A 250 hp compressor operates with modulating controls The dr

A 250 hp compressor operates with modulating controls. The drive motor efficiency is 95%, and at full flow conditions the machine delivers 1000 cfm of air. When fully through leaks. Energy costs are $0.06 per kWh and $4.50 per kW-month, and the machine operates 7,404 hours/year. Estimate the annual savings if airflow is modulated (no flow), the motor delivers 150 hp to the screws. An energy audit reveals the compressed air system leaks about 40% of air produced reduced by 186 cfm through a leak repair program.

Correct answer is $7,277, need to know how to get this! thanks!

Solution

The driving motor capacity = (compressor capacity+ screw losses)/ motor efficiency

or, motor capacity= (250+150)/0.95 =400/0.95 = 421 hp

now, 1hp= 0.746kw

so, the motor capacity is 421hp=314.1watt= 0.314kw

the machine operates 7404hr/year.

so, the operation cost will be, 0.314*7404*0.06= 139.54$/year

Given, the machine delivers 1000cfm when fully through leaks and the compressed air system leaks about 40% of the air produced.

So, the actual air production is 1000/0.6= 1666.7 cfm

the leak repair program can reduce 186 cfm air flow through the leak.

so the new air genaration should be 1666.7-186= 1480.7 cfm

the new overall load to the driving motor is (1480.7/1666.7)*100%= 0.8884*100%= 88.84% of the initial load

Now the new operating cost will be 139.54*0.8884=123.97$

So the annual saving will be 139.54-123.97=15.57$