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Settling basins and clarifiers should be designed based on the settling velocity (v s) of the smallest particle to be theoretically 100% removed. The overflow rate is defined as: [citation needed] Overflow rate (v o) = Flow of water (Q (m 3 /s)) /(Surface area of settling basin (A(m 2))
Stokes' law is the basis of the falling-sphere viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube.
where w is the settling velocity, ρ is density (the subscripts p and f indicate particle and fluid respectively), g is the acceleration due to gravity, r is the radius of the particle and μ is the dynamic viscosity of the fluid. Stokes' law applies when the Reynolds number, Re, of the particle is less than 0.1.
Generally, for small particles (laminar approximation), it can be calculated with Stokes' Law. For larger particles (turbulent particle Reynolds numbers), fall velocity is calculated with the turbulent drag law. Dietrich (1982) compiled a large amount of published data to which he empirically fit settling velocity curves. [21] Ferguson and ...
This method is mainly used for particles smaller than 1 μm. The smaller or lighter particles rise to the top (overflow) because their terminal sedimentation velocities are lower than the velocity of the rising fluid. The terminal velocity of any particle in any medium can be calculated using Stokes' law if the particle's Reynolds number is ...
The hydrometer method of determining soil texture is a quantitative measurement providing estimates of the percent sand, clay, and silt in the soil based on Stokes' law, which expresses the relationship between the settling velocity and particle size. [11] According to this law the particles settle down because of the weight and gravity action.
The retention time is the average time that a particulate remains in the clarifier. The turbidity is a measure of cloudiness. Higher values for turbidity removal efficiency correspond to less particulates remaining in the clarified stream. The settling velocity of a particulate can also be determined by using Stokes' law. [17]
The particle Reynolds number is important in determining the fall velocity of a particle. When the particle Reynolds number indicates laminar flow, Stokes' law can be used to calculate its fall velocity or settling velocity. When the particle Reynolds number indicates turbulent flow, a turbulent drag law must be constructed to model the ...