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In this experiment, a bench-scale granular filter was backwashed. Our bench scale model consists of a 5 cm deep sand filter with a diameter of 2.5 cm (see Figure 1, (b)). The sand (classified as D60) has a diameter of 0.5mm and porosity of 0.4. The diameter of the flow control orifice is 0.2 cm. We essentially introduced a backwash flowrate of water of known velocity from the bottom and measured the bed expansion. An attenuator, or small tank filled with water, was installed between the pump and the filter to eliminate the pulsing action of the pump (see Figure 1, (a)). The bed expansion flow rate was increased from 20 mL/min to 380 mL/min (0.4-9 mm/s) (380 mL/min being the max rated flowrate for our bench scale pump configuration). The fluidization velocity is based on the ratio of original filter depth to expanded filter depth, so the velocity doesn't change with a larger depth. 

{latex}
\large
$$
V = K_e (\overline \varepsilon  )^{n_e }
$$
{latex}

{latex}
\large
$$
\overline \varepsilon   = 1 - {D \over {D_e }}(1 - \varepsilon )
$$
{latex}

Figure 1: (a) Fluidization Velocity Experiment Set-Up                                                            (b) 5 cm Filter Bed of Sand in Tube Unexpanded & Expanded

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