The Black Mesa pipeline transports 660 tons / hr of solid coal ground to 8 mesh (2.4 mm) as a 50 wt % slurry in water with an estimated sg of 1.26 for 273 miles across northern Arizona. The pipeline ID is 18 inches and the slurry flow rate (coal and water) is 4200 gal/min. There are four pumping stations which divide the 273 miles into four sections. The slurry behaves as a power law fluid with n = 0.2 and K (kg / m s (2-n) )= 0.58.
a) The pressure drop in each 68.3 mile section.
b) The total pumping power required for all four stations assuming the pump efficiency is 70 percent.
The Attempt at a Solution
For this problem, I calculated the reynold's number and found that it is turbulent flow. Then I used the attached chart to find the fanning friction factor, which I knew I needed for the head friction for Bernoulli's equation. From there, I can't find the pressure drop using any experimentally derived formulas since those deal with laminar flow. At this point I wasn't sure how to calculate the pressure drop, so I took a peek at the solution.
What they do is use bernoulli's equation (I was doing the same), but the peculiar thing that was done was setting the work per unit mass to zero. I was under the impression that there is a pump, therefore W should not be zero.
I posted the solution, which corresponds to question 3 on that set