Solution: Engineers plan to build a pipeline 1,000 km in length to transport water to a drought-stricken region. They wish to have a volume flow rate of 10 million gallons per day, and the maximum pipe diameter they can use is .5 m. The engineers do not wish to place a pump more frequently than every 20 km. The pipe material will be galvanized iron, roughness .15 mm. Determine: a) The average velocity of the water in the pipe and the Reynolds number, b) The pressure gradient along the pipe and the total pressure drop over its full length, c) The power of the pumps at each pumping station, assuming they are thermodynamically recersible.

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Engineers plan to build a pipeline 1,000 km in length to transport water to a drought-stricken region. They wish to have a volume flow rate of 10 million gallons per day, and the maximum pipe diameter they can use is .5 m. The engineers do not wish to place a pump more frequently than every 20 km. The pipe material will be galvanized iron, roughness .15 mm. Determine: a) The average velocity of the water in the pipe and the Reynolds number, b) The pressure gradient along the pipe and the total pressure drop over its full length, c) The power of the pumps at each pumping station, assuming they are thermodynamically recersible.