Hydraulics. A city needs a certain amount of water from a river that is 300 feet below and three miles from the city’s water treatment plant. The city engineer must decide on the internal diameter of...

Hydraulics. A city needs a certain amount of water from a river that is 300 feet below and three miles from the city’s water treatment plant. The city engineer must decide on the internal diameter of the pipeline to the city and the head capacity of the pump to be installed at the river. The engineer knows that a smaller pipe is less expensive but results in greater head loss due to friction and therefore requires a greater head capacity for the pump, which increases the cost of the pump. Conversely, a larger pipe is more expensive, but permits a less expensive pump to meet the fixed head and flow requirement at the water treatment plant. The engineer is also aware that the range of pump capacities and pipeline diameters is limited in order to avoid a long waiting period for delivery. The most economical pump/pipe combination is desired.