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The capstan equation [1] or belt friction equation, also known as Euler–Eytelwein formula [2] (after Leonhard Euler and Johann Albert Eytelwein), [3] relates the hold-force to the load-force if a flexible line is wound around a cylinder (a bollard, a winch or a capstan).
The goal is to find the steady velocity vector V and pressure p in a plane, subject to the condition that far from the cylinder the velocity vector (relative to unit vectors i and j) is: [1] = +, where U is a constant, and at the boundary of the cylinder
Schematic view of an SPH convolution Flow around cylinder with free surface modelled with SPH. See [1] for similar simulations.. Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows.
Then for an ideal gas the compressible Euler equations can be simply expressed in the mechanical or primitive variables specific volume, flow velocity and pressure, by taking the set of the equations for a thermodynamic system and modifying the energy equation into a pressure equation through this mechanical equation of state. At last, in ...
[1] The Magnus effect is named after Heinrich Gustav Magnus , the German physicist who investigated it. The force on a rotating cylinder is an example of Kutta–Joukowski lift, [ 2 ] named after Martin Kutta and Nikolay Zhukovsky (or Joukowski), mathematicians who contributed to the knowledge of how lift is generated in a fluid flow.
Washburn's equation is also used commonly to determine the contact angle of a liquid to a powder using a force tensiometer. [ 5 ] In the case of porous materials, many issues have been raised both about the physical meaning of the calculated pore radius r {\displaystyle r} [ 6 ] and the real possibility to use this equation for the calculation ...
The cylindrical harmonics for (k,n) are now the product of these solutions and the general solution to Laplace's equation is given by a linear combination of these solutions: (,,) = | | (,) (,) where the () are constants with respect to the cylindrical coordinates and the limits of the summation and integration are determined by the boundary ...
In convective heat transfer, the Churchill–Bernstein equation is used to estimate the surface averaged Nusselt number for a cylinder in cross flow at various velocities. [1] The need for the equation arises from the inability to solve the Navier–Stokes equations in the turbulent flow regime, even for a Newtonian fluid .