(a) Consider the following equation valid for flow through a packed bed. The equation is known as the Ergun equation - where symbols have their usual meaning. P(uo2(1)3)(LDp)=Re150+1.75 Stating the necessary assumptions, derive the corresponding d'Arcy equation for the superficial velocity u0 through porous media. [ 5 marks] (b) In fluidised beds, define the term minimum fluidisation velocity and explain the difference between particulate and aggregative fluidisation. [5 marks] Calculate the minimum fluidisation velocity in an aggregative fluidised bed of large g=10kg/m3. The dynamic viscosity of the gas is g=2105kg/ms and the void fraction at fluidisation is 0=0.5. [4 marks] (c) Consider a two-phase flow - gas and liquid - in a vertical pipe. (i) Differentiate between the bubble and slug flow regimes and state the conditions for the transition from bubble to slug flow. [ 5 marks] (ii) For a vertical pipe with a diameter D=0.1m, a void fraction =0.5 and an inlet liquid flow rate L that is half the value of the inlet gas flow rate G, estimate the value of the superficial gas velocity uo=AG. [ 6 marks] You may find the following equations useful: Single slug velocity in a stagnant liquid: ub=0.35gD Slug rise velocity in a rising liquid: us=1.2AG+L+ub where G=usA