Ramakrishnan

187 Reputation

5 Badges

4 years, 144 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.

MaplePrimes Activity


These are replies submitted by Ramakrishnan

Hope attached doc helps you to an extent. Please note, the function values, only you can determine with values of constants and variable r values.
 

Let r = r1, r2, r3, r4 and r5

At r, find V and E0

V := [1, 2, 3, 4, 5, 6]; E0 := [6, 5, 4, 3, 2, 1]

[6, 5, 4, 3, 2, 1]

(1)

E0B0 := [12, 20, 8, 12, 4, 4]

Plot of V vs E0 is given below. Only points are plotted

plot(`<|>`(`<,>`(1, 2, 3, 4, 5, 6), `<,>`(6, 5, 4, 3, 2, 1)), style = point)

 

NULL

B0 := [2, 4, 2, 4, 2, 4]

[2, 4, 2, 4, 2, 4]

(2)

Plot of V vs B0 is given below.

plot(`<|>`(`<,>`(1, 2, 3, 4, 5, 6), `<,>`(2, 4, 2, 4, 2, 4)), style = line)

 

``

Plot of V vs E0 is given below.

NULL

NULLSimilarly, find E0*B0 as a list and plot as below

plot(`<|>`(`<,>`(1, 2, 3, 4, 5, 6), `<,>`(12, 20, 8, 12, 4, 4)), style = pointline)

 

NULL


 

Download howDoIplot.mw

Cheers. Ramakrishnan V

@Preben Alsholm 

it is great. Nice way for using it in a session. But any way out for only few lines in a session?

Cheers. Thanks.

Ramakrishnan V

@Christopher2222 

Dear Christopher, Thank you for the tips. It works and label are not visible. I also unselected [ Format -> Equation Labels -> Worksheet] and labels were removed.

I was wondering how the equations (two cells) between 10 and 11 and two equations (cells) were not included. I found the after typing the assignment command, if "ctrl+equal" to is entered, label  is not coming. If i use just "enter", then equan label comes out. I donot know if it is proper that way only or not.

In your recommendation, i believe no labels are provided for all lines (all labels are removed). If a few labels are needed and a few are not needed, then,i just wanted to know wheter use of " ctrl+equal " for no label  and " enter key " for label requirement are ok or not. There must be a way out in maple for this. I am just searching for it.

Thanks for you tips again as it works well for me.

Cheers. Ramakrishnan V

@Kitonum 

Hope the contents of file enclosed will be ok.

Thanks for comments and help

Ramakrishnan VExperimentalData.xlsxRequest_Plot_from_ProfKitonum.mw
 

restart; with(ExcelTools)

plotplease := proc (f1, f2, f3, f4, f5) description "plotting the curves"; plot([f1, f2, f3, f4, f5], x = 2 .. 5, color = [red, blue, green, black, orange], view = [2 .. 5, 20 .. 45], legend = Legend, title = Title, caption = Caption, color = [black], linestyle = [1, 2, 4, 3, 6], thickness = [3, 1, 2, 4, 2], labels = [xdataVar, ydataVar], labeldirections = ["horizontal", "vertical"]) end proc

proc (f1, f2, f3, f4, f5) description "plotting the curves"; plot([f1, f2, f3, f4, f5], x = 2 .. 5, color = [red, blue, green, black, orange], view = [2 .. 5, 20 .. 45], legend = Legend, title = Title, caption = Caption, color = [black], linestyle = [1, 2, 4, 3, 6], thickness = [3, 1, 2, 4, 2], labels = [xdataVar, ydataVar], labeldirections = ["horizontal", "vertical"]) end proc

(1)

``

ObtainyValues := proc (P, a::list) local j, yVal, z; j := 0; yVal := []; for z in a do if j = 0 then yVal := evalf[3](eval(S2, [x = z])) else yVal := yVal, evalf[3](eval(S2, [x = z])) end if; j := j+1 end do; yVal end proc

proc (P, a::list) local j, yVal, z; j := 0; yVal := []; for z in a do if j = 0 then yVal := evalf[3](eval(S2, [x = z])) else yVal := yVal, evalf[3](eval(S2, [x = z])) end if; j := j+1 end do; yVal end proc

(2)

M1 := Import("C:/Users/dell/Desktop/ExperimentalData.xlsx", 1)

Matrix(%id = 18446746374273448774)

(3)

``

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[i][j] end do end do; y := a*x^2+b*x+c; for i from 2 to 21 do d[i] := [d[i]] end do

``

d[1]

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

(4)

d[1]

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

(5)

xdataVar := d[1][1]

"BrakePower"

(6)

ydataVar := "Brake Thermal Efficiency" = "Brake Thermal Efficiency"NULL

``

xdata := [d[1][2], d[1][5], d[1][7]]

[2.356, 3.534, 4.32]

(7)

S2BTE := d[2][1]

"S2"

(8)

S2_BTE_ydata := [d[2][2], d[2][5], d[2][7]]

