Mason-Weaver equation and time dependend solutions

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The discussion focuses on the Mason-Weaver concentration equation, specifically in relation to the sedimentation of coffee particles in a cylindrical vessel. The user seeks guidance on how concentration varies with time at a fixed height, in addition to qualitative changes with height. They express difficulty finding comprehensive examples beyond basic information available online, particularly from Wikipedia. The concept of settling velocity, which is influenced by particle size, density differences, and fluid viscosity, is highlighted as potentially relevant to their problem. Overall, the user is looking for more detailed insights and practical applications of the Mason-Weaver equation in their specific context.
Rosengrip
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Hello,

I need your help or rather guidance in relation to Mason-Weaver concentration equation. I would like to learn more on that matter because I need to describe a specific problem with it (sedimentation of coffee particles in a cylindrical vessel).

I can qualitatively describe how concentration changes with respect to height in vessel (exponent function), but what I would need is a relation to how concentration changes with respect to time on a fixed height and approx. values of different constants that take place in the equation.

All the material I got from the internet is from Wikipedia page, I can't find any good examples to point me in the right direction, so I came asking here.

Thanks for your time.
 
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The concept of "settling velocity", the terminal velocity of a particle in a medium exhibiting non-zero bouyancy (either positive or negative), might be useful here.
Terminal velocity is dependent on the size (radius) of the particle, the difference in density, and the viscosity of the fluid.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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