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Direction of pressure in a liquid

  1. Oct 2, 2012 #1
    In a liquid, when we use P=hρg, how do we take the h? I always thought that we take it from the bottom of the liquid but in a question, they showed that you can take it from the top so I'm pretty confused about this. Here is an example: http://postimage.org/image/oki3fq131/full/ [Broken]

    So from this I'm pretty confused about what direction my pressure will act on. Is it upwards or downwards? Because in this example, i took the pressure of the liquid to act downwards: http://postimage.org/image/bbf5ow2mj/full/ [Broken]

    so i'm really confused about the direction of pressure in the liquid. Since the pressure can exert a upwards force then aren't my assumptions wrong in the second image? Can someone clear this up for me? Thanks for the help!
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Oct 2, 2012 #2


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    Staff: Mentor

    Because fluids move, pressure acts in all directions. But the pressure is caused by the weight of the fluid above the point at which you are measuring pressure. Its like if you stack a bunch of 10lb bricks. The force under the fifth brick from the top is 50lb regardless of how many more are underneath.
  4. Oct 2, 2012 #3
    Pressure has no direction, it's a scalar field. The force arises due to a pressure difference, and this force acts in the direction of the steepest drop in the pressure field.*

    In the case of P=hρg, you're describing the contribution to the liquid pressure at a depth of h (due to the weight of all the water above this depth), so it's measured from the liquid's upper surface. As you ascend, the depth (h) decreases, so the force due to this pressure field acts upwards (according to *).

    Can you help me understand the second image? Do you have a water droplet suspended in an upside-down test-tube? We know the pressure of the air underneath is atmospheric pressure, and we know that the pressure at the bottom interface must match this, but also be equal to hρg+p1, where h is the height of the droplet and p1 is the pressure inside the cavity. This tells us that p1 = p0 - hρg.

    So your answers are correct, but I don't think you should be associating pressures with arrows. They don't point in any direction.

    The answers in the second figure to the right also look correct.
  5. Oct 2, 2012 #4
    Oh so when I measure my pressure it is always from top down? I think I got a brain fart thinking it was down up for the fast few days.
  6. Oct 2, 2012 #5
    What you were thinking of in my second pic was what correct :smile: I now understand that pressure exerts at all direction. So at the top would cant there be a upwards pressure? Since when I place a box into water the pressure exerts all around the box. Or is it because at the top the h in hρg is 0m so there is no upwards pressure?

    So within a fluid, technically the pressure can only exert downwards as thats where there is the maximum h? Then what about the stuff in between like the middle?

    So all in all here's what I cleared up. hρg's h is taken from top down, pressure of a fluid exerts in all directions, at the top of the fluid there is no upwards pressure as h is zero.

    Are these correct? Thanks for the help :smile:
  7. Oct 2, 2012 #6
    It is sometimes loosely said "pressure acts in any direction"

    Just to reinforce one thing Russ said.

    Pressure acts in all directions at once and all the time.

    So you may select any direction for consideration.

    You may also like to look at this thread

    Last edited: Oct 2, 2012
  8. Oct 2, 2012 #7
    I think we are slightly contradicting, I was always taught that pressure doesn't act in any direction because it's not a force and it's also a scalar. The force is -grad(P) for the continuum liquid or INT(over surface) of P*dA for a submerged body.

    Especially for questions like "calculate the pressure at..." I don't think it helps or has any meaning to assign arrows to pressures.

    Perhaps I'm being picky, but it seems to be the root of confusion in this particular case.
  9. Oct 2, 2012 #8
    It is true the pressure is not a vector, but it is not true to say that it has no direction.

    A quantity does not have to be a vector in order to possess direction, for instance the quantity "height relative to sea level or elevation or altitude" can be positive or negative and offers two directions up and down.
  10. Oct 2, 2012 #9


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    That sounds like you are making the point that even though pressure is not a vector that it still can have a "direction" by virtue of possibly going negative and becoming suck instead of blow.
  11. Oct 2, 2012 #10
    Pressure itself cannot be negative, only pressure gradients (or differences) can be. And that's exactly what gives rise to the associated vector forces.
  12. Oct 2, 2012 #11
    No, pressure can be negative, even in liquids (but not in gases).

    Compare with solids, where stress is directional - but not a vector!

    Under Newton IIIrd Law, each force (which in itself is a vector) causes equal and opposite counterforce.

    So, the force and counterforce taken together have a specific direction in space - but it is bilateral direction, not unilateral.

    If a hammer hits anvil, then the force of hammer is down. The force of anvil is up. So the pressure between hammer and anvil is in up-down direction - but it is not up or down, it is both up and down.

    The pressures, if any, along the anvil face are, in solids, independent of the pressure across the face.

    Not in liquid, however! Since liquids and gases have no shear strength, they can and will transmit pressure equally in all directions.

    Now, in solids, negative pressure has meaning. If the hammer is glued to the anvil then the glue can transmit tension. Again, the tension is neither up nor down - it is in up-down direction. The negative of a hammer pushing down against the anvil is not, in this context, happer pushing up, but hammer pulling up.

    Now, liquids may be ruptured relatively easily once sizable bubbles of gas including vapour exist inside the liquid or against container walls. Then as the pressure of the liquid falls below its (positive) vapour pressure, the bubbles will expand against the (small) surface tension of the liquid and prevent further fall of pressure.

    However, if the liquid is well devoid of bubbles or ways of initiating them then the pressure of liquid can be made lower than its vapour pressure - whether by lowering the pressure or by increasing the temperature and thus vapour pressure.

    The pressure of a liquid can be made negative and liquids can exert significant amount of tension. But since the liquid has no shear strength, the tension/negative pressure would be isotropic.

    Since ggases and supercritical fluids have no surface tension, they cannot be put under negative pressure, unlike liquids.
  13. Oct 2, 2012 #12

    So many unnecessary complications.

    Can't we just say pressure is a scalar and so it has no direction?
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