We are interested in transporting coal from a mine in Pennsylvania to Ohio by slurry pipeline. For this it is necessary to fist crush the coal, mix it with water, and send it down the pipe. The mixture is 50% by weight slurry and has a density of 1250 kg / m3. We want to send it 570 km away in a 0.3 m i.d. pipeline with four pumping stations. For this it usually takes 3 days (5pt).

What total pumping power is needed if our pumps are 70% efficient.

How much does it cost us to send the coal to its destination? Report it in ₵ / ton of coal. 

Information: Coal slurry behaves like a power law fluid: n = 0.2 and K = 0.58 (kg / ms2-n).

Electricity: 3 ₵ / kWh

Initially the slurry is in an open container and it delivers to an open container. Also, the altitude in Pennsylvania is 67 m and in Ohio 260 m.