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Mechanical Operations - Engineering

Q1:

The resistance offered by the filter used in a bag filter is proportional to (where, c = dust concentration, and s = particle size )

A c/s

B s/c

C s . c

D 1/s . c

ANS:A - c/s

The resistance offered by the filter used in a bag filter is proportional to cs\frac{c}{s}sc​, where ccc is the dust concentration and sss is the particle size.

Explanation:

  • Bag Filter Operation: In a bag filter, air containing dust particles passes through a fabric bag. The dust particles are captured on the surface of the bag while clean air passes through.
  • Resistance: The resistance or pressure drop across the bag filter depends on various factors, including the dust concentration ccc (mass of dust per unit volume of air) and the particle size sss (diameter of the dust particles).
  • Proportionality: The resistance RRR is directly proportional to the ratio of dust concentration ccc to particle size sss: R∝csR \propto \frac{c}{s}R∝sc​
  • Interpretation of Options:
    • c/sc/sc/s: This represents the correct proportionality relationship between dust concentration and particle size affecting the resistance of the bag filter.
    • s/cs/cs/c: This ratio does not correctly reflect how the resistance changes with dust concentration and particle size.
    • s⋅cs \cdot cs⋅c and 1s⋅c\frac{1}{s} \cdot cs1​⋅c: These expressions do not correctly represent the proportional relationship of resistance in a bag filter.
Therefore, the resistance offered by the filter in a bag filter is proportional to cs\frac{c}{s}sc​, indicating that higher dust concentrations or smaller particle sizes generally lead to increased resistance across the filter medium.