7
APPENDIX A
Appendix A
164
7 APPENDIX A
The theoretical power consumption due to a 10 mm leak with rough edges will be calculated by using Equation 4. This equation is provided again for reference purposes.
motor line k n n comp line inlet line e disch electrical T k kR k p p n T T p n C A P
η
η
+ ⋅ + ⋅ − ⋅ − ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = − − 1 2 1000 * 1 2 1 ) 1 ( 1 1 / ) 1 ( 1 2 arg Where: electrical P = Electrical power (kW)A = Minimum cross-sectional area
discharge
C
= Discharge coefficientn = Polytropic compression exponent
line
p = Line pressure (kPa)
inlet
T
= Inlet temperature (Kelvin)line
T
= Line temperature (Kelvin)comp
η
= Compressor efficiency2
p = Compressor discharge pressure (kPa)
1
p = Compressor inlet pressure (kPa) k = Specific heat ratio
Appendix A
165 The electrical power consumption will be calculated according to the following input parameters: A = 4 01 . 0 01 . 0 × ×
π
dischargeC
= 0.65 n = 1.3 line p = 589 kPa inletT
= 293 K lineT
= 303 K compη
= 0.8 2 p = 589 kPa 1 p = 89 kPa k = 1.4 R = 0.287 kJ/kg.KEquation 4 can then be populated as follows:
9 . 0 1 303 1 4 . 1 2 287 4 . 1 1 4 . 1 2 1 89 589 ) 1 3 . 1 ( 8 . 0 303 293 589 3 . 1 65 . 0 4 01 . 0 01 . 0 1 4 . 1 1 3 . 1 / ) 1 3 . 1 ( × × + × × + × − × − × × × × × × × × = − −
π
electrical P = electrical P 19 kWAppendix A
166 The theoretical power consumption due to a 200 mm open ended pipe will be calculated by using Equation 4. The electrical power consumption will be calculated according to the following input parameters:
A = 4 2 . 0 2 . 0 × ×
π
dischargeC
= 0.97 n = 1.3 line p = 589 kPa inletT
= 293 K lineT
= 303 K compη
= 0.8 2 p = 589 kPa 1 p = 89 kPa k = 1.4 R = 0.287 kJ/kg.KEquation 4 can then be populated as follows:
9 . 0 1 303 1 4 . 1 2 287 4 . 1 1 4 . 1 2 1 89 589 ) 1 3 . 1 ( 8 . 0 303 293 589 3 . 1 97 . 0 4 2 . 0 2 . 0 1 4 . 1 1 3 . 1 / ) 1 3 . 1 ( × × + × × + × − × − × × × × × × × × = − −
