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Pascal's law, pressure, consequences 
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#1
Feb2411, 04:31 PM

P: 951

Yes equations say its the same pressure, but its soooooooo non intuitive!!!!
Can you please explain, and try to near this problem to me, i can't sleep!! How come the pressure at A and B is the same, although we don't have same amount of water ... pascal's law says it is... But i don't get it... 


#2
Feb2411, 06:03 PM

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To see that the pressure at depth [itex]h[/itex] is always [itex]\rho g h [/itex] (i.e. the weight of a column of water above that depth, up to the free surface), forget about the shape of the container. Think about a little cube of water somewhere in the container. This is a statics situation. There is no flow or movement of the water. So the forces on that little cube have to be in equilibrium. Therefore, the force on the bottom of the cube must be equal to the force on the top of the cube, plus the weight of the cube itself. It this was not true, the little cube of water would move, because of the unbalanced forces acting on it. Write the force on the top and bottom as (pressure x area), and the weight as (g x mass) = (g x density x volume) = (g x density x area x height), cancel out the areas, and you get Pascal's law. 


#3
Feb2411, 06:07 PM

P: 3,387

I've removed my post because I think yours covers it far better. 


#4
Feb2511, 06:09 AM

P: 951

Pascal's law, pressure, consequences
What bothers me, is that how come the pressure is the same. Look, i figure that tube of water in B tank is longer, i figure there is more fluid there ergo more pressure at the bottom... But at A tank that tube is much smaller in my intuition pressure would be lower that in the tank B... How do fluids add up? do they stack each other like, i don't know layers and each layer is affected by the one before, or are you watching only discreet sections of the fluid by it self. I think this misunderstanding what i have is mainly because i am used to solids... 


#5
Feb2511, 06:41 AM

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The simplest answer to that, I think, is that, if the pressure were not the same, then water would FLOW to equalise it. Where would it go in your diagram? The bottom of the 'boot' is already full.
Remember, where you have a fluid, the pressure acts in all directions  sideways as well as up or down. The upwards pressure on the underside of the 'boot' shape is the same as the sideways pressure on the sides at that height and equal to the downwards pressure on the water below. ANother way to think of it: if the pressure were different in different directions then you could make a craft that would travel around, utilising this force difference and not use any energy. And we all know that's a big no no. 


#6
Feb2511, 01:41 PM

P: 569

What is pressure?
Pressure is the force divided by the area perpendicular to its application. The interesting thing about pressure is that, when everything is in equilibrium, it is equal in every direction. The force in question here is the weight. For a given area on the ground, the weight of the atmospheric air column acting on this area will give us the atmospheric pressure. So when we say that the atmospheric pressure is 14,7 pounds per squared inch, that means that for every square of 1" X 1", the quantity of air over that surface weights 14,7 lb. This is why when we go up in altitude, the pressure drops: the column of air over us is shorter. At ground level, two sidebyside areas have the same air pressure acting on them, therefore there is equilibrium, the air does not displace sideways and pressure is equal in all directions. Now if we replace some of that air with, say, water, the new weight will be the weight of the (now shorter) air column PLUS the weight of the water column. Just like the case for air only, if there is no displacement, this means that the pressure has to be equal in every directions at the bottom of the water column. This is why the pressure is equal in both of your example: if at one place there is a column of water of equal height (and the same weight of air over it), the pressure at the bottom will be the same in both cases. And because there is equilibrium, in a horizontal plane (same height), the pressure has to be the same everywhere in that plane. By the way the proper equation is: [tex]P = P_{o} + \rho gh[/tex] Where [tex]\rho gh[/tex] is the pressure due to a column of a given height and density (a column of water for example) and [tex]P_{o}[/tex] is the pressure acting over that column (the column of air over that column of water for example). 


#7
Feb2511, 02:04 PM

P: 951




#8
Feb2511, 10:40 PM

P: 569




#9
Feb2511, 11:10 PM

P: 412

That is why heavy sheets of plywood get pushed out of the beds of pickup trucks. The ambient pressure under them is greater than the dynamicallyreduced pressure over them. Similarly, wind blowing past a vented building will cause an undampened barometer inside to "pump" with variations in the wind velocity. Consequently, one may assume that if the wind is blowing at any elevation at all, a barometer at the base of the column of air will not correctly measure the weight of the overlying air. I like the kinetic gas explanation of gas pressure better. Pressure is simply the mean number of molecular impacts per unit area times the mean impulse transferred per impact. 


#10
Feb2611, 03:42 AM

P: 951




#11
Feb2611, 09:07 AM

#12
Feb2611, 03:06 PM

P: 951

I am getting some things mixed up here. When go down the ocean what happens?
We have low pressure at top and high pressure at bottom, what why doesnt water then rush from bottom to top? And another question, WHY is pressure distributed in all directions evenly(without gravity case, for simplicity), Can someone go to atomic scale and explain this? 


#13
Feb2611, 04:47 PM

P: 569

The key word in all these problems is equilibrium. 


#14
Feb2611, 08:22 PM

P: 951

I think i got it, thanks all



#15
Apr113, 12:25 PM

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