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A $0.80 \: m$ 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 $0.4$. 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 _______
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