A fruit juice is concentrated using an ultrafiltration membrane. A feed stream at $10 \mathrm{~kg} / \mathrm{min}$ with $6 \%$ total solids (by weight) is increased to $20 \%$ total solids (by weight). The membrane tube has $10 \: \mathrm{cm}$ inside diameter and the pressure difference across the membrane is $2000 \: \mathrm{ kPa}$. If the permeability constant of the membrane is $5 \times 10^{-5} \mathrm{~kg} \text{ water} / ( \mathrm{m}^{2} \: \mathrm{kPa} \: \mathrm{s}$ ), the length of membrane tube (in $\mathrm{m}$ ) is $\_\_\_\_\_\_$ (rounded off to $2$ decimal places)
