In a geothermal district heating system, 10,000 kg/sof hot water must be delivered a distance of 10 km in ahorizontal pipe. The minor losses are negligible, and the onlysignificant energy loss arises from pipe friction. The frictionfactor is taken to be 0.015. Specifying a larger-diameter pipewould reduce water velocity, velocity head, pipe friction, andthus power consumption. But a larger pipe would also costmore money initially to purchase and install. Otherwise stated,there is an optimum pipe diameter that will minimize the sumof pipe cost and future electric power cost.Assume the system will run 24 h/day, every day, for 30 years.During this time the cost of electricity remains constant at$0.06/kWh. Assume system performance stays constant overthe decades (this may not be true, especially if highly mineralizedwater is passed through the pipeline—scale may form).The pump has an overall efficiency of 80 percent. The cost topurchase, install, and insulate a 10-km pipe depends on thediameter D and is given by Cost = $106 D2, where D is in m.Assuming zero inflation and interest rate for simplicity andzero salvage value and zero maintenance cost, determine theoptimum pipe diameter.
In a geothermal district heating system, 10,000 kg/s
of hot water must be delivered a distance of 10 km in a
horizontal pipe. The minor losses are negligible, and the only
significant energy loss arises from pipe friction. The friction
factor is taken to be 0.015. Specifying a larger-diameter pipe
would reduce water velocity, velocity head, pipe friction, and
thus power consumption. But a larger pipe would also cost
more money initially to purchase and install. Otherwise stated,
there is an optimum pipe diameter that will minimize the sum
of pipe cost and future electric power cost.
Assume the system will run 24 h/day, every day, for 30 years.
During this time the cost of electricity remains constant at
$0.06/kWh. Assume system performance stays constant over
the decades (this may not be true, especially if highly mineralized
water is passed through the pipeline—scale may form).
The pump has an overall efficiency of 80 percent. The cost to
purchase, install, and insulate a 10-km pipe depends on the
diameter D and is given by Cost = $106 D2, where D is in m.
Assuming zero inflation and interest rate for simplicity and
zero salvage value and zero maintenance cost, determine the
optimum pipe diameter.
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