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## Q. 11.4

A compressed air system has a mechanical power requirement of 50 kW with a motor efficiency of 90 percent. Determine the cost savings of reducing the discharge absolute pressure from 800 kPa to 700 kPa. Assume that:
• The compressor is operating 4,000 hours per year with an average load factor of 70 percent.
• The cost of electricity is $0.05/kWh. ## Step-by-Step ## Report Solution ## Verified Solution Assuming that the intake air pressure of the compressor is equal to 100 kPa (i.e., 1 atm), the reduction in the discharge pressure corresponds to a reduction in the pressure ratio $P_{o}/P_{i}$ from 8 to 7. The percent reduction in the mechanical power requirement $\%W_{m}$ can be calculated using either Eq.(11.3) or Eq.(11.4): For an isothermal compression: $\dot{W}_{m}=\dot{m}_{a}.R_{a}.T_{i}.Ln(\frac {P_{o}}{P_{i}})$ (11.3) $\dot{W}_{m}=\frac {\dot{m}_{a}.R_{a}.T_{i}.γ}{γ-1}[(\frac {P_{o}}{P_{i}})^{\frac {γ-1}{γ}} -1]$ (11.4) $\%W_{m}=\frac {LN(8)-LN(7)}{LN(8)}=6.4\%$ Using Eq. (11.8), the electrical energy savings can be calculated: $ΔkWh_{comp}=\frac {\dot{W}_{m}.LF_{comp}.N_{h,comp}.(T_{i,e}-T_{i,r})}{η_{M}.T_{i,e}}$ (11.8) $ΔkWh_{comp}=\frac {0.064*50kW*4000hrs/yr*0.70}{0.90}=9950k Wh/yr$ Thus, the cost savings due to a reduction in the discharge air pressure are about$500/yr. For an adiabatic compression:

$\%W_{m}=\frac {(8)^{1.4-1/1.4}-(7)^{1.4-1/1.4}}{(8)^{1.4-1/1.4}}=5.7\%$

Using Eq. (11.8), the electrical energy savings can be calculated:

$ΔkWh_{comp}=\frac {0.057*50kW*4000hrs/yr*0.70}{0.90}=8870k Wh/yr$

Thus, the cost savings for reducing the discharge air pressure are about \$450/yr.