GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

Question : 51 of 65

Marks: +1, -0

0.80 {m}

deep bed of sand filter (length

4 {m}

and width

3 {m}

) is made of uniform particles

(

diameter

=0.40 {mm}

, specific gravity

=2.65

, shape factor

=0.85

) with bed porosity of 0 .the bed has to be backwashed at a flow rate of

3.60 {m}^{3} {/} {min}

. During backwashing, if the terminal settling velocity of sand particles is

0.05 {m} {/} {s}

, the expanded bed depth (in

{m}

, round off to 2 decimal places) is

Solution:

n_{ {\ex}}=(\;{ {v}_{ {B}}}/{ {V}_{ {t}}})^{0.22}

V_{ {B}}=\;{3.6}/{4 × 3 × 60}=5 × 10^{-3} {m} {/} {\sec}

n_{ {\ex}}=(\;{5 × 10^{-3}}/{0.05})^{0.22}

{n}_{ {\ex}}=0.6025

then

L_{\ex}(1-n_{e x})=L(1-n)

⇒ {L_{\ex}}(1-0.6025)=0.8 ×(1-0.4)

{L}_{ {\ex}}=1.2075 {m}

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