Can a Dam Turbine Meet a Paper Mill's Energy Needs?

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SUMMARY

A dam turbine can supply a portion of a paper mill's energy needs, specifically when the river flow exceeds 50 cubic feet per second. The mill requires 5000 kW to operate at full capacity and the turbine's efficiency is 75%. By calculating the potential energy of the water using the formula E = mgh, where m is the mass of the water, g is the acceleration due to gravity, and h is the height of the dam (10m), one can determine the power output of the turbine. This output can then be compared to the mill's energy requirement to find the percentage of power supplied.

PREREQUISITES
  • Understanding of basic physics concepts, particularly potential energy and kinetic energy.
  • Familiarity with the formula E = mgh for calculating energy.
  • Knowledge of turbine efficiency and its impact on power output.
  • Basic calculations involving cubic feet to mass conversion for water.
NEXT STEPS
  • Calculate the potential energy of water at the dam using E = mgh.
  • Determine the mass of water flowing at 50 cubic feet per second.
  • Calculate the actual power output of the turbine considering its 75% efficiency.
  • Compare the turbine's output to the mill's 5000 kW requirement to find the percentage supplied.
USEFUL FOR

Energy engineers, paper mill operators, and anyone involved in renewable energy solutions for industrial applications.

aud11888
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a mill requires 5000kW to operate at full capacity, produces 14tons of paper per hour, purchases electricty for $.10/kW*hr

There is a dam 10m high that supplies water to a turbine. the river can be used only if the flow is above 50 cubic ft/sec. efficiency of generator is 75%

how am i supposed to find "What percentage of the mill's power requirement can the dam supply?" I'm so lost
 
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Each second, 50 ft^3 of water transfers its kinetic energy to the mill. This energy will be equal the water's potential energy at the top of dam. So E = m g h, where m is the mass of the water (mass = density * volume), and h is the height of the damn (let's assume the water comes out at the bottom). So the power is .75 * E per second. Divide this into how much power the mill needs to get the percentage.
 

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