[27.0, 32.8, 34.0]

(9)

S4_BTE_yVar := d[3][1]

"S4"

(10)

S4_BTE_ydata := [d[3][2], d[3][5], d[3][7]]

[32.0, 40.0, 41.6]

(11)

D4P5U_BTE_yVar := d[4][1]

"D4P5U"

(12)

D4P5U_BTE_ydata := [d[4][2], d[4][5], d[4][7]]

[29.4, 36.3, 37.7]

(13)

D4P10U_BTE_yVar := d[5][1]

"D4P10U"

(14)

D4P10U_BTE_ydata := [d[5][2], d[5][5], d[5][7]]

[30.1, 37.3, 38.7]

(15)

D4P15U_BTE_yVar := d[6][1]

"D4P15U"

(16)

D4P15U_BTE_ydata := [d[6][2], d[6][5], d[6][7]]

[28.7, 35.4, 36.8]

(17)

D4P5C_BTE_yVar := d[7][1]

"D4P5C"

(18)

D4P5C_BTE_ydata := [d[7][2], d[7][5], d[7][7]]

[29.2, 36.0, 37.5]

(19)

D4P10C_BTE_yVar := d[8][1]

"D4P10C"

(20)

D4P10C_BTE_ydata := [d[8][2], d[8][5], d[8][7]]

[31.4, 39.2, 40.7]

(21)

D4P15C_BTE_yVar := d[9][1]

"D4P15C"

(22)

D4P15C_BTE_ydata := [d[9][2], d[9][5], d[9][7]]

[30.7, 37.6, 39.1]

(23)

NULL

NULL

NULL

NULL

S2BTE := d[2][1]

"S2"

(24)

S2_BTE_ydata := [d[2][2], d[2][5], d[2][7]]

[27.0, 32.8, 34.0]

(25)

S4_BTE_yVar := d[3][1]

"S4"

(26)

S4_BTE_ydata := [d[3][2], d[3][5], d[3][7]]

[32.0, 40.0, 41.6]

(27)

D6P5U_BTE_yVar := d[10][1]

"D6P5U"

(28)

D6P5U_BTE_ydata := [d[10][2], d[10][5], d[10][7]]

[30.0, 36.9, 38.3]

(29)

D6P10U_BTE_yVar := d[11][1]

"D6P10U"

(30)

D6P10U_BTE_ydata := [d[11][2], d[11][5], d[11][7]]

[30.7, 38.1, 39.5]

(31)

D6P15U_BTE_yVar := d[12][1]

"D6P15U"

(32)

D6P15U_BTE_ydata := [d[12][2], d[12][5], d[12][7]]

[29.4, 35.6, 37.1]

(33)

D6P5C_BTE_yVar := d[13][1]

"D6P5C"

(34)

D6P5C_BTE_ydata := [d[13][2], d[7][5], d[7][7]]

[30.0, 36.0, 37.5]

(35)

D6P10C_BTE_yVar := d[14][1]

"D6P10C"

(36)

D6P10C_BTE_ydata := [d[14][2], d[14][5], d[14][7]]

[31.7, 39.5, 41.1]

(37)

D6P15C_BTE_yVar := d[15][1]

"D6P15C"

(38)

D6P15C_BTE_ydata := [d[15][2], d[14][5], d[9][7]]

[30.6, 39.5, 39.1]

(39)

NULL

NULL

``

S2BTE := d[2][1]

"S2"

(40)

S2_BTE_ydata := [d[2][2], d[2][5], d[2][7]]

[27.0, 32.8, 34.0]

(41)

S4_BTE_yVar := d[3][1]

"S4"

(42)

S4_BTE_ydata := [d[3][2], d[3][5], d[3][7]]

[32.0, 40.0, 41.6]

(43)

D8P5U_BTE_yVar := d[16][1]

"D8P5U"

(44)

 

D8P5U_BTE_ydata := [d[16][2], d[16][5], d[16][7]]

[29.1, 35.8, 37.1]

(45)

D8P10U_BTE_yVar := d[17][1]

"D8P10U"

(46)

D8P10U_BTE_ydata := [d[17][2], d[17][5], d[17][7]]

[29.5, 36.2, 37.5]

(47)

D8P15U_BTE_yVar := d[18][1]

"D8P15U"

(48)

D8P15U_BTE_ydata := [d[18][2], d[18][5], d[18][7]]

[28.2, 34.9, 36.2]

(49)

 

D8P5C_BTE_yVar := d[19][1]

"D8P5C"

(50)

D8P5C_BTE_ydata := [d[19][2], d[19][5], d[19][7]]

[28.7, 35.5, 37.0]

(51)

D8P10C_BTE_yVar := d[20][1]

"D8P10C"

(52)

D8P10C_BTE_ydata := [d[20][2], d[20][5], d[20][7]]

[31.1, 38.7, 40.2]

(53)

D8P15C_BTE_yVar := d[21][1]

"D8P15C"

(54)

