Skip to main content

plotting - Trying to plot a velocity profile in x-y plane


I have a velocity profile for two liquids on top of each other in a pressure driven channel. The profile is supposed to be parabolic. I plotted them up, but I can't manage to plot them in the x-y plane, it only plots with velocity on the vertical coordinate and y as the horizontal coordinate. Is there any way I can plot them in the x-y plane so that I can clearly see which liquid is ahead of the other in the channel and their parabolic profile? I am also trying to define v1 on a certain interval from y=0 to y=ha, and v2 from y=ha to y=H, so v1 and v2 are sort of piecewise.


Here is my code, this is for mercury(just to start somewhere) and water



v1[y_, μ1_, P_, ha_, H_, μ2_] :=
  P*(1/(2*μ1))*y*(y + ((ha^2*(μ2 - μ1) - H*μ2)/(ha*(μ2 - μ1) + H*μ1)))

v2[y_, μ1_, P_, ha_, H_, μ2_] :=
  P*(1/(2*μ2))*(y^2 + ((ha^2*(μ2 - μ1) - H*μ2)/(ha*(μ2 - μ1) + H*μ1))* y +
   (ha *  H/μ1)*( (μ1 - μ2)*(H*μ2 - ha * μ1)/(ha*(μ2 - μ1) + H*μ1 )))

Plot[{v1[y, 0.00157, -6, 1, 2, 0.001], v2[y, 0.00157, -6, 1, 2, 0.001]}, {y, 0, 10}]

Velocity vs y



Profile



Answer



How about using ParametricPlot?


ParametricPlot[{{v1[y, 0.00157, -6, 1, 2, 0.001], 
   y}, {v2[y, 0.00157, -6, 1, 2, 0.001], -y}}, {y, 0, 10}, 
 AspectRatio -> 1/GoldenRatio, PlotStyle -> Black, Frame -> True]

Mathematica graphics


For more precise control, you may need two separate ParametricPlots and combine the output using Show[plot1, plot2, PlotRange -> All].


Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more