Plot Taylor–Couette flow ilustratation plotWhy are these flow lines cut short?Strange opacity behaviorWhite Lines in Contour Plot and 3D PlotRemove the extra white-space padding introduced by implicit use of Inset in GraphicsColumncdf player poiseuille flow3D flow charts / block diagrams?Plot: 2D potential vortex embedded in 2D uniform flowTrouble with discrete MeshRegions: Integrating over plane slicesProblem with plotting Taylor polynomialsPlotting a 3d surface along the vector field flow
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Plot Taylor–Couette flow ilustratation plot
Why are these flow lines cut short?Strange opacity behaviorWhite Lines in Contour Plot and 3D PlotRemove the extra white-space padding introduced by implicit use of Inset in GraphicsColumncdf player poiseuille flow3D flow charts / block diagrams?Plot: 2D potential vortex embedded in 2D uniform flowTrouble with discrete MeshRegions: Integrating over plane slicesProblem with plotting Taylor polynomialsPlotting a 3d surface along the vector field flow
$begingroup$
I am trying to plot a set up for a classic problem of physics of fluids using Mathematica, see Wikipedia for a reference.
The problem is the movement of two concentric cylinders with two radii and velocities, as is shown in the figure.
I could generate two concentric cylinders using the following lines
u1 = ContourPlot3D[4 == x^2 + y^2, x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, PlotPoints -> 20, ColorFunction -> Black];
u2 = ContourPlot3D[x^2 + y^2 == 1, x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, ColorFunction -> Blue];
Show[u1, u2]
It is possible to add vectors, radii, velocities? Any suggestions are welcome.
plotting graphics graphics3d
edited May 30 at 8:15
C. E.
52.4k3102209
asked May 30 at 8:08
irondonioirondonio
814
$endgroup$
add a comment |
$begingroup$
I am trying to plot a set up for a classic problem of physics of fluids using Mathematica, see Wikipedia for a reference.
The problem is the movement of two concentric cylinders with two radii and velocities, as is shown in the figure.
I could generate two concentric cylinders using the following lines
u1 = ContourPlot3D[4 == x^2 + y^2, x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, PlotPoints -> 20, ColorFunction -> Black];
u2 = ContourPlot3D[x^2 + y^2 == 1, x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, ColorFunction -> Blue];
Show[u1, u2]
It is possible to add vectors, radii, velocities? Any suggestions are welcome.
plotting graphics graphics3d
edited May 30 at 8:15
C. E.
52.4k3102209
asked May 30 at 8:08
irondonioirondonio
814
$endgroup$
1
$begingroup$
It's funny that I found a video just two days ago which is actually really nice and demonstrates this: Unmixing Color Machine (Ultra Laminar Reversible Flow)
$endgroup$
– halirutan♦
May 30 at 14:46
$begingroup$
@halirutan Same, that cannot be a coincidence!
$endgroup$
– IllidanS4
May 30 at 22:22
add a comment |
$begingroup$
I am trying to plot a set up for a classic problem of physics of fluids using Mathematica, see Wikipedia for a reference.
The problem is the movement of two concentric cylinders with two radii and velocities, as is shown in the figure.
I could generate two concentric cylinders using the following lines
u1 = ContourPlot3D[4 == x^2 + y^2, x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, PlotPoints -> 20, ColorFunction -> Black];
u2 = ContourPlot3D[x^2 + y^2 == 1, x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, ColorFunction -> Blue];
Show[u1, u2]
It is possible to add vectors, radii, velocities? Any suggestions are welcome.
plotting graphics graphics3d
edited May 30 at 8:15
C. E.
52.4k3102209
asked May 30 at 8:08
irondonioirondonio
814
$endgroup$
I am trying to plot a set up for a classic problem of physics of fluids using Mathematica, see Wikipedia for a reference.
The problem is the movement of two concentric cylinders with two radii and velocities, as is shown in the figure.
