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## Q. 11.2

Determine the increase in energy cost of a 100-kW air compressor operating 8,000 hours per year due to a contaminated air filter. Assume that:
• The electrical motor efficiency is 90 percent.
• The pressure drop is 1.0 kPa for a clean air filter but becomes 3 kPa for a contaminated filter.
• The cost of electricity is \$0.05/kWh.

## Verified Solution

Using a rule of thumb, it can be stated that for every 1 kPa increase in the pressure drop across the air filter, the mechanical power is increased by 1 percent (because the mechanical power is proportional to the mass flow rate). Thus, the energy cost penalty $EC_{filter}$, of using a contaminated air filter, can be estimated as follows:

$EC_{filter}=\frac {100kW * 8,000hrs/yr*\0.05/k Wh}{0.90} *(\frac{3 kPa}{1kPa})*0.01=\1.330/yr$