ASPEN vs Bernoulli Equation

This problem involves a direct comparison between the performances of ASPEN plus and solving a problem by hand using the Bernoulli Equation. Both methods are used to come to a conclusion about the problem stated below:

Shantal, an intern you supervise at the chemical company you work for, notices a flow rate problem with one of the water pipes on your production floor. The poor flow rate is due to three reasons: The city water pressure at the water meter is poor (P=200 kPa); the piping has a small diameter (D=1.27 cm) and has been crudded up, increasing its roughness (e/D=0.05); and the inlet to the reactor using the water is 15 m higher than the water meter.

Shantal proposes two possible solutions to the problem. Option 1 is replacing all the piping after the water meter with new smooth piping (e/D=0.00) with a diameter of 1.9 cm. Option 2 is installing a booster pump while keeping the original pipes; the booster pump has an outlet pressure of 300 kPa, which would be installed at ground-level on your production floor. She has taken it upon herself to do the math and comes to the conclusion that Option 2 would increase the pressure (P₂) at the pipe outlet more than Option 1 would.

Is she correct in her calculations? Neglect minor losses (i.e., don’t account for valves, elbows etc. – just major head loss). Assume a water flow of 2 gallons/minute and for your Bernoulli Equation calculations use friction factors of 0.075 for the original “rough” pipe and 0.045 for the potential replacement “smooth” pipe.

The problem was solved using both an ASPEN Plus Simulation using the Peng-Robinson property method and by hand using the Bernoulli Equation. The Aspen flowsheet, stream results, and handwritten work are given in the images below:

The comparison of the stream results to the calculations of the Bernoulli Equation indicate that although the exact values obtained have slight differences (as 1 bar = 100kpa), both methods indicate the same trend and the same conclusion that Shantal is correct in her assessment that the addition of a booster pump to the system would increase outlet pressure more than replacing the crudded pipe would. This indicates that although these methods are not exactly in agreement with regard to specific values, the general trend is the same and can be used as estimations of each other.