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

Chapter 7 | 395

The work needed to compress a unit mass of air at 20°C from the

atmospheric pressure of 101 kPa to 700 
 101 801 kPa is

The cross-sectional area of the 3-mm-diameter hole is

Noting that the line conditions are 297 K and 801 kPa, the mass flow rate of

the air leaking through the hole is determined to be

Then the power wasted by the leaking compressed air becomes

The compressor operates 4200 h/yr, and the motor efficiency is 0.92. Then

the annual energy and cost savings resulting from repairing this leak are

determined to be

Discussion Note that the facility will save 11,700 kWh of electricity worth

$913 a year when this air leak is fixed. This is a substantial amount for a

single leak whose equivalent diameter is 3 mm.

$913/yr

 1 11,700 kWh>yr 21 $0.078>kWh 2

Cost savings 1 Energy savings 21 Unit cost of energy 2

11,700 kWh/yr

 1 2.563 kW 21 4200 h>yr2>0.92

Energy savings 1 Power saved 21 Operating hours2>hmotor

2.563 kW

 1 0.008632 kg>s 21 296.9 kJ>kg 2

Power wastedm

#

airwcomp,in

0.008632 kg>s



B

1 1.4 21 0.287 kJ>kg#K2a

1000 m^2 >s^2

1 kJ>kg

ba

2

1.4
 1

b1297 K 2

 1 0.652a

2

1.4
 1

b

1 >11.4 12

¬

801 kPa

1 0.287 kPa#m^3 >kg#K 21 297 K 2

1 7.069 10 ^6 m^22

m#airCdischargea

2

k
 1

b

1 >1k (^12) Pline
RTline
¬A
B
kRa
2
k
1
bTline
ApD^2 > 4 p 13  10 ^3 m 22 > 4 7.069 10 ^6 m^2

1 1.4 21 0.287 kJ>kg#K 21 293 K 2
1 0.8 21 1.4 12
¬ca
801 kPa
101 kPa
b
0.4>1.4
 1 d296.9 kJ>kg
wcomp,in
nRT 1
hcomp 1 n 12
¬ca
P 2
P 1
b
1 n 1 2>n
 1 d
2 Installing High-Efficiency Motors
Practically all compressors are powered by electric motors, and the electrical
energya motor draws for a specified power output is inversely proportional
to its efficiency. Electric motors cannot convert the electrical energy they
consume into mechanical energy completely, and the ratio of the mechanical
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