GATE CE 2019 Set 1 — Question 30
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Environmental Engineering → Drinking Water Treatment → Sedimentation
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Question
A completely mixed dilute suspension of sand particles having diameters and are filled in a transparent glass column of diameter and height . The suspension is allowed to settle without any disturbance. It is observed that all particles of diameter settle to the bottom of the column in . For the same period of , the percentage removal (round off to integer value) of particles of diameters and from the suspension is ___________
Correct answer
100 to 100
Solution
According to Stokes' Law, the settling velocity () of a particle is proportional to the square of its diameter ():Given that particles of diameter settle completely (reach the bottom from the top) in , their settling velocity is:For particles with larger diameters ( and ), the settling velocity will be higher because .
Since and , then and .This means that in the same period, these larger particles will travel a distance greater than the height of the column (). Therefore, of the particles with diameters and will reach the bottom and be removed from the suspension.Percentage removal = .
Since and , then and .This means that in the same period, these larger particles will travel a distance greater than the height of the column (). Therefore, of the particles with diameters and will reach the bottom and be removed from the suspension.Percentage removal = .
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