page_title: Jurin's law
section_title: Derivation
hierarchical_section_title: Jurin's law / Derivation
caption_attribution_description: English: Jurin equation Русский: Уравнение Жюрена
context_page_description: Jurin's law, or capillary rise, is the simplest analysis of capillary action—the induced motion of liquids in small channels—and states that the maximum height of a liquid in a capillary tube is inversely proportional to the tube's diameter. Capillary action is one of the most common fluid mechanical effects explored in the field of microfluidics. Jurin's law is named after James Jurin, who discovered it between 1718 and 1719. His quantitative law suggests that the maximum height of liquid in a capillary tube is inversely proportional to the tube's diameter. The difference in height between the surroundings of the tube and the inside, as well as the shape of the meniscus, are caused by capillary action. The mathematical expression of this law can be derived directly from hydrostatic principles and the Young–Laplace equation. Jurin's law allows the measurement of the surface tension of a liquid and can be used to derive the capillary length.
context_section_description: The height  of the liquid column in the tube is constrained by the hydrostatic pressure and by the surface tension. The following derivation is for a liquid that rises in the tube; for the opposite case when the liquid is below the reference level, the derivation is analogous but pressure differences may change sign.
caption: Scheme showing the relevant variables to the problem for a positive height.
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