I could generate two concentric cylinders using the following lines
u1 = ContourPlot3D[4 == x^2 + y^2, x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, PlotPoints -> 20, ColorFunction -> Black];
u2 = ContourPlot3D[x^2 + y^2 == 1, x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, ColorFunction -> Blue];
Show[u1, u2]
It is possible to add vectors, radii, velocities? Any suggestions are welcome.
plotting graphics graphics3d
plotting graphics graphics3d
edited May 30 at 8:15
C. E.
52.4k3102209
asked May 30 at 8:08
irondonioirondonio
814
edited May 30 at 8:15
C. E.
52.4k3102209
asked May 30 at 8:08
irondonioirondonio
814
edited May 30 at 8:15
C. E.
52.4k3102209
edited May 30 at 8:15
C. E.
52.4k3102209
edited May 30 at 8:15
C. E.
52.4k3102209
52.4k3102209
asked May 30 at 8:08
irondonioirondonio
814
asked May 30 at 8:08
irondonioirondonio
814
asked May 30 at 8:08
irondonioirondonio
814
814
1
$begingroup$
It's funny that I found a video just two days ago which is actually really nice and demonstrates this: Unmixing Color Machine (Ultra Laminar Reversible Flow)
$endgroup$
– halirutan♦
May 30 at 14:46
$begingroup$
@halirutan Same, that cannot be a coincidence!
$endgroup$
– IllidanS4
May 30 at 22:22
add a comment |
1
$begingroup$
It's funny that I found a video just two days ago which is actually really nice and demonstrates this: Unmixing Color Machine (Ultra Laminar Reversible Flow)
$endgroup$
– halirutan♦
May 30 at 14:46
$begingroup$
@halirutan Same, that cannot be a coincidence!
$endgroup$
– IllidanS4
May 30 at 22:22
1
1
$begingroup$
It's funny that I found a video just two days ago which is actually really nice and demonstrates this: Unmixing Color Machine (Ultra Laminar Reversible Flow)
$endgroup$
– halirutan♦
May 30 at 14:46
$begingroup$
It's funny that I found a video just two days ago which is actually really nice and demonstrates this: Unmixing Color Machine (Ultra Laminar Reversible Flow)
$endgroup$
– halirutan♦
May 30 at 14:46
$begingroup$
@halirutan Same, that cannot be a coincidence!
$endgroup$
– IllidanS4
May 30 at 22:22
$begingroup$
@halirutan Same, that cannot be a coincidence!
$endgroup$
– IllidanS4
May 30 at 22:22
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
color = RGBColor[0.454, 0.695, 0.875];
u1u2 = ContourPlot3D[4 == x^2 + y^2, x^2 + y^2 == 1,
x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, PlotPoints -> 20, Lighting -> "Ambient", White,
ContourStyle -> FaceForm[Opacity[0], Opacity[1, color]],
Opacity[1, LightGray]];
arrows = Graphics3D[FaceForm[Opacity[1, color]],
Polygon[Append[#, -2] & /@ CirclePoints[0, 0, 2, Pi, 100]],
Arrowheads[Large, Appearance -> "Projected"],
Arrow[0, 0, 2, #2 Cos@#, #2 Sin@#, 2 & @@@ Transpose[0, - Pi/2, 2, 1]],
Arrow[Append[Reverse@#, 3] & /@ CirclePoints[0, 0, 1, 0, 100]],
Arrow[Append[#, -3] & /@ CirclePoints[0, 0, 2, 0, 100]],
Arrowheads[.03, 1, .03, 1/3, .03, 2/3, Appearance -> "Projected"] ,
Table[Arrow[Append[#, i] & /@ CirclePoints[0, 0, 1.5, Pi, 100]],
i, Subdivide[-1, 1, 2]]];
Show[u1u2, arrows, PlotRange -> All, Boxed -> False, Axes -> False, BoxRatios -> 1, 1, 2]
answered May 30 at 9:09
kglrkglr
198k10223449
$endgroup$
add a comment |
$begingroup$
You can do this with graphics primitives. The only real problem I encountered was the size of the arrowheads. For some reason, they blow up randomly...
