Ramakrishnan

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4 years, 28 days
I have retired as Professor-Mechanical in Sri Venkateswara College of Engineering and Technology under Anna University affiliated colleges in TamilNadu, India. I have 19 years of Industrial and 20 years of teaching experience. I am learning Maple for the past three and half years hoping to make atleast one appreciable maple presentation.

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These are questions asked by Ramakrishnan

Pl. help me remove the equation labels or hide the equation labels in my doc enclosed. What should i do to prevent equation labels from forming in my document. Please refer last two rows in the table below from the document.

Thanks for helping.Ramakrishnan V
 

restart

Conversion from ppm to % vol is 1ppm = 0.0001 %

Conversion from % vol to ppm is % = 10000*ppm

Avagadro's law between mass and volume is

"22.4 nm^(3)=1 kg mol; 22.4 lit = 1 g mol; at  101.325 kPa*(normal pressure) and (273+C ) K;"

ppm = 0.8205e-1*T*mg/(M*nm^3); mg/nm^3 = M*ppm/(0.8205e-1*T)

where T is abs temperature and M is molecular weight;

M/(0.08205T)]*ppm*((A/F)*EA+1) /ρex; Emission is mg/kg fuel

If SFC is x g/kWhr; then Mass flow of exhaust is  (x/1000)*[M/(0.08205T)]*ppm*((A/F)*EA+1) /ρex; Emission is mg/kWhr

If the distance covered per liter is DCL km/liter, then (SFC/1000)*(DCL)/`ρ__f`  is distance covered in km/kWhrNULL

[kg*km/(kWh*liter)*(liter/kg) = km/kWh]

1 g/cc = 1 kg/lit; 1kg/m3 = 1 g/lit; Fuel density`ρ__f`  is 0.77 kg/litNULL

Emission in mg/km = 0.77*Emission is mg/kg fuel/(km/liter fuel)

[(kg/liter*(mg/kg))*km/liter = mg/km]

SFC is in g/kWhr  

Measured emission is  E in ppm  ``

Excess Air percentage is EA in per unit point

Molecular Weight of pollutant is M g/mol

Molecular weight of air = .21*32+.79*28 = 28.84 g/mol

 

SFC

       SFC := 200 g/kWh

`ρ__f`

rho__f

(1)

        `ρ__f` := .77   kg/liter

DCL

   DCL := 50    km/liter fuel

A/F

AFR := 14.5``

EA

EA := .1NULL

T__exh

T__exh

(2)

   T__exh := 450     K

`ρ__ex`

rho__ex

(3)

      `ρ__ex` := .457 kg/m3   

 

c := (AFR*EA+1)/`ρ__ex` = 5.361050328 

NULL

CO

CO2

HC

NO2

O2

N2

Air

M [g/mol]

M__co := 28

NULL

M__co2 := 44

NULL

M__hc := 17

M__no2 := 46

M__o2 := 32

M__n2 := 28

M__air := 28.84

Emission [% ] or[ppm]

E__co := 10

                %

E__co2 := 10

                %

E__hc := 110

                ppm

E__no2 := 10

                ppm

E__o2 := 10

              %

E__n2 := 10

                 %

E__air := 10

                    %

Emission [mg/Nm3]

0.8205e-1*T__exh/M__co

1.318660714

(4)

0.8205e-1*T__exh/M__co2

.8391477273

(5)

0.8205e-1*T__exh/M__hc

2.171911765

(6)

0.8205e-1*T__exh/M__no2

.8026630435

(7)

0.8205e-1*T__exh/M__o2

1.153828125

(8)

0.8205e-1*T__exh/M__n2

1.318660714

(9)

0.8205e-1*T__exh/M__air

1.280253121

(10)

