Assumptions:
- The settling of grit particles can be approximated by Stokes’ Law.
- The flow in the channel is laminar.
- The particle size distribution is homogeneous.
- There is no turbulence or eddy currents in the channel.
The settling velocity (Vs) of a particle can be calculated using Stokes’ Law:
Vs = (2⁄9) * ((𝜌p - 𝜌f) / 𝜇) * g * r^2
where, 𝜌p = density of the particle 𝜌f = density of the fluid 𝜇 = dynamic viscosity of the fluid g = acceleration due to gravity r = radius of the particle
Since, d = 0.15 mm, radius ® = d/2 = 0.075 mm
Given, Density of particle (𝜌p) = 2500 kg/m^3 Channel depth (h) = 2 mm Horizontal flow velocity (v) = 0.4 m/s
Assuming that water is used as the fluid medium, its density and dynamic viscosity at room temperature are 𝜌f=1000 kg/m^3 and 𝜇=0.001 Pa*s respectively.
The critical velocity for sedimentation can be calculated using: vcrit=(Vs* h)/L
where L is length of the channel required to settle the particle.
Substituting values into Stokes’ Law equation, we get:
Vs = (2⁄9) * ((2500 - 1000) / 0.001) * 9.81 * (0.075*10^-3)^2 ≈ 1.49 ×10^-5 m/s
Using this value and substituting given values into the critical velocity formula, we get:
vcrit=(1.49 ×10^-5*2)/L=0.4 L=(1.49 ×10^-5*2)/0.4 L=7.45×10^-6 m
Therefore, the minimum channel length required to settle a grit particle with a diameter of 0.15 mm and density of 2500 kg/m^3 is approximately 7.45 mm (or 0.00745 m).
Figure:
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h->|_________________________________________|
<-------- L = 7.45 mm -------->
Note: The figure is not to scale
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