D8P15C_BTE_ydata := [d[21][2], d[21][5], d[21][7]]

[30.1, 37.3, 38.8]

(55)

NULL

``

NULL

NULL

with(CurveFitting)

NULL

Title := " Effect on Brake Thermal Efficiency for 5 % Uncooled EGR"; Caption := "Fig.4.1 Brake Power Vs Brake Thermal Efficiency  for 5 % Uncooled EGR"; Legend := ["S2 ", "S4 ", "D4P5U", "D6P5U", "D8P5U"]

S2 := PolynomialInterpolation(xdata, S2_BTE_ydata, x, form = Lagrange)

11.67016483*(x-3.534)*(x-4.32)-35.42468582*(x-2.356)*(x-4.32)+22.02494779*(x-2.356)*(x-3.534)

(56)

"(->)"

eval(S2, [x = 3])

30.76559126

(57)

BP := xdata

[2.356, 3.534, 4.32]

(58)

NULL

addList := 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

(59)

NULL

NULL

S4 := PolynomialInterpolation(xdata, S4_BTE_ydata, x, form = Lagrange)

13.83130647*(x-3.534)*(x-4.32)-43.20083637*(x-2.356)*(x-4.32)+26.94817141*(x-2.356)*(x-3.534)

(60)

NULL

NULL

D4P5U := PolynomialInterpolation(xdata, D4P5U_BTE_ydata, x, form = Lagrange)

12.70751282*(x-3.534)*(x-4.32)-39.20475900*(x-2.356)*(x-4.32)+24.42178034*(x-2.356)*(x-3.534)

(61)

````

``

D6P5U := PolynomialInterpolation(xdata, D6P5U_BTE_ydata, x, form = Lagrange)

12.96684982*(x-3.534)*(x-4.32)-39.85277155*(x-2.356)*(x-4.32)+24.81045589*(x-2.356)*(x-3.534)

(62)

D8P5U := PolynomialInterpolation(xdata, D8P5U_BTE_ydata, x, form = Lagrange)

12.57784432*(x-3.534)*(x-4.32)-38.66474855*(x-2.356)*(x-4.32)+24.03310479*(x-2.356)*(x-3.534)

(63)

NULLM1[1][1]

"BrakePower"

(64)

NULLNULL

NULLNULL

plotplease(S2, S4, D4P5U, D6P5U, D8P5U)

 

NULL

NULL

Title := " Effect on Brake Thermal Efficiency for 5 % Cooled EGR"; Caption := "Fig.4.2 Brake Power Vs Brake Thermal Efficiency  for 5 % Cooled EGR"; Legend := ["S2 ", "S4 ", "D4P5C", "D6P5C", "D8P5C"]

D4P5C := PolynomialInterpolation(xdata, D4P5C_BTE_ydata, x, form = Lagrange)

12.62106715*(x-3.534)*(x-4.32)-38.88075273*(x-2.356)*(x-4.32)+24.29222182*(x-2.356)*(x-3.534)

(65)

NULLNULL

NULL

D6P5C := PolynomialInterpolation(xdata, D6P5C_BTE_ydata, x, form = Lagrange)

12.96684982*(x-3.534)*(x-4.32)-38.88075273*(x-2.356)*(x-4.32)+24.29222182*(x-2.356)*(x-3.534)

(66)

D8P5C := PolynomialInterpolation(xdata, D8P5C_BTE_ydata, x, form = Lagrange)

12.40495299*(x-3.534)*(x-4.32)-38.34074228*(x-2.356)*(x-4.32)+23.96832553*(x-2.356)*(x-3.534)

(67)

````

````

plotplease(S2, S4, D4P5C, D6P5C, D8P5C)

 

NULL

NULL

NULL

Title := " Effect on Brake Thermal Efficiency for 10 % Uncooled EGR"; Caption := "Fig.4.3 Brake Power Vs Brake Thermal Efficiency  for 10 % Uncooled EGR"; Legend := ["S2 ", "S4 ", "D4P10U", "D6P10U", "D8P10U"]

D4P10U := PolynomialInterpolation(xdata, D4P10U_BTE_ydata, x, form = Lagrange)

13.01007265*(x-3.534)*(x-4.32)-40.28477991*(x-2.356)*(x-4.32)+25.06957292*(x-2.356)*(x-3.534)

(68)

````

``

D6P10U := PolynomialInterpolation(xdata, D6P10U_BTE_ydata, x, form = Lagrange)

13.26940965*(x-3.534)*(x-4.32)-41.14879664*(x-2.356)*(x-4.32)+25.58780699*(x-2.356)*(x-3.534)

(69)

D8P10U := PolynomialInterpolation(xdata, D8P10U_BTE_ydata, x, form = Lagrange)

12.75073565*(x-3.534)*(x-4.32)-39.09675691*(x-2.356)*(x-4.32)+24.29222182*(x-2.356)*(x-3.534)

(70)

