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A water filtration unit is made of uniform-size sand particles of $\text{0.4 mm}$ diameter with a shape factor of $0.84$ and specific gravity of $2.55$. The depth of the filter bed is $\text{0.70 m}$ and the porosity is $0.35$. The filter bed is to be expanded to a porosity of $0.65$ by hydraulic backwash. In the terminal settling velocity of sand particles during backwash is $\text{4.5 cm/s}$, the required backwash velocity is

  1. $5.79 \times 10^{-3}\text{ m/s}$
  2. $6.35 \times 10^{-3}\text{ m/s}$
  3. $0.69 \text{ cm/s}$
  4. $0.75 \text{ cm/s}$
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