It takes 45 minutes to filter 0.2 m³ suspension of Bacillus subtilis cells under p = 20 psi, for recovery of protease. The filter area is 0.25 m2, and the filtrate viscosity is 15 cP. The cell suspension deposits 50 g cake per liter of filtrate and forms a compressible cake.
If α' = 0.35 [min/m²⋅Cₚ⋅psiˢ⁻¹(g/L)], and resistance due to filter medium is negligible.
(a) What is the compressibility factor s'?
(b) Find the time required to filter a volume of filtrate such that V/A ratio is increased by a factor of 5 (i. e. V/A 5 times the initial VA)

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.