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Chapter 11

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

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.