- #1
Alexander83
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I've always found pressure fairly intuitive to understand when dealing with ideal gases, but am struggling a little with a thought experiment concerning pressure changes in a liquid.
Here's a simple thought experiment I'm struggling with. I'm thinking of a still volume of pure water at constant temperature in the Earth's gravitational field. The water has a constant temperature and thus, its density should be constant throughout. Per the hydrostatic equilibrium equation, the pressure in the volume of water should increase as one moves deeper in the water column. Given that water is taken to be incompressible, this change in pressure should not affect its density.
My conceptual difficulty is in understanding what's happening at a molecular level to cause this increase in pressure. I keep wanting to think of the ideal gas case where pressure can be visualized as a net force per unit area exerted over a hypothetical surface in the fluid owing to random molecular collisions. Trying to apply this model to the water would seem to imply that, in order for the pressure to increase with depth one of two things should occur. Either the density would have to increase in order to have more molecules collide with the surface (this violates the incompressibility assumption). Or, the average speed of the molecules at constant density would have to increase (this violates the constant temperature assumption).
I'm left with one of two conclusions.
1. Either my simple model of an incompressible, constant temperature liquid in a gravitational field is impossible, OR
2. My model of what "causes pressure" in a liquid like water is wrong. Can pressure in a liquid still be visualized as due to the effects of random molecular collisions as in an ideal gas? If not, what's the appropriate mental model?
Thanks everyone for your input!
Alex
Here's a simple thought experiment I'm struggling with. I'm thinking of a still volume of pure water at constant temperature in the Earth's gravitational field. The water has a constant temperature and thus, its density should be constant throughout. Per the hydrostatic equilibrium equation, the pressure in the volume of water should increase as one moves deeper in the water column. Given that water is taken to be incompressible, this change in pressure should not affect its density.
My conceptual difficulty is in understanding what's happening at a molecular level to cause this increase in pressure. I keep wanting to think of the ideal gas case where pressure can be visualized as a net force per unit area exerted over a hypothetical surface in the fluid owing to random molecular collisions. Trying to apply this model to the water would seem to imply that, in order for the pressure to increase with depth one of two things should occur. Either the density would have to increase in order to have more molecules collide with the surface (this violates the incompressibility assumption). Or, the average speed of the molecules at constant density would have to increase (this violates the constant temperature assumption).
I'm left with one of two conclusions.
1. Either my simple model of an incompressible, constant temperature liquid in a gravitational field is impossible, OR
2. My model of what "causes pressure" in a liquid like water is wrong. Can pressure in a liquid still be visualized as due to the effects of random molecular collisions as in an ideal gas? If not, what's the appropriate mental model?
Thanks everyone for your input!
Alex