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To save on electricity costs, a town water supply system uses gravitydrivenflow from five large storage tanks during the day and then refillsthese tanks from 10 P.M. to 6 A.M. at a cheaper night rate of 7 ¢/kWh. Thetotal resupply needed each night varies from 5×105 to 2×106 gal, with nomore than 5×105 gallons to any one tank. Tank elevations vary from 40to 100 ft. A single constant-speed pump, drawing from a largegroundwater aquifer and valved into five different cast iron tank supplylines, does this job. Distances from the pump to the five tanks varyevenly from 1 to 3 mi. Each line averages one elbow every 100 ft andhas four butterfly valves that can be controlled at any desirable angle.Select a suitable pump family from the manufacturers. Assume idealsimilarity (no Reynolds number or pump roughness effects). The goal isto determine pump and pipeline sizes that achieve minimum total costover a 5-year period. Some suggested cost data are:1. Pump and motor: $2500 plus $1500 per inch of pipe size2. Valves: $100 plus $100 per inch of pipe size3. Pipelines: 50¢ per inch of diameter per foot of lengthSince the flow and elevation parameters vary considerably, a randomdaily variation within the specified ranges might give a realistic approach.
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