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## Q. 11.3

A compressed air system has a mechanical power requirement of 100 kW with a motor efficiency of 87 percent. The intake air for the compressor is from the interior of the mechanical room (where the compressor is located and where the average annual temperature is 35°C). Determine the payback period of installing an insulated piping section to connect the intake of the compressor to the ambient outdoor air. Use the following information:
• The total cost of the piping system is $850. • The annual average outdoor air is 12°C. • The compressor is operating 5,000 hours per year with an average load factor of 80 percent. • The cost of electricity is$0.05/kWh.

## Verified Solution

Using Eq. (11.8), the electrical energy savings due the reduction in the intake air temperature can be estimated:

$ΔkWh_{comp}=\frac {\dot{W}_{m}.LF_{comp}.N_{h,comp}.(T_{i,e}-T_{i,r})}{η_{M}.T_{i,e}}$                   (11.8)

$ΔkWh_{comp}=\frac {\100kW-*0.8*5000hrs/yr*[(35-12)K]}{0.87*[(273+12)]K}=34330k Wh/yr$

Therefore, the simple payback period for the installation of the piping system to connect the intake of the compressor to the outside air is:

$SPB=\frac {\850}{34330k Wh/yr*\0.05/kWh}=0.5 years=6 months$