Emission

mg/kWh

k__1 := E__co*c/(1.318660714)
= 40.65526690NULL

k__2 := E__co*c/(.8391477273) = 63.88684799NULL

k__3 := E__co*c/(2.171911765)
 = 24.68355489NULL

k__4 := E__co*c/(.8026630435) = 66.79079562NULL

k__5 := E__co*c/(1.153828125)
 = 46.46316216NULL

k__6 := E__co*c/(1.318660714) = 40.65526690 

NULL

k__7 := E__co*c/(1.280253121) = 41.87492489NULL

Emission

mg/kg fuel

k__1f := k__1*SFC
 = 8131.053380NULL

k__2f := k__2*SFC
 = 12777.36960  NULL

k__3f := k__3*SFC
 =

4936.710978

(11)

 

k__4f := k__4*SFC =

13358.15912

(12)

 

k__5f := k__5*SFC
 =

9292.632432

(13)

 

k__6f := k__6*SFC
 = 8131.053380 =

``

k__7f := k__7*SFC
 = 8374.984978 

Emission

[mg/km]

 

Why in the above row, col2 and col3 have no equn nos?

What should i do to remove the equn numbers 11, 12 and 13?

 

 

Temperature of exhaust is in T K

Density of exhaust is say `ρ__ex` kg/m3 

DCL is distance covered per kWh

SFC := 100*g/kWh; ppm := 4.3; EA := .2; M := 28; `ρ__ex` := .457; T = 400

100*g/kWh

(14)

Emission in g/kWhr is

Emission g/g of fuel = Emission in g/kWhr/SFC in g/kWhrper

Emission in mg/km = 0.77*Emission is mg/kg fuel*(km/liter fuel)


 

Download ppm_to_g_per_km_conversion.mw

I have spent much of my time earlier to make curve fitting possible. Somehow, because of my mistakes, the format for curve fitting changed. Can any one help me with getting my answer for curve fitting in the doc and from the excel data enclosed. Data imported, but donot know how to order the way it wants. I know the way,but do not iknow how to get it now.

Thanks

Ramakrishnan VExperimentalData.xlsxPleasePlot_Doubt.mw
 

restart; with(ExcelTools)

D6EFF := [20, 25, 23, 29]

[20, 25, 23, 29]

(1)

D6EFFP := evalf[3](CurveFitting:-LeastSquares(BP, D4EFF, v, curve = a*v^2+b*v+c))

58.8-19.8*v+2.75*v^2

(2)

 

M1 := Import("C:/Users/dell/Desktop/ExperimentalData.xlsx", 2)

Matrix(%id = 18446745680754394150)

(3)

M1[1, 11]

"D6P10U"

(4)

M1[1, 10]

"D6P5U"

(5)

M1[2, 15]

.267

(6)

NULL

for i to 21 do N[i] := NULL; for j to 7 do N[i] := N[i], M1[j, i] end do; d[i] := NULL; for j to 7 do d[i] := d[i], [N[1][j], N[i][j]] end do end do; y := a*x^2+b*x+c; for i from 2 to 21 do d[i] := [d[i]]; c[i] := CurveFitting[LeastSquares](d[i], x, curve = y) end do

Error, (in CurveFitting:-LeastSquares) data points not in recognizable format

 

d[1]

["BrakePower", "BrakePower"], [2.356, 2.356], [2.749, 2.749], [3.142, 3.142], [3.534, 3.534], [3.927, 3.927], [4.32, 4.32]

(7)

d[2]

[["BrakePower", "S2"], [2.356, .303], [2.749, .271], [3.142, .256], [3.534, .249], [3.927, .244], [4.32, .241]]

(8)

d[3]

["BrakePower", "S4"], [2.356, .256], [2.749, .225], [3.142, .211], [3.534, .205], [3.927, .2], [4.32, .197]

(9)

NULL

``


 

Download PleasePlot_Doubt.mw

 


Dear colleagues, Can anyone explain what (a::list,b::list) will be understood by the programme?

I thought the programme is made for only adding the numbers in the list. But it seems there is something more than that, i could not get.