polygonPts =
Table[Cos[th], Sin[th], z, z, 0, 3, th, 0, Pi, Pi/50];
polygons =
MapThread[Polygon@Join[#, Reverse[#2]] &,
Partition[#, 2, 1] & /@ polygonPts];
arrowPts =
Transpose@
Table[((1 + r)/2) Cos[th], ((1 + r)/2) Sin[th], z, th, 0, 2 Pi,
Pi/50, z, 0.8, 1.6, 2.4];
cylinderOutlinePts =
Table[Cos[th], Sin[th], 3, th, 0, Pi, Pi/50];
lowerArrowPts =
Table[0.9 Cos[th], 0.9 Sin[th], -0.5, th, -Pi/2, 2 Pi - Pi/2,
Pi/50];
upperArrowPts =
Table[0.5 Cos[th], 0.5 Sin[th], 3.25, th, -Pi/2, 2 Pi - Pi/2,
Pi/50];
r = 0.6;
Graphics3D[
Line[-r, 0, 0, -r, 0, 3],
Line[r, 0, 0, r, 0, 3],
Line[-1, 0, 0, -1, 0, 3],
Line[1, 0, 0, 1, 0, 3],
Line[cylinderOutlinePts],
Arrow[lowerArrowPts],
Arrow[upperArrowPts],
Arrowheads[Automatic, 0, Automatic, 0.5,
Appearance -> "Projected"],
Arrow[arrowPts],
LightGray,
Cylinder[0, 0, 0, 0, 0, 3, r],
LightBlue,
Cylinder[0, 0, 0, 0, 0, 0.001],
EdgeForm[None],
polygons
, Lighting -> "Ambient", White, Boxed -> False]
answered May 30 at 9:58
C. E.C. E.
52.4k3102209
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
color = RGBColor[0.454, 0.695, 0.875];
u1u2 = ContourPlot3D[4 == x^2 + y^2, x^2 + y^2 == 1,
x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, PlotPoints -> 20, Lighting -> "Ambient", White,
ContourStyle -> FaceForm[Opacity[0], Opacity[1, color]],
Opacity[1, LightGray]];
arrows = Graphics3D[FaceForm[Opacity[1, color]],
Polygon[Append[#, -2] & /@ CirclePoints[0, 0, 2, Pi, 100]],
Arrowheads[Large, Appearance -> "Projected"],
Arrow[0, 0, 2, #2 Cos@#, #2 Sin@#, 2 & @@@ Transpose[0, - Pi/2, 2, 1]],
Arrow[Append[Reverse@#, 3] & /@ CirclePoints[0, 0, 1, 0, 100]],
Arrow[Append[#, -3] & /@ CirclePoints[0, 0, 2, 0, 100]],
Arrowheads[.03, 1, .03, 1/3, .03, 2/3, Appearance -> "Projected"] ,
Table[Arrow[Append[#, i] & /@ CirclePoints[0, 0, 1.5, Pi, 100]],
i, Subdivide[-1, 1, 2]]];
Show[u1u2, arrows, PlotRange -> All, Boxed -> False, Axes -> False, BoxRatios -> 1, 1, 2]
answered May 30 at 9:09
kglrkglr
198k10223449
$endgroup$
add a comment |
$begingroup$
color = RGBColor[0.454, 0.695, 0.875];
u1u2 = ContourPlot3D[4 == x^2 + y^2, x^2 + y^2 == 1,
x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, PlotPoints -> 20, Lighting -> "Ambient", White,
ContourStyle -> FaceForm[Opacity[0], Opacity[1, color]],
Opacity[1, LightGray]];
arrows = Graphics3D[FaceForm[Opacity[1, color]],
Polygon[Append[#, -2] & /@ CirclePoints[0, 0, 2, Pi, 100]],
Arrowheads[Large, Appearance -> "Projected"],
Arrow[0, 0, 2, #2 Cos@#, #2 Sin@#, 2 & @@@ Transpose[0, - Pi/2, 2, 1]],
Arrow[Append[Reverse@#, 3] & /@ CirclePoints[0, 0, 1, 0, 100]],
Arrow[Append[#, -3] & /@ CirclePoints[0, 0, 2, 0, 100]],
Arrowheads[.03, 1, .03, 1/3, .03, 2/3, Appearance -> "Projected"] ,
Table[Arrow[Append[#, i] & /@ CirclePoints[0, 0, 1.5, Pi, 100]],
i, Subdivide[-1, 1, 2]]];
Show[u1u2, arrows, PlotRange -> All, Boxed -> False, Axes -> False, BoxRatios -> 1, 1, 2]
answered May 30 at 9:09
kglrkglr
198k10223449
$endgroup$
add a comment |
$begingroup$
color = RGBColor[0.454, 0.695, 0.875];
u1u2 = ContourPlot3D[4 == x^2 + y^2, x^2 + y^2 == 1,
x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, PlotPoints -> 20, Lighting -> "Ambient", White,
ContourStyle -> FaceForm[Opacity[0], Opacity[1, color]],
Opacity[1, LightGray]];
arrows = Graphics3D[FaceForm[Opacity[1, color]],
Polygon[Append[#, -2] & /@ CirclePoints[0, 0, 2, Pi, 100]],
Arrowheads[Large, