h = 2γ·cosθ / (ρ·g·r)

Compute how far a liquid rises inside a narrow tube from surface tension, contact angle and tube radius by Jurin's law, for soil physics, paper wicking and microfluidic capillary effects.

📐 计算公式

毛细上升高度 h = 2×表面张力 γ × cos θ ÷ (密度 ρ × 重力加速度 g × 管半径 r)，接触角 θ 先由度 ×π÷180 化弧度参与计算，结果 ×1000 以 mm 展示。校验：γ、θ、ρ、r、g 五项非空合法数值守卫。判据：γ 越大或管半径越小上升越高，θ >90°（不润湿）时 cos θ 为负、液面反而下降。

液体在细管中因表面张力上升。

表面张力 γ (N/m)

接触角 θ (°)

密度 ρ (kg/m³)

管半径 r (m)

重力加速度 g (m/s²)

Formula & Standard References

Item	Formula	Source / Standard
Capillary rise	h = 2·gamma·cos(theta)/(rho·g·r)	Jurin law
Contact angle	theta < 90 degrees means wetting	wetting
Tube radius	h inversely proportional to r	capillarity

📌 计算说明

h = 2γcosθ/(ρgr)。
水在细玻管中明显上升。

📐 Property Data

Reference surface tensions and related constants with their sources (surface tension varies with temperature and purity)

Constant	Value	Unit	Source
Water–air surface tension (20 ℃)	72.75e-3	N·m⁻¹	IAPWS 1994 surface-tension equation (same value in NIST)
Water–air surface tension (25 ℃)	71.97e-3	N·m⁻¹	IAPWS 1994 / CRC Handbook
Standard acceleration of gravity g_n	9.80665	m·s⁻²	ISO 80000-3 / BIPM conventional value (exact)
Density of pure water (20 ℃)	998.207	kg·m⁻³	IAPWS-95 formulation

Note: h = 2γcosθ/(ρgr); the contact angle θ depends on all three phases (θ ≈ 0° for clean glass–water). Contamination can raise θ substantially, even above 90°, which makes the liquid level fall instead.

h = 2γ·cosθ / (ρ·g·r)

Formula & Standard References

📐 Property Data

📚 深度解析：毛细上升

💡 常见使用场景

❓ 常见问题（FAQ）

毛细上升高度计算器

h = 2γ·cosθ / (ρ·g·r)

Formula & Standard References

📐 Property Data

🔗 相关工具

📚 深度解析：毛细上升

💡 常见使用场景

❓ 常见问题（FAQ）