The principle of filtration is based on the so-called Hagen-Poiseuille Equation (1c). (1c) 4 ao! where V = the volume of filtrate collected (m) t = filtration time (s) A = filter area (m) P = total pressure across the system (Pa) m = weight of cake per unit volume of filtrate (kg m u = filtrate viscosity (Pas) a = cake-specific resistance r=resistance of the filter ) In a typical filtration experiment, a plot of t/V vs V is given in Figure 1c. ooo t/V (s cm) 1000 2000 5000 6000 7000 3000 4000 V(cm) Figure 1c. 1) What are the units for a and [4 Marks] I) Based on Equation (1a), show the mathematical procedures to obtain a relationship between t/V and V. Based on Figure 1a and the following known parameters: y = 10- Pas, A = 2 m2, P = 2 bar and 6 = 10 kg m-, calculate the values of a andr.
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