NULLNULL

NULLNULL

NULLNULL

plotplease(S2, S4, D4P10U, D6P10U, D8P10U)

 

NULL

NULL

Title := " Effect on Brake Thermal Efficiency for 10 % Cooled EGR"; Caption := "Fig.4.4 Brake Power Vs Brake Thermal Efficiency  for 10% Cooled EGR"; Legend := ["S2 ", "S4 ", "D4P10C", "D6P10C", "D8P10C"]

D4P10C := PolynomialInterpolation(xdata, D4P10C_BTE_ydata, x, form = Lagrange)

13.57196947*(x-3.534)*(x-4.32)-42.33681964*(x-2.356)*(x-4.32)+26.36515809*(x-2.356)*(x-3.534)

(71)

````

``

D6P10C := PolynomialInterpolation(xdata, D6P10C_BTE_ydata, x, form = Lagrange)

13.70163797*(x-3.534)*(x-4.32)-42.66082591*(x-2.356)*(x-4.32)+26.62427512*(x-2.356)*(x-3.534)

(72)

D8P10C := PolynomialInterpolation(xdata, D8P10C_BTE_ydata, x, form = Lagrange)

13.44230098*(x-3.534)*(x-4.32)-41.79680919*(x-2.356)*(x-4.32)+26.04126180*(x-2.356)*(x-3.534)

(73)

NULLNULL

NULLNULL

plotplease(S2, S4, D4P5C, D6P5C, D8P5C)

 

NULL

``

NULL

NULL

Title := " Effect on Brake Thermal Efficiency for 15 % Uncooled EGR"; Caption := "Fig.4.5 Brake Power Vs Brake Thermal Efficiency  for 15 % Uncooled EGR"; Legend := ["S2 ", "S4 ", "D4P15U", "D6P15U", "D8P15U"]

D4P15U := PolynomialInterpolation(xdata, D4P15U_BTE_ydata, x, form = Lagrange)

12.40495299*(x-3.534)*(x-4.32)-38.23274019*(x-2.356)*(x-4.32)+23.83876702*(x-2.356)*(x-3.534)

(74)

D6P15U := PolynomialInterpolation(xdata, D6P5C_BTE_ydata, x, form = Lagrange)

12.96684982*(x-3.534)*(x-4.32)-38.88075273*(x-2.356)*(x-4.32)+24.29222182*(x-2.356)*(x-3.534)

(75)

D8P15U := PolynomialInterpolation(xdata, D8P15U_BTE_ydata, x, form = Lagrange)

12.18883883*(x-3.534)*(x-4.32)-37.69272973*(x-2.356)*(x-4.32)+23.45009147*(x-2.356)*(x-3.534)

(76)

 

````

``NULL

plotplease(S2, S4, D4P15U, D6P15U, D8P15U)

 

NULL

NULL

Title := " Effect on Brake Thermal Efficiency for 15 % Cooled EGR"; Caption := "Fig.4.6 Brake Power Vs Brake Thermal Efficiency  for 15 % Cooled EGR"; Legend := ["S2 ", "S4 ", "D4P15C", "D6P15C", "D8P15C"]

D4P15C := PolynomialInterpolation(xdata, D4P15C_BTE_ydata, x, form = Lagrange)

13.26940965*(x-3.534)*(x-4.32)-40.60878619*(x-2.356)*(x-4.32)+25.32868996*(x-2.356)*(x-3.534)

(77)

NULLNULL

NULL

D6P15C := PolynomialInterpolation(xdata, D6P15C_BTE_ydata, x, form = Lagrange)

13.22618681*(x-3.534)*(x-4.32)-42.66082591*(x-2.356)*(x-4.32)+25.32868996*(x-2.356)*(x-3.534)

(78)

D8P15C := PolynomialInterpolation(xdata, D8P15C_BTE_ydata, x, form = Lagrange)

13.01007265*(x-3.534)*(x-4.32)-40.28477991*(x-2.356)*(x-4.32)+25.13435218*(x-2.356)*(x-3.534)

