1

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Chapter 3Appendix B

Development of ObjectiveFunction

2

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3)L/D rule standard .( ???1

4

4

solve and different.

4

2

~4

:constraint eliminate

4..

,2

min

31

31

2

2

2

2

vsD

L

VL

VD

D

VDC

D

VL

LD

Vts

LD

DDLC

opt

opt

opt

Optimize L/D for a Pressure Vessel

3

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erroneous assumptions

(1) dished ends (not flat)Ae = 2(1.16 D2) = 2.32 D2

(2) thickness is a function of D (not constant)(3) fabrication costs

$ ends > $ sides (1.5x)

2

0

0

3.48

fab cost of sides ($/lb.)

t thickness

density

(corrosion allowance) 117002 250250

.125 0.0108 0.125

C S DLt S D t

S

PDt t psi

P psi

t inch t D

4

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.7.31

.11

solution analytical no

/167029.144304.0263.

nkgallon ta 25,000

Lfor solve

)3(4

heads) (dished constraint volume

fcn. obj.in S,neglect

23

2

ftL

ftD

DDDC

DLD

V

opt

opt

5

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capacity pressure psi

gal 100 250 400

2500 1.7 2.4 2.9

25000 2.2 2.9 4.3

10 DLP

6

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7

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8

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9

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10

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11

.05.004167

12i

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12

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13

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14

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15

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16

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17

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18

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19

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20

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21

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22

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nn

i

F

i

F

i

FP

)1(...

)1(1orth present w

221

Insulation example -- fixed vs. operating costs (Fi)

annualization factor (repayment multiplier)

021

01

or

d)(discounte investment

savings cumulative initial

1)1(

)1(

rIFfrf

r

FIf

i

iir

n

n

for Fi = constant = F (cash flow)

23

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There are several disadvantages to using IRR in optimization (requires iterative solution).NPV can be shown to be equivalent to using an annualization factor (series present worth factor).

- Steam Generator Example

24

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25

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20

0

0 0

2 0

$ (steam generated)

area ($25/ft )

/ vs.

(1 ) 1. /

(1 )

( , , , )

n

n

optp

Fyr

I

ROI F I

iNPV F I F r I

i i

T w r c U

Steam Generator Flow Diagram

26

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27

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In the previous section we only briefly mentioned the financial assumptions used in profitability analysis. Any detailed analysis of a project requires specifying the following parameters:

(1)initial investment(2)future cash flows(3)salvage value(4)economic life(5)depreciation(6)depletion(7)investment tax credit(8)taxes(9)inflation(10)debt/equity ratio

28

REVENUEOPERATIONS

SALESINCOME

MANUFACTURING(CASH OPERATING)

EXPENSES

OPERATING INCOME (PROFIT)

NET INCOME BEFORE TAXES

FEDERAL INCOME TAXESNET INCOMEAFTER TAXES

CASH

FLOW

SALVAGE VALUE

DEPRECIATION

Figure 3.3 Computation of Cash Flow

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29

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30

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31

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32

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37

InsulationThickness

x (cm)

InsulationCost($)

Valueof fuelsaved

($/year)

Payback period(years)

Return on investment

(% per year)

NetPresentvalue

($)

Internalrate ofreturn

(%)

1 2,135 5,281 1.27 79 16,013 247

2 4,270 8,182 1.64 61 23,847 191

3 6,405 10,020 2.01 50 28,028 155

4 8,540 11,288 2.38 42 30,250 130

5 10,675 12,215 2.75 36 31,301 112

6 12,810 12,984 3.10 32 31,809 98

7 14,945 13,480 3.48 29 31,378 86

A summary of the calculations is

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