Young Equation
Compute γSL = γSV − γLV·cos(θ) from Young's equation.
γSL (mN/m)
—
Surface tension and the Young–Laplace equation
Surface tension γ is the force per unit length acting along a liquid's surface (N/m), and it comes from cohesive forces that don't cancel out at the interface. The Young–Laplace equation ties the pressure jump across a curved interface to γ and the radii of curvature: ΔP = γ·(1/R₁ + 1/R₂). A spherical droplet gives ΔP = 2γ/r, while a cylinder gives ΔP = γ/r. Some reference values at 20 °C: water sits at γ = 72.8 mN/m, mercury at 485 mN/m (so high it beads into round droplets) and ethanol at just 22 mN/m. Surfactants such as soap and detergents knock γ down sharply. As an example, a water droplet of 1 mm radius carries an internal overpressure of ΔP = 2·0.0728/0.001 ≈ 146 Pa.
Applications
Formulating detergents and shampoos, where lowering γ helps "wet" surfaces. Cosmetics. Agricultural spraying, where adjuvants boost leaf coverage. Pulmonary mechanics, since lung surfactant keeps alveoli from collapsing, and its absence brings on respiratory distress syndrome in premature infants. Then microfluidics, ink-jet printing and inkjet droplet formation.
FAQ
Why does mercury form beads and water spreads? Mercury has a very high γ and barely sticks to most surfaces, so cohesion wins over adhesion. Water carries a lower γ and wets clean glass nicely, because its adhesion to silica beats its own cohesion.
How does soap lower surface tension? Surfactant molecules carry a hydrophilic head and a hydrophobic tail. They crowd the interface and break up the hydrogen bonding between water molecules, which pulls γ down from about 72 to roughly 30 mN/m.
Does temperature affect γ? It does. γ falls off roughly linearly as temperature rises. Water goes from 75.6 mN/m at 0 °C down to 58.9 mN/m at 100 °C, and near the critical point γ drops all the way to zero.
Related Tools
Weber Number
Compute the Weber number We = (ρ·v²·L)/σ.
Gear Contact Stress (Hertz)
Calculate the Hertzian contact stress on gear tooth surfaces, σ_H = C_p·√(F_t ÷ (b·d·I)), from the elastic coefficient C_p (√MPa, a function of the pair's elastic moduli), the tangential force F_t (N), the face width b (mm), the pinion pitch diameter d (mm) and the geometry factor I (dimensionless). This is the basis of SURFACE FATIGUE (pitting) design — the second fundamental gear failure mode, distinct from bending breakage. When two teeth touch, the contact is practically a LINE, and even moderate loads create very high contact stresses (hundreds of MPa) in the tiny contact area, per Hertz theory. Under repeated cycles, these stresses cause sub-surface fatigue that flakes off small bits of material, forming craters (pitting) that progress, destroy the tooth profile, generate noise and vibration and lead to failure. The elastic coefficient C_p gathers the materials' elastic properties (steel-steel, steel-bronze, etc.), and the geometry factor I, the curvature and contact ratio. Contact stress is compared with the material's pitting resistance (which depends strongly on surface HARDNESS — so gears are often case-hardened). It is one of the two central AGMA criteria. Enter the elastic coefficient, tangential force, face width, diameter and geometry factor.
Maximum Surface Settlement (Tunnel)
Calculate the maximum surface settlement, over the tunnel axis, S_max = Vs ÷ (i·√(2π)), from the settlement trough volume per metre of tunnel Vs (m³/m, the lost soil volume surfacing) and the trough-width parameter i (m, Peck's method). Since the trough is Gaussian, integrating the curve gives Vs = √(2π)·i·S_max, isolating the maximum settlement, which occurs right over the axis. This is the critical value for damage assessment: compared to allowable limits (typically 10-25 mm for sensitive structures), it decides whether the excavation is safe or needs mitigation. Enter the trough volume and the width parameter.
Cable Voltage Drop
Compute voltage drop ΔV = 2·ρ·L·I/A in cable.
Vessel Allowable Stress (ASME)
Calculate the design allowable stress of a pressure-vessel material by the ASME criterion, S = σ_uts ÷ n, from the material minimum tensile strength σ_uts (MPa) and the safety factor n (3.5 in the current ASME VIII Div. 1 edition for tensile strength). The allowable stress S is the MAXIMUM stress permitted in the vessel material in service, and is the basis of all thickness and MAWP calculations — it embeds the safety margin against failure. The ASME code sets the allowable stress as the SMALLEST among several criteria: a fraction of the TENSILE strength (σ_uts/3.5 in the current edition — formerly /4.0, reduced as materials and inspection advanced), a fraction of the YIELD strength (2/3 of σ_yield), and, at high temperatures, criteria based on CREEP and creep rupture (since at high temperature the material deforms slowly under constant load). For each material and temperature, the code TABULATES the S value — this formula shows the tensile-strength criterion, often governing at moderate temperatures. Using the correct allowable stress (from the code, for the right material and temperature) is absolutely essential: it is the safety margin protecting against vessel explosion. Enter the tensile strength and the safety factor.
Ohm’s Law Calculator
Calculate voltage (V), current (I), resistance (R) and power (P) using Ohm’s Law. Provide any two values and the calculator finds the other two. Useful for electronics and electrical work. Everything in your browser.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.