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While deriving the equation of height to which the fluid rises, we say that the surface tension pulls the water till the weight of water balances it, my doubt is that how can any force pull on something that is liquid?

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When you are sucking a liquid with a straw, you are pulling a liquid by creating a low pressure in your mouth. This is similar with capillary rise: the surface tension has for effect to reduce the pressure of the water beneath the air-water interface. As a result, water rises until the pressure is balanced. The "pull" is transmitted down by the cohesion force between water molecules.

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