Hey guys, there is this superhard question (atleast for me). Ive been trying at it for days but I seem to get nowhere.(adsbygoogle = window.adsbygoogle || []).push({});

The Trans-Alaska Pipeline System (TAPS) carries around 100,000m^{3}of oil per day from the Northern Alaskan oil fields to the nearest ice-free port of Valdez, around 1300km away. The pipe has an outer diameter of 1.22m and a wall thickness of 12mm. Eleven pumping stations are used along the total length of the pipeline to transport the oil.

Note: Assume that the pumping stations are equally spaced along the pipeline, that the pipe is roughly straight and horizontal, and that the flow with the pipe is laminar, Newtonian and steady-state. Also assume that the pumps are 100% efficient so that all energy consumed by the pumps is dissipated by the fluid. The density and kinematic viscosity of the oil are (rho)=890 kg/m^{3}and (nu)= 7.17 x 10^{-4}m^{2}/s respectively.

(a) Starting from first principles, estimate the pressure increase that must be generated by each of the eleven pumping stations to maintain the flow.

(b) The rate that energy is dissipated D(W) by a fluid when it flows through a horizontal pipe under the influence of a pressure difference is given by

D = (delta)P x Q

where (delta)P is the difference in pressure between the inlet and outlet to the pipe (Pa), and Q is the volumetric flowrate through the pipe (m^{3}/s). How much power (rate of energy use) is required to maintain the flowrate of oil through the entire pipeline?

If oil is burned to power the pumps, and 3.6 x 10^{4}MJ of energy can be harnessed from burning 1 m^{3}of oil, what percentage of the total flowrate needs to be burnt to maintain the flow?

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# Transport Processes problem regarding viscosity/fluid flow and energy.

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