ANS:A - over cake

The specific cake resistance for compressible sludges is a function of the pressure drop over the cake. Here’s why:

1. Specific Cake Resistance:
   • Specific cake resistance (α\alphaα) is a parameter used to characterize the resistance of a filter cake to liquid flow during filtration.
   • It is defined as the ratio of the pressure drop across the cake (ΔP_c) to the filtration rate (v): α=ΔPcv\alpha = \frac{\Delta P_c}{v}α=vΔPc​​
   • The specific cake resistance provides insight into the compressibility and porosity of the filter cake formed during the filtration process.
2. Compressible Sludges:
   • Compressible sludges have a significant volume reduction capability under pressure, leading to changes in their porosity and permeability.
   • The specific cake resistance for compressible sludges is influenced by the pressure drop specifically across the cake itself, reflecting how the sludge compressibility affects the filtration process.
3. Pressure Drop Considerations:
   • The pressure drop over the cake is critical because it directly affects the formation and characteristics of the filter cake.
   • It represents the resistance encountered as the liquid passes through the accumulated solids in the filter cake, which depends on the compressibility and filtration conditions.
4. Other Options:
   • Over Medium: Refers to the pressure drop across the filter medium (filter cloth or medium). While important, it does not directly determine the specific cake resistance.
   • Overall: This could refer to the total pressure drop in the filtration system, including across the medium and other components. However, specific cake resistance specifically relates to the pressure drop across the cake.