Equn label (6) onwards, I donot understand, how the answer was obtained.

Thanks for explaining.

Ramakrishnan V

with(MathematicalFunctions:-Evalf); -1; addList1 := proc (a::list, b::integer)::integer; local x, i, s; description "add a list of numbers and multiply by a constant"; x := b; s := 0; for i in a do s := s+a[i] end do; s := s*x end proc

proc (a::list, b::integer)::integer; local x, i, s; description "add a list of numbers and multiply by a constant"; x := b; s := 0; for i in a do s := s+a[i] end do; s := s*x end proc

(1)

s := addList1([1, 2, 3, 4], 2)

20

(2)

s := addList1([2, 2, 3, 4], 2)

22

(3)

x := 2 = 2NULL

s := addList1([x, 2, 3, 4], 2)

22

(4)

s := addList1([2, x, 3, 4], 2)

22

(5)

sumList := addList1([4, 3, 1, 3, 4, 3], 2)

26

(6)

s := addList1([4, 3, 1, 3, x, 3, 4, 3], 2)

34

(7)

s := addList1([2, 2, 3, 4], 2)

22

(8)

s := addList1([4, 3, 1, 8, x, 3, 4, 3], 2)

58

(9)

x

2

(10)

``


 

Download Doubt_on_list.mw

Dear friends,


 

 

 

Effect of A and B on z values

``

A

``

B

x values

y = 5

y = 10

y = 15

y = 5

y = 10

y = 15

x = 4

"[ 4 5 1.9]"

"[ 4 10 1.8]"

"[ 4 15 3.2]"

"[ 4 5 2.2]"

"[ 4 5 2.0]"

"[ 4 15 3.3]"

x = 6

"[ 6 5 1.7]"

"[ 6 10 1.5]"

"[ 6 15 2.2]"

"[ 6 5 1.9]"

"[ 6 10 1.7]"

"[ 6 15 2.3]"

x = 8

"[ 8 5 3.0]"

"[ 8 10 1.7]"

"[ 8 15 3.1]"

"[ 8 5 3.2]"

"[ 8 10 1.9]"

"[ 8 15 3.2]"

``

``

Table 1: Effect of Modified Parameters on z output

 

Dear friends.,
I want a suitable plot for the above data. I have given the values as [ x  y  z] for z values to be plotted for the two cases, A and B in the same graph to compare and get the best option x ,    y and A or B .

Mathematically an x vs y vs z plot. Any bar or similar plot is what seems suitable to me.

I could not locate any help for plotting 3D data values in help page.

Any suggestions and solution please.

Thanks.

Ramakrishnan V

NULL


 

Download 3Dplot_given_Data_xyz.mw

Can any one disprove maple answer in the attached document?
If not, what is the conclusion?
 

restart

coulditbe(3*I > 0)

false

(1)

coulditbe(3*I > 0)

false

(2)

coulditbe(3*I < 0)

false

(3)

coulditbe(-2+3*I = 0)

false

(4)

coulditbe(abs(I) > 0)

true

(5)

true

(6)

coulditbe(2+3*I < 0)

true

(7)

``

``

What is your opinion?

My opinion from the above is : When a is real and b is complex, a and b can not be compared.

Like number of goats and number of lions  can not be added to give an answer in number of lions alone or number of goats alone!!
Riemann's function Zeta is a function of Complex number

 

solve(abs(Zeta(s+2*I)) = 0, s)

-2*I+RootOf(Zeta(_Z))

(8)

"(->)"

-2.0000-2.*I

(9)

NULL

solve(Zeta(s+2*I) = 0, s)

-2*I+RootOf(Zeta(_Z))

(10)

"(->)"

-2.0000-2.*I

(11)

What does the above results convey??

Am I correct if i state that 's' should be a complex number only and not a real number.


 

Download s_is_complex.mw

s_is_complex.mw

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