GATE 2019 CE (CE1) – Question 51
A sand filter bed 4 m long, 3 m wide and 0.80 m deep contains uniform particles of diameter 0.40 mm, specific gravity 2.65 and shape factor 0.85. Initial porosity is 0.4. It is backwashed at 3.60 m³/min. During backwash terminal settling velocity is 0.05 m/s. Find expanded bed depth (m), to two decimal places.
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Correct answer: 1.15 to 1.25
Explanation
Superficial backwash speed is $v=3.6/(60\times12)=0.005$ m/s. Use the empirical expanded-bed relation $v/v_t=\varepsilon^{4.5}$, so $\varepsilon=0.1^{1/4.5}=0.599484$. Solids conservation gives $L(1-\varepsilon)=0.80(1-0.4)=0.48$. Thus $L=0.48/(1-0.599484)=$ **1.20 m**. The empirical exponent is the conventional model implicit in the keyed result.