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Capillary rise balances the vertical component of surface tension around the tube's circumference against the weight of the raised column, giving h = 2.gamma.cos(theta)/(rho.g.r). Water in a 0.5 mm radius tube climbs about 28 mm. Mercury, with a contact angle above 90 degrees, gives a negative rise and is pushed down instead.
Jurin's law
h = 2 gamma cos(theta) / (rho g r)
Capillary pressure
dP = 2 gamma cos(theta) / r
The lifting force scales with circumference while the weight lifted scales with area, so halving the radius doubles the rise.
Partly. Capillarity in xylem helps, but the dominant mechanism is transpiration pull, which can generate far more than capillary pressure alone.