Capillary Rise

The Capillary Rise calculator equation computes the height of liquid in a small diameter tube due to capillary force on the liquid.  

INSTRUCTIONS: Choose units and enter the following:

• (σ) Surface Tension of Fluid (Default: Surface Tension of Water at STP)
• (λ) Meniscus Angle
• (ρ_w) Density of Fluid (Default: Density of Water at STP)
• (R) Radius of Capillary Tube

Capillary Rise (h_c): The calculator returns the rise in millimeters.  However this can be automatically converted into other length units via the pull-down menu.

The Math / Science

The formula for the capillary rise is:

h_c = (2·σ·cos(λ))/(ρ·g·R)

where:

• h_c is the capillary rise
• σ is the surface tension
• λ is the meniscus angle
• ρ is the density
• R is the radius of the tube

The force on the fluid is caused by the attraction between the solid and the liquid which pulls the water up into the tube.  The water rises until the force of capillary attraction is offset by the force due to gravity on the water column.  The surface of the water in the tube meets the walls of the tube at a contact angle that is unique to the fluid, in this case water, creating a concave upper surface to the water.  The rise of the water is computed from the following:
 surface tension of the water

• angle of the meniscus, the angle at which the water surface intersects the sides of the tube
• density of the fluid
• local acceleration due to gravity (assumed at sea level)
• the radius of the tube

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