(79)

``````

plotplease(S2, S4, D4P15C, D6P15C, D8P15C)

 

``

``

NULL

NULL

NULL

Title := " Effect on Brake Thermal Efficiency for varying manifold orifice "; Caption := "Fig.4.7 Brake Power Vs Brake Thermal Efficiency  for 10 mm orifice and Cooled EGR"; Legend := ["S2 ", "S4 ", "D6P5C", "D6P10C", "D8P15C"]

plotplease(S2, S4, D6P5C, D6P10C, D8P15C)

 

NULL

NULL

NULL

``

xVal := [d[1][2], d[1][3], d[1][4], d[1][5], d[1][6], d[1][7]]

xVal

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

(80)

NULL

S2_BTE_ydataNew := [ObtainyValues(S2, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(81)

Export(S2_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B2")

NULL

NULL

S4_BTE_ydataNew := [ObtainyValues(S4, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(82)

Export(S4_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B3")

NULL

D4P5U_BTE_ydataNew := [ObtainyValues(D4P5U, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(83)

Export(D4P5U_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B4")

NULL

NULL

D6P5U_BTE_ydataNew := [ObtainyValues(D6P5U, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(84)

Export(D6P5U_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B5")

NULL

D8P5U_BTE_ydataNew := [ObtainyValues(D8P5U, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(85)

Export(D8P5U_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B6")

NULL

NULL

D4P5C_BTE_ydataNew := [ObtainyValues(D4P5C, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(86)

Export(D4P5C_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B7")

NULL

D6P5C_BTE_ydataNew := [ObtainyValues(D6P5C, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(87)

Export(D6P5C_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B8")

NULL

D8P5C_BTE_ydataNew := [ObtainyValues(D8P5C, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(88)

Export(D8P4C*_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B9")

NULL

NULL

D4P10U_BTE_ydataNew := [ObtainyValues(D4P10U, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(89)

Export(D4P10U_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B10")

NULL

D6P10U_BTE_ydataNew := [ObtainyValues(D6P10U, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(90)

Export(D6P10U_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B11")

NULL

D8P10U_BTE_ydataNew := [ObtainyValues(D8P10U, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(91)

Export(D8P10U_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B12")

NULL

NULL

D4P10C_BTE_ydataNew := [ObtainyValues(D4P10C, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(92)

Export(D4P10C_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B13")

NULL

D6P10C_BTE_ydataNew := [ObtainyValues(D6P10C, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(93)

Export(D6P10C_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B14")

NULL

D8P10C_BTE_ydataNew := [ObtainyValues(D8P10C, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(94)

Export(D8P10C_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B15")

NULL

NULL

D4P15U_BTE_ydataNew := [ObtainyValues(D4P15U, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(95)

Export(D4P15U_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B16")

NULL

D6P15U_BTE_ydataNew := [ObtainyValues(D6P15U, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(96)

Export(D6P15U_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B17")

NULL

D8P15U_BTE_ydataNew := [ObtainyValues(D8P15U, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(97)

Export(D8P15U_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B18")

NULL

NULL

D4P15C_BTE_ydataNew := [ObtainyValues(D4P15C, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(98)

Export(D4P15C_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B19")

NULL

D6P15C_BTE_ydataNew := [ObtainyValues(D6P15C, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(99)

Export(D6P15U_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B20")

NULL

D8P15C_BTE_ydataNew := [ObtainyValues(D8P15C, xVal)]

[26.8, 29.3, 31.3, 32.7, 33.7, 34.1]

(100)

Export(D8P15C_BTE_ydataNew, "C:/Users/dell/Desktop/RoughExperimentalData.xlsx", "NewBTE", "B21")

NULL

NULL

NULL


 

Download Request_Plot_from_ProfKitonum.mw

 

@Kitonum 

Dear Kitonum,

BP is brake power in kW, D4 EFF is efficiency value for model with 4 mm Dia orifice for a particular  say 5%EGR (P5) and with Cooling (P5C) or without cooling (P5U).

A curve needs to be obtained for each model for each parameter (Efficiency here).

