ANS:D -
To calculate the settling velocity of a particle in a sedimentation tank, we can use Stokes' law, which describes the settling velocity of small spherical particles in a fluid. Stokes' law is given by:
Vs=2g (ρs−ρf)r^2 / 9μ
Where:
- Vs is the settling velocity of the particle,
- g is the acceleration due to gravity (approximately 9.81 m/s29.81m/s2),
- ρs is the density of the particle,
- ρf is the density of the fluid (in this case, the density of water),
- r is the radius of the particle,
- μ is the dynamic viscosity of the fluid (water).
Now, let's solve this equation for the settling velocity Vs. Assuming the sedimentation tank has a length L, width B, and depth D, and a discharge Q, the settling velocity of the particle for this discharge can be calculated as follows:
Vs=Q/ L×B×D
This equation gives the settling velocity of the particle per unit area of the sedimentation tank.
If you have specific values for the parameters such as the density of the particle, density of water, particle radius, and dynamic viscosity of water, you can substitute them into the Stokes' law equation to find the settling velocity. Similarly, if you have the values for the dimensions of the sedimentation tank and the discharge, you can use the second equation to find the settling velocity per unit area of the tank. Let me know if you need further assistance with specific calculations!
