Fluid Mechanics

(a) State Newton's law of viscosity and define briefly the variables it relates to one[3 marks]another.

(b) Combine the equation for the shear stress at a pipe wall with the expression for the friction factor for laminar flow,to provide the following expression for the viscosity of a Newtonian fluid in laminar flow through a pipe of circular cross section:

\mu=\frac{h \rho g d^{2}}{128 L} \frac{\pi d^{2}}{Q}, \text { where the symbols have their usual meanings. }

(c) A 3-stage ultrafiltration (UF) plant is to be used to recover and concentrate an enzyme in wash water from a textile plant. The inlet flow rate is 5 m3 h-1 and the overall volume concentration factor (VCF) is 9.1. The VCF in stage 1 is 1.65; the membrane area in each stage is 20 m2. The flux in stage 2 is 77.1 L m-2 h-1(LMH). Use this information to calculate:

(i)The retentate and permeate flow rate from each stage.

(ii)The VCF and flux in each stage, and the effective average flux for thesystem as a whole.

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