I enclose the doc new one which works, but feel needs improvement.

Regarding the errors, I found out of the many,  two of them made here were

d[i] has in its first pair, strings [["BrakePower", "S2"],[x1,y1]...]. Hence an error

M1 could not be assigned because import file was open without saving in my PC. I closed it and then it was fine.

                              -15                    
          -2.99760216648792 10    + 1.00000000000000 x
                                  -16  2
             + 3.88578058618805 10    x
The above answer is incorrect. For S2 one equation and S4 another equation are required.
d[2][1];PleasePlot_Doubt_(1).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))

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

 

 

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

Matrix(%id = 18446746264177821774)

(2)

M1[1, 11]

"D6P10U"

(3)

M1[1, 10]

"D6P5U"

(4)

M1[2, 15]

.267

(5)

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

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

 

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

 

CurveFitting[LeastSquares]([[2.356, .303], [2.749, .271], [3.142, .256], [3.534, .249], [3.927, .244], [4.32, .241]], x, curve = y)

HFloat(0.5862119576375505)-HFloat(0.17186946196596695)*x+HFloat(0.02140719191937303)*x^2

(6)

``

A := Matrix([[["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]], [["BrakePower", "S2"], [2.356, .303], [2.749, .271], [3.142, .256], [3.534, .249], [3.927, .244], [4.32, .241]], [["BrakePower", "S4"], [2.356, .256], [2.749, .225], [3.142, .211], [3.534, .205], [3.927, .2], [4.32, .197]]]); y := a*x^2+b*x+c; CurveFitting[LeastSquares](convert(A[1, 2 .. -1], list), x, curve = y)

-HFloat(2.9976021664879227e-15)+HFloat(0.9999999999999998)*x+HFloat(3.885780586188048e-16)*x^2

(7)

``

The above answer is incorrect. For S2 one equation and S4 another equation are required.

d[2][1]

["BrakePower", "S2"]

(8)

``


Download PleasePlot_Doubt_(1).mw

Thanks.


 

 

Comparison of Performance of Two-Stroke Engine with Four-Stroke Engine

 Brake Power Vs Brake EfficiencyNULL

E2BD1P5 := [[1000, 20], [2000, 21], [3000, 32], [4000, 23], [5000, 23]]

``

Equn1 := CurveFitting[LeastSquares](E2BD1P5, x, curve = y)

52/5+(179/17500)*x-(11/7000000)*x^2

(1)

data2 := [[1000, 25], [2000, 26], [3000, 33], [4000, 25], [5000, 24]]

Equn2 := CurveFitting[LeastSquares](data2, x, curve = y)

18+(549/70000)*x-(19/14000000)*x^2

(2)

data3 := [[1000, 26], [2000, 27], [3000, 34], [4000, 26], [5000, 25]]

Equn3 := CurveFitting[LeastSquares](data3, x, curve = y)

19+(549/70000)*x-(19/14000000)*x^2

(3)

data4 := [[1000, 27], [2000, 28], [3000, 35], [4000, 27], [5000, 25]]

Equn4 := CurveFitting[LeastSquares](data4, x, curve = y)

97/5+(17/2000)*x-(3/2000000)*x^2

(4)

``

y := a*x^2+b*x+c

a*x^2+b*x+c

(5)

``

Equn1

52/5+(179/17500)*x-(11/7000000)*x^2

(6)

NULL

NULL

NULL

NULL

 

 

``

``

 

Comparison of Performance of Two-Stroke Engine with Four-Stroke Engine

 Brake Power Vs Brake Efficiency``

plot([Equn1, Equn2, Equn3, Equn4], x = 1000 .. 5000, color = [red, blue, green, gold], size = [800, 500], scaling = unconstrained, discont)

 

NULL

NULL

NULL

 

 

NULL

plot([18+(549/70000)*x-(19/14000000)*x^2, 19+(549/70000)*x-(19/14000000)*x^2, 52/5+(179/17500)*x-(11/7000000)*x^2, 97/5+(17/2000)*x-(3/2000000)*x^2], x = 1000 .. 5000, color = [red, blue, green, gold], size = [800, 500], scaling = unconstrained, discont)

 

NULL


 

Download CurveFitting_BrakeEfficiency.mwCurveFitting_BrakeEfficiency.mw
 

 

Comparison of Performance of Two-Stroke Engine with Four-Stroke Engine

 Brake Power Vs Brake EfficiencyNULL

E2BD1P5 := [[1000, 20], [2000, 21], [3000, 32], [4000, 23], [5000, 23]]

``

Equn1 := CurveFitting[LeastSquares](E2BD1P5, x, curve = y)

52/5+(179/17500)*x-(11/7000000)*x^2

(1)

data2 := [[1000, 25], [2000, 26], [3000, 33], [4000, 25], [5000, 24]]

Equn2 := CurveFitting[LeastSquares](data2, x, curve = y)

18+(549/70000)*x-(19/14000000)*x^2

(2)

data3 := [[1000, 26], [2000, 27], [3000, 34], [4000, 26], [5000, 25]]

Equn3 := CurveFitting[LeastSquares](data3, x, curve = y)

19+(549/70000)*x-(19/14000000)*x^2

(3)

data4 := [[1000, 27], [2000, 28], [3000, 35], [4000, 27], [5000, 25]]

Equn4 := CurveFitting[LeastSquares](data4, x, curve = y)

97/5+(17/2000)*x-(3/2000000)*x^2

(4)

``

y := a*x^2+b*x+c

a*x^2+b*x+c

(5)

``

Equn1

52/5+(179/17500)*x-(11/7000000)*x^2

(6)

NULL

NULL

NULL

NULL

 

 

``

``

 

Comparison of Performance of Two-Stroke Engine with Four-Stroke Engine

