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Plateau–Rayleigh instability

The Plateau–Rayleigh instability, often just called the Rayleigh instability, explains why and how a falling stream of fluid breaks up into smaller packets ... more

Capillary pressure in a tube (contact angle)

In a sufficiently narrow tube of circular cross-section of radius “a”, the interface between two fluids forms a meniscus that is a portion of the surface ... more

Capillary pressure in a tube

In a sufficiently narrow tube of circular cross-section of radius “a”, the interface between two fluids forms a meniscus that is a portion of ... more

Conic section equation

In geometry, the conic constant (or Schwarzschild constant, after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the ... more

Lensmaker's equation

A lens is a transmissive optical device which affects the focusing of a light beam through refraction. A simple lens consists of a single piece of ... more

Gaussian beam ( radius of curvature )

In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are well ... more

Hyperbolic paraboloid equation

The hyperbolic paraboloid (not to be confused with a hyperboloid) is a doubly ruled surface shaped like a saddle. In a suitable coordinate system, a ... more

Maximum Velocity in Friction Banked Turn

A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more

Minimum Velocity in Friction Banked Turn

A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more

Pressure inside an ideal soap bubble

The pressure inside an ideal (one surface) soap bubble can be derived from thermodynamic free energy considerations. At constant temperature and in ... more

Descartes' theorem ( externally tangent circle to three given kissing circles)

In geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain ... more

Descartes' theorem ( internally tangent circle to three given kissing circles)

n geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic ... more

Velocity in Frictionless Banked Turn

A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more

Maximum contact pressure between two spheres

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Radius of the rim of a paraboloidal dish

The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point. In a suitable coordinate system with three axes x, y, and z, it ... more

Maximum Pressure on a Contact Area between two cylinders with parallel axes

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Capillary Action - height of the meniscus

Capillary action (sometimes capillarity, capillary motion, or wicking) is the ability of a liquid to flow in narrow spaces without the assistance of, and ... more

Centripetal Force - angular velocity

Centripetal force (from Latin centrum “center” and petere “to seek”) is a force that makes a body follow a curved path: its ... more

Liquid in a vertical tube (The height to which the column is lifted )

If a tube is sufficiently narrow and the liquid adhesion to its walls is sufficiently strong, surface tension can draw liquid up the tube in a phenomenon ... more

Blood pressure ( related to the wall tension of artery or vein)

Blood pressure is related to the wall tension of the artery or vein, according to the Young–Laplace equation (assuming that the thickness of the vessel ... more

Curvature of a Bimetallic Beam

A bimetallic strip is used to convert a temperature change into mechanical displacement. The strip consists of two strips of different metals which expand ... more

Depth of the contact region between a rigid conical indenter and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Hyperbolic law of cosines - 1st law

In hyperbolic geometry, the law of cosines is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar ... more

Elliptic paraboloid equation

The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point. In a suitable coordinate system with three axes x, y, and z, it ... more

Force on a Contact Area between a rigid cylinder and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Radius of a Contact Area between two cylinders with parallel axes

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Stress (mechanical)

Stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other. Any strain ... more

Resonant frequency of string

Acoustic resonance is the tendency of an acoustic system to absorb more energy when it is forced or driven at a frequency that matches one of its own ... more

Buckling Coefficient

In science, buckling is a mathematical instability that leads to a failure mode.

When a structure is subjected to compressive stress, buckling may ... more

Fluid Thread Breakup - Linear Stability of Inviscid Liquids

Fluid thread breakup is the process by which a single mass of fluid breaks into several smaller fluid masses. The process is characterized by the ... more

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