GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

Question : 31 of 65

Marks: +1, -0

A completely mixed dilute suspension of sand particles having diameters

0.25,0.35,0.40

0.45

and

0.50 {mm}

are filled in a transparent glass column of diameter

10 {cm}

and height

2.50

{m}

. The suspension is allowed to settle without any disturbance. It is observed that all particles of diameter

0.35 {mm}

settle to the bottom of the column in

30 {s}

. For the same period of 30 s, the percentage removal (round off to integer value) of particles of diameters

0.45

and

0.50

mm from the suspension is _____________.

Solution:

As we know that settling velocity for discrete particles is given by stokes law as

{V}_{ {T}}=\;{( {G}-1) γ {d}^{2}}/{18 µ} ⇒ {V}_{ {T}} ∝ {d}^{2}

For 30 second duration if

0.35 {mm}

particle size settles completely then

\%

removal of particle size

0.45 {mm}

and

0.50 {mm}

will be

100 \%

respectively for each. As settling velocity of particle size

0.45 {mm}

and

0.50 {mm}

will be greater than settling velocity of size

0.35 {mm}( {V}_{ {T}} ∝ {d}^{2})

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