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Hydrostatic pressure and consequences of pascal's law

  1. Apr 11, 2014 #1
    I've had a doubt about the following (somewhat contradictory) statements.
    1) pressure applied to an incompressible fluid is equally transmitted at all points.
    2) pressure at points at different heights in a fluid placed in a container in a gravitational field are different.

    Gravity applies a pressure on the fluid. If the fluid transmits the pressure equally at all points, then how is pascal's law valid?
  2. jcsd
  3. Apr 11, 2014 #2


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    For many purposes the hydrostatic pressure is equal everywhere.

    But as the scale of the containment increases it must be realized that the weight of the water column increases the pressure ... and more so the further down you go.

    This is very significant in the oceans; insignificant in a barrel of water.

    You have found an example of physical laws with limitations to their applicability; this happens all the time.
  4. Apr 11, 2014 #3
    Number (1) is stated incorrectly. It should read "pressure within an incompressible fluid acts equally in all directions at a given point in the fluid." This is Pascal's law observation.

  5. Apr 12, 2014 #4
    If it acts equally in all directions at a given point, then why isn't the net pressure at all points in a fluid zero?
  6. Apr 12, 2014 #5
    It's at a given point not at all points.
  7. Apr 12, 2014 #6
    I think 1) is a reasonable restatement of Pascal's Law.

    For 2) you are essentially summing up all the pressures from the weight of the fluid. So as you work your way down the effect is cumulative.

    I don't see a contradiction between the two, rather 2) follows as a consequence of 1).
  8. Apr 12, 2014 #7
    Alright, consider one point at a certain depth in a fluid. If the pressure along all directions is equal, then the net pressure there is zero. So why do fluids have pressure at all?
  9. Apr 12, 2014 #8
    Paisiello, thanks for the response. But imagine gravity pushing down on the fluid, thus applying a pressure to it which, according to pascal's law is equally transmitted at all points. Then why do points at different heights in the fluid have different pressures.
  10. Apr 12, 2014 #9
    If you take a tiny cube of fluid at a given location in the fluid as a free body and the fluid is static, then the pressure on each of the 6 sides of the cube is p. The cube is in static equilibrium, and the net force on the cube is zero, but that doesn't mean that the force on each of its sides is equal to zero.

  11. Apr 12, 2014 #10
    True, but the NET pressure at every point is zero. Then why does fluid pressure exist?
  12. Apr 12, 2014 #11
    If you have a solid cube (e.g., not submerged in liquid), and you apply equal normal forces on all six of its sides so that the NET force on the cube is zero, are you asking why force exists?

  13. Apr 12, 2014 #12


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    Pressure is a scalar so it doesnt sum to zero, but even if it did, summing to zero doesn't mean the force is zero, it just means there is no motion. If you put your hand in a vise and crank it down, the forces sum to zero too - but it still hurts!
    Last edited: Apr 12, 2014
  14. Apr 12, 2014 #13


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    In all directions, not at all points.

    Do you feel more pressure sitting on top of a pile of bricks or under it.
  15. Apr 12, 2014 #14


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    There is no such thing as "net pressure". Pressure is a scalar, not a vector.
  16. Apr 12, 2014 #15


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    I always thought that pressure is defined as force per unit area; thus pressure can have a direction.

    See http://hyperphysics.phy-astr.gsu.edu/hbase/press.html

    This is usually most important at the boundaries - for example, inside the bubble the pressure is pointing outwards at the surface, and the air pressure is pointing inwards.

    For ball under water the external pressure is all pointing inwards - until the ball (or submarine) is crushed.
  17. Apr 12, 2014 #16
    Here is another example to illustrate item (1). Suppose you have a dam. At any given depth (location) right next to the dam, the water pressure is not only acting up and down. It is also pressing sideways (horizontally) on the face of the dam. This is all that item (1) is saying.

    Another example is a submarine hull. The water pressure doesn't only press down on the top of the hull and up on the bottom of the hull. It also presses sideways on the sides of the hull.

    The same happens to you when you go down to the bottom of a swimming pool at the deep end. If you are standing on the bottom at the deep end (say, held down by weights), the water presses horizontally on your sides as well as on the top of your head, even though your sides are nearly vertical.

  18. Apr 12, 2014 #17
    Actually, if we are getting technical, pressure is the isotropic part of the (second order) stress tensor. Under hydrostatic conditions, the stress tensor is equal to p times the identity tensor. To get the force per unit area acting on a surface, one simply dots (contracts) the stress tensor with a unit normal vector to the surface. This yields the pressure times the unit normal. So the pressure always acts normal to surfaces, as UltrafastPED has indicated.

  19. Apr 12, 2014 #18
    Gravity does not apply pressure equally it's stronger the nearer you are to the body that's attracting. Pascal's law allows pressure to be to be equally transmitted when gravity is ignored or pressure is applied in it's absence.
  20. Apr 12, 2014 #19
    Variation of gravitiational attraction with distance between the attracting bodies is typically not a significant contributor to hydrostatic pressure variations in practice (on the scale of a swimming pool or a glass of water, or even the depth of the ocean). The main contributor is the weight of the overlying fluid. Irrespective of this, I stand by what I said. The pressure at any given location is pushing equally in all directions. This applies whether the pressure is the result of a hydrostatic column of liquid, or whether the liquid is in a cylinder being squeezed by a piston. In fact, it applies not only to incompressible liquids but also to compressible gases.

  21. Apr 12, 2014 #20
    What causes the variation in the pressure of the overlying fluid.
    Why is there more pressure at the bottom of a column of water than the top.I agree that at any given location or point the pressure is equall but if you measured the pressure at a piont at the bottom of a column of water and then at another point at the top won't the two locations be pushing with different amounts of force when compared.
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