Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

394 | Thermodynamics

Air inlet

101 kPa

700 kPa

24 °C

Air leak

D ≈ 3 mm

Air

Motor Compressor

20 °C

FIGURE 7–75

Schematic for Example 7–22.

Then the mass flow rate of airthrough a leak of minimum cross-sectional

area Abecomes

(7–90)

where kis the specific heat ratio (k1.4 for air) and Cdischargeis a discharge

(or loss) coefficient that accounts for imperfections in flow at the leak site.

Its value ranges from about 0.60 for an orifice with sharp edges to 0.97 for a

well-rounded circular hole. The air-leak sites are imperfect in shape, and

thus the discharge coefficient can be taken to be 0.65 in the absence of actual

data. Also,Tlineand Plineare the temperature and pressure in the compressed-

air line, respectively.

Once m.airand wcomp,inare available, the power wastedby the leaking com-

pressed air (or the power saved by repairing the leak) is determined from

Power savedPower wastedm#^ airwcomp,in (7–91)

m

#

airCdischarge a

2

k
 1

b

1 >1k (^12) Pline
RTline
¬A
B
kRa
2
k
1
bTline
EXAMPLE 7–22 Energy and Cost Savings by Fixing Air Leaks
The compressors of a production facility maintain the compressed-air lines at
a (gauge) pressure of 700 kPa at sea level where the atmospheric pressure is
101 kPa (Fig. 7–75). The average temperature of air is 20°C at the
compressor inlet and 24°C in the compressed-air lines. The facility operates
4200 hours a year, and the average price of electricity is $0.078/kWh. Taking
the compressor efficiency to be 0.8, the motor efficiency to be 0.92, and the
discharge coefficient to be 0.65, determine the energy and money saved per
year by sealing a leak equivalent to a 3-mm-diameter hole on the compressed-
air line.
Solution An air leak in the compressed air lines of a facility is considered.
The energy and money saved per year by sealing the leak are to be
determined.
Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas. 3
Pressure losses in the compressed air lines are negligible.
Analysis We note that the absolute pressure is the sum of the gauge and
atmospheric pressures.