Moisture from a noncondensable gas at T
1 and P
1 needs to be removed by compression and then cooling so that the gas will finally contain no more than 0.5% moisture (%v). The compression and cooling costs (in $) are C
1 and C
2, respectively. Assume that in gas compression, gas temperature increase following the expression of ∆T= α (∆P)
β, where α and β are constant and ∆ indicates the change in T or P.
C
1= m (P
2 –P
1)
1.2, where P
1 and P
2 in KPa, are the inlet and the outlet pressures of the compressor, respectively.
C
2= n (T
2 –T
3)
1.8, where T
2 and T
3 in K, are the gas temperatures at the cooler's inlet and the outlet, respectively. Both m and n are constants.
Define and list the objective function, the independent and the dependent variables, and all the constraints (equality and inequality). Do not solve the problem.
Note that the vapor pressure of water is related to the temperate by the Antoin's equation of:
Log
10P = A-B/(C+T)
Where A, B and C are constants, and P and T are the vapor pressure of water and gas temperature, in KPa and K, respectively.
List stationary point(s) and their classification (maximum, minimum, saddle point) of:
f(x) = (x1 –x2)
4+ (x2-2)
4You may want to investigate function values at and near the stationary point f(x
1*, x
2*) and f(x
1* + e
1, x
2*+ e
2)
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