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In fluid dynamics, the tea leaf paradox is a phenomenon where tea leaves in a cup of tea migrate to the center and bottom of the cup after being stirred rather than being forced to the edges of the cup, as would be expected in a spiral centrifuge. The correct physical explanation of the paradox was for the first time given by James Thomson in 1857.
The early identification of self-similar solutions of the second kind can be found in problems of imploding shock waves (Guderley–Landau–Stanyukovich problem), analyzed by G. Guderley (1942) and Lev Landau and K. P. Stanyukovich (1944), [3] and propagation of shock waves by a short impulse, analysed by Carl Friedrich von Weizsäcker [4] and ...
In computational fluid dynamics, the projection method, also called Chorin's projection method, is an effective means of numerically solving time-dependent incompressible fluid-flow problems. It was originally introduced by Alexandre Chorin in 1967 [1] [2] as an efficient means of solving the incompressible Navier-Stokes equations.
This is an example of an implicit method since the unknown u(n + 1) has been used in evaluating the slope of the solution on the right hand side; this is not a problem to solve for u(n + 1) in this scalar and linear case. For more complicated situations like a nonlinear right hand side or a system of equations, a nonlinear system of equations ...
1643 – Evangelista Torricelli provides a relation between the speed of fluid flowing from an orifice to the height of fluid above the opening, given by Torricelli's law. He also builds a mercury barometer and does a series of experiments on vacuum. [1] 1650 – Otto von Guericke invents the first vacuum pump. [1]
The Boussinesq approximation is applied to problems where the fluid varies in temperature (or composition) from one place to another, driving a flow of fluid and heat transfer (or mass transfer [1]). The fluid satisfies conservation of mass , conservation of momentum and conservation of energy .
The Reynolds number Re is taken to be Re = V D / ν, where V is the mean velocity of fluid flow, D is the pipe diameter, and where ν is the kinematic viscosity μ / ρ, with μ the fluid's Dynamic viscosity, and ρ the fluid's density. The pipe's relative roughness ε / D, where ε is the pipe's effective roughness height and D the pipe ...
A physical paradox indicates flaws in the theory.. Fluid mechanics was thus discredited by engineers from the start, which resulted in an unfortunate split – between the field of hydraulics, observing phenomena which could not be explained, and theoretical fluid mechanics explaining phenomena which could not be observed – in the words of the Chemistry Nobel Laureate Sir Cyril Hinshelwood.