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An advantage of the plug flow model is that no part of the solution of the problem can be perpetuated "upstream". This allows one to calculate the exact solution to the differential equation knowing only the initial conditions. No further iteration is required. Each "plug" can be solved independently provided the previous plug's state is known.
The solution presented explains how to solve the problem in a spreadsheet, showing the calculations column by column. Within Excel, the goal seek function can be used to set column 15 to 0 by changing the depth estimate in column 2 instead of iterating manually.
In fluid dynamics, Rayleigh problem also known as Stokes first problem is a problem of determining the flow created by a sudden movement of an infinitely long plate from rest, named after Lord Rayleigh and Sir George Stokes. This is considered as one of the simplest unsteady problems that have an exact solution for the Navier-Stokes equations.
Based on wind resistance, for example, the terminal velocity of a skydiver in a belly-to-earth (i.e., face down) free-fall position is about 195 km/h (122 mph or 54 m/s). [3] This velocity is the asymptotic limiting value of the acceleration process, because the effective forces on the body balance each other more and more closely as the ...
The case for an oscillating far-field flow, with the plate held at rest, can easily be constructed from the previous solution for an oscillating plate by using linear superposition of solutions. Consider a uniform velocity oscillation (,) = far away from the plate and a vanishing velocity at the plate (,) =. Unlike the stationary fluid in ...
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
When finally the tube BC is removed (Figure (c)) the water should again lift up to this height, which is named AD in Figure (c). The reason for that behavior is the fact that a droplet's falling velocity from a height A to B is equal to the initial velocity that is needed to lift up a droplet from B to A.
where M k are the components of the applied torques, I k are the principal moments of inertia and ω k are the components of the angular velocity. In the absence of applied torques, one obtains the Euler top. When the torques are due to gravity, there are special cases when the motion of the top is integrable.