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We consider an element in a liquid at hydrostatic equilibrium such that continuum is maintained. Now to calculate the forces on it we consider body forces and surface force. Our system is simply a liquid kept in a glass with just gravity as its body force. For surface force we consider just the force due to the weight of the liquid above it. Why don't we consider the force by the movement of liquid molecules due to their thermal energy? If we don't consider it due to its low value, then just for the sake of rigorous calculation what equations will we write when we consider this. (If someone says that it will be same in every direction on the element, but still it will create some stress and compression.)

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Why don't we consider the force by the movement of liquid molecules due to their thermal energy?

This does not change the pressure. Essentially, increased thermal energy will make there be fewer collisions that are individually more energetic.

You can think of a ball bouncing on a floor. Regardless of the energy of the ball the average force is the same and equal to the ball’s weight. Similarly, the average force on a fluid molecule in hydrostatic equilibrium is equal to the molecule’s weight, irrespective of its energy or temperature.

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In a gas, the pressure on a surface is associated with the momentum change of rebounding molecules. Extra pressure requires a higher density or temperature in the gas. In a liquid you must add the contact forces between the molecules. The total pressure results from a combination of both, and the upward component must be adequate to support the weight of the fluid above.

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