post
H!
we have a glass full of water we know that pressure in down of glass is most than the up but why the water dont flow in glass??
(Sorry for my bad English)
Sorry, I'm not sure I understand your question. Are you asking why the difference in pressure between the bottom and top of the water in the glass doesn't cause the water to flow?

From Newton's 2nd Law we know that F=ma, wher F is the sum of forces acting on an object. Imagine a thin layer of water in the glass of thickness h, with its upper surface at depth D (hence its lower surface is at depth D+h). Pressure from all the water above the layer is pressing down - if the glass has cross-section area A then this force is F_1=DpgA, where p = density of water and g = acceleration due to gravity. The pressure acting upward on the bottom of the layer results in a force equal to F_2 = (D+h)pgA. Finnally the weight of the water itself is W=hpgA. So the sum of forces acting in the downward direction on the layer of water is DpgA + hpgA, and the sum of forces acting upward is (D+h)pgA. Consequently the forces cancel out, so there is no acceleration of the water either up ior down. You can repeat this for all the layers of water in the glass - all layers are in equilibrium and so none of them will accelerate on their own, and there is no water flow without an outside disturbance.
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Old Feb 1st 2014, 03:05 AM   #3
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how did you calculate F1 and F2??
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Old Feb 1st 2014, 03:07 AM   #4
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I think that for calculate F2 and F1 you suppose that the water is stable and you used this for your proof.i think that this is not correct way.
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Old Feb 1st 2014, 04:19 AM   #5
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I think chip is correct. The original question itself says the water does not move, which implies equilibrium. If you heat it from below, the water there expands and its density falls. This causes buoyancy to increase, resulting in an unbalanced force, and that layer tries to move up
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Old Feb 1st 2014, 04:36 AM   #6
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Yes, I assume the water is stable so that all layers are in equilibrium. Your original question was "why the water doesn't flow?", which implies the water is stable and you want to know why it doesn't instantaneously start to flow on its own. Of course if the water is originally circulating in the glass (i.e. it has some initial kinetic energy), then Newton's first law says it will keep circulating. Or if you add energy from an outside source it can cause circulation to start. If you have some other situation in mind please let us know.

Last edited by ChipB; Feb 1st 2014 at 04:39 AM.
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Old Feb 1st 2014, 04:37 AM   #7
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but i dont realize that why water is stable and im not sure about that.
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