It is desired to ship 150,000 bbl/day of bitumen via a pipeline of 20 ID. Solvent, (diluent) is being used to dilute the bitumen for its transportation. The pipeline length is 100 km with zero elevation difference and both ends are open to the same pressure. Bitumen density is 1050 kg/m Diluent density is 750 kg/m The diluted bitumen viscosity, Amix, is given by logo lumix= 5.2 - 16.89 + 1702 - 5.863. mPas Pipe relative roughness is 0.001 Head loss, h = fm Power = W, = g rimix hp, where mix is the mass flow rate of the diluted bitumen mixture, kg/s a) What is the equivalent mass flow rate, (mg) of bitumen in kg/s? b) Write an equation for the density of the diluted bitumen (bitumen and solvent mixture) Pmix in terms of the bitumen, Pb, and the solvent density, Ps, and mass (weight) fraction of the solvent in the diluted mixture, X. c) Show that mg = x and mix e) As the correlation for the diluted bitumen viscosity, Amix, is provided in terms of solvent volume fraction in the mixture, 0, rather than mass fraction x, show that: ms mees s PB h) Write down the final applicable energy balance as you have learned it in your fluid mechanics class to show that the head loss h_ is equal to the power head, hp