As a chemical engineer you are tasked to design and specify equipment for transporting 100% acetic acid (SG = 1.0, μ = 1 cP) at a rate of 60 gal/min (gpm) from a large vessel at ground level into a storage tank that is 20 ft above the vessel. The line includes 500 ft of pipe and eight standard 90° elbows. It is necessary to use stainless steel for the system (pipe is hydraulically smooth), and you must determine the most economical size pipe to use. You have 1.5 in. and 2 in. nominal schedule 40 pipes available for the job. Cost may be estimated from the following approximate formulas:

Pump cost: Cost (Php) = 75.2 (gpm)^0.3 (ft of head)^0.25

Motor cost: Cost (Php) = 75 (hp)^0.85

Pipe cost: Cost (Php)/ft = 2.5 (nom. dia, in.)^3/2

90° elbow: Cost (Php) = 5 (nom. dia, in)^1.5

Power: Cost = 8.43 Php/kWh

(a) Calculate the total pump head (i.e., pressure drop) required for each size pipe, in ft of head.

(b) Calculate the motor hp required for each size pipe assuming 80% pump efficiency (motors available only in multiples of 1/4 hp)

(c) Calculate the total capital cost for pump, motor, pipe, and fittings for each size pipe.

(d) Assuming that the useful life of the installation is 5 years, calculate the total operating cost over this period for each size pipe.

(e) Which size pipe results in the lowest total cost over the 5-year period?