 Brake Power Vs Brake Efficiency``

plot([Equn1, Equn2, Equn3, Equn4], x = 1000 .. 5000, color = [red, blue, green, gold], size = [800, 500], scaling = unconstrained, discont)

 

NULL

NULL

NULL

 

 

NULL

plot([18+(549/70000)*x-(19/14000000)*x^2, 19+(549/70000)*x-(19/14000000)*x^2, 52/5+(179/17500)*x-(11/7000000)*x^2, 97/5+(17/2000)*x-(3/2000000)*x^2], x = 1000 .. 5000, color = [red, blue, green, gold], size = [800, 500], scaling = unconstrained, discont)

 

NULL


 

Download CurveFitting_BrakeEfficiency.mw
The following recommended code with matrix A defined, gives me a single equation whereas my antincipation was for >1. I cld not workout the way it worked. Please do find the mistakes if possible. Thanks.

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))

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

 

 

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

Matrix(%id = 18446745901927778382)

(2)

M1[1, 11]

"D6P10U"

(3)

M1[1, 10]

"D6P5U"

(4)

M1[2, 15]

.267

(5)

``

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]

(6)

d[2]

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

(7)

d[3]

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

(8)

``

A := Matrix([[["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]], [["BrakePower", "S2"], [2.356, .303], [2.749, .271], [3.142, .256], [3.534, .249], [3.927, .244], [4.32, .241]], [["BrakePower", "S4"], [2.356, .256], [2.749, .225], [3.142, .211], [3.534, .205], [3.927, .2], [4.32, .197]]]); y := a*x^2+b*x+c; CurveFitting[LeastSquares](convert(A[1, 2 .. -1], list), x, curve = y)

-HFloat(2.9976021664879227e-15)+HFloat(0.9999999999999998)*x+HFloat(3.885780586188048e-16)*x^2

(9)

``

``


 

Download PleasePlot_Doubt.mw

 

 

@Kitonum 

@Kitonum 

Thank you.

Ramakrishnan V

@Kitonum 

The technique of defining the funations using an intermediate function g is quite wonderful.

Could you please explain in a few more lines as to how this is performed. Maple understands quite well! But i am still wondering how no error is shown for x1,y1,x2,y2. Is it because assignments are done prior to always.

How the functions f1, f2, f3 are not altered to, i wonder, though an interpolation g comes in between? Is there any accuray loss in this way?

or f1 f2 f3 are just a list of two end points and hence a set of straightlines will be always?

Just want to know, whether i am clear in my understanding.

Thanks.

Ramakrishnan V

 

@tomleslie 

Thank you very much. I was not aware of that assignment till now. Here after, i shall be doubly careful when i see an = sign!

Thanks for spending your valuable time and saving my time as well in quickly removing the error.

Ramakrishnan V

I could get in two methods? Why the error in the first method below? Thanks for answering.

Ramakrishnan V
 

with(Statistics)

D4P5C = 1.9; D6*P5C = 1.7; D8P5C = 3.0; E4P10C = 1.8; D6P10C = 1.5; D8P10C = 1.7; D4P15C = 3.2; D6P15C = 2.2; D8P15C = 3.1

D4P5U = 2.2; D6P5U = 1.9; D8P5U = 3.2; D4P10U = 2.0; D6P10U = 1.7; D8P10U = 1.9; D4P15U = 3.3; D6P15U = 2.3; D8P15U = 3.2

C := Array([D4P5C, D6*P5C, E8*P5C, D4P5C, D6P5C, D8P5C, D4P5C, D6P5C, D8P5C])

Array(%id = 18446746484452843638)

(1)

NULL

rtable_options(C)

datatype = anything, subtype = Array, storage = rectangular, order = Fortran_order

(2)

U := Array([D4P5U, D6P5U, D8P5U, D4P5U, D6P5U, D8P5U, D4P5U, D6P5U, D8P5U])

Array(%id = 18446746484452839782)

(3)

ColumnGraph([C, U], title = "Optimum Performance", legend = ["Cooled", "Uncooled"])

Error, (in Statistics:-ColumnGraph) unable to store 'D4P5C' when datatype=float[8]

 

How do I correct the error above?

Thanks.

Ramakrishnan V

 

with(Statistics); A := Array([1.9, 1.7, 3.0, 1.8, 1.5, 1.7, 3.2, 2.2, 3.1])

Array(%id = 18446746484452836526)

(4)

NULL

NULL

E := Array([2.2, 1.9, 3.2, 2, 1.7, 1.9, 3.3, 2.3, 3.2])

Array(%id = 18446746484452838686)

(5)

ColumnGraph([A, E], title = "Column Graph", legend = ["COL A", "COL B"], offset = 1, distance = .5, width = 2.5)

 

How do I change colour above here?

Thanks for help.

Ramakrishnan V

dataDF := DataFrame( < 1.9, 1.7, 3.0; 1.8, 1.5, 1.7; 3.2, 2.2, 3.1;2.2, 1.9, 3.2; 2, 1.7, 1.9; 3.3, 2.3, 3.2>, 'rows' = [ 'r1','r2','r3','r4','r5','r6'], 'columns' = [ 'c1', 'c2', 'c3'] ):

colorDF := DataFrame( < yellow,green,black; yellow,green,black;yellow,green,black;yellow,green,black; yellow,green,black;yellow,green,blue >, 'rows' = [ 'r1','r2','r3','r4','r5','r6'], 'columns' = [ 'c3', 'c1', 'c2'] ):

ColumnGraph(dataDF, color = colorDF);

 

NULL


 

Download doPlot_3.mw

@Ramakrishnan 

@tomleslie 

Dear Prof., Thank you so much. [4,10,2] is right as you mentioned. I also did not mention that x and y are references and numbers as such. 4 mm diameter(x) with 10% recirculation(y) for cooled exhausr recirculation case(A) is referred to as case A [4,10, z] in which case please recommend a suitable command for (column) chart which is easy to visualise given a proper scale and width of each column.

Is it ok if i assume COLA [col1 is A 4 5,; col2 is A 4 10; col3 is A 4 15; ]

COLB[col4 is A 6 5,; col5 is A 6 10; col6 is A 6 15;]

COLC [col7 is A 8 5,; col8 is A 8 10; col9 is B 8 15; ]

COLE [col10 is B 4 5,; col11 is B 6 5; col2 is B 8 5;]

COLF [col13 is B 4 10,; col14 is B 6 10; col15 is B 8 10; ]

COLG
 

COLA to COLG are defined as A to G (D omitted)

with(Statistics); A := Array([1.9, 1.7, 3.0])

Array(%id = 18446746509132408942)

(1)

B := Array([1.8, 1.5, 1.7])

Array(%id = 18446746509132410502)

(2)

C := Array([3.2, 2.2, 3.1])

Array(%id = 18446746509132404366)

(3)

E := Array([2.2, 1.9, 3.2])

Array(%id = 18446746509132405686)

(4)

F := Array([2, 17, 1.9])

Array(%id = 18446746509132398950)

(5)

G := Array([3.3, 2.3, 3.2])

Array(%id = 18446746509132400150)

(6)

ColumnGraph([A, B, C, E, F, G], title = "Column Graph", legend = ["5%C-A", "10%C-B", "15%C-C", "5%U-E", "10%U-F", "15%U-G"], offset = 1, distance = 1, width = 1)

 

The chart i want is different in 6 groups and not 3 groups. Colour also i need to change. Please do help me with right commands. Thanks.

Ramakrishnan v

 

Effect of A and B on z values

NULL

Cooled Recirculation

``

Uncooled Recirculation

x                y

5% EGR

10% EGR

15% EGR

5% EGR

10% EGR

15% EGR

4 mm

1.9

1.8

3.2

2.2

1.9

3.2

6 mm

1.7

1.5

2.2

2.0

1.7

1.9

8 mm

30

1.7

3.1``

3.3

2.3

3.2

NULL

NULL

Table 1: Effect of Modified Parameters on z output

 

Dear Prof.,
Thank you for your answer given below. It helped me understand simple ideas. 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

with(plots):
Avals:= [ [ 4, 5, 1.9],  [ 6, 5, 1.7],  [ 8, 5, 3.0],
          [ 4, 10, 1.8], [ 6, 10, 1.5], [ 8, 10, 1.7],
          [ 4, 15, 3.2], [ 6, 15, 2.2], [ 8, 15, 3.1]
        ]:
Bvals:= [ [ 4, 5, 2.2],  [ 6, 5, 1.9],  [ 8, 5, 3.2],
          [ 4, 5, 2.0],  [ 6, 10, 1.7], [ 8, 10, 1.9],
          [ 4, 15, 3.3], [ 6, 15, 2.3], [ 8, 15, 3.2]
        ]:
p1:=pointplot3d(Avals, symbol=sphere, symbolsize=20, color=red):
p2:=pointplot3d(Bvals, symbol=sphere, symbolsize=20, color=blue):
display([p1, p2]);

 

``


 

Download doPlot_1.mw

[col16 is B 4 15,; col7 is B 6 15; col8 is B 8 15;] 

Your answer has given me the way to proceed in a simpler way for the combinations i have. After seein the plot in your doc only, i realised that giving values to x and y is a gross mistake because point plots show scattered points and difficult to notice the corresponding optimum case combination. Thank you again. Ramakrishnan V

@Daniel Skoog 

Dear Daniel,

Thank you very much for being very practical in your answers to the doubts raised by me long ago. In fact I was about to lose hope of getting help, when this response from you has rekindled my energy to continue working with plot components more and more. Very useful answer it is for me.

Cheers. Ramakrishnan V


 

The following supporting points may be considered.

restart

sqrt(x)=-I can be solved as follows;Hence coulditbe(sqrt(x)=-I)  is true as per Maple.

sqrt(x) = -I

x := (-I)^2

-1

(1)

Dividing by zero is undefined; Hence solve(1/x=0,x) is not answered by Maple.

However as an approximation, 0.00001 is zero.Hence coulditbe(1/x)=0) is true as per Maple.

solve(1/x1 = 0.1e-7, x1)"(->)"0.10000e6

1/1000000

1/1000000

(2)

"(->)"

0.10000e-5

(3)

solve(sqrt(x2) = -I, x2)``

Also, Maple keeps silence for above statement, because (-I)^2 is not defined.


 

Download coulditbe_points.mw

coulditbe_points.mw

@_Maxim_ 

@Markiyan Hirnyk 

I have not executed the doc after changing the < sign and hence the mistake. I am sorry. Maple gives the same correct answer always.


 

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)

``

coulditbe(2+3*I < 0)

false

(6)

NULL

NULL

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))

(7)

"(->)"

-2.0000-2.*I

(8)

``

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

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

(9)

"(->)"

-2.0000-2.*I

(10)

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

1 2 3 4 5 6 7 Last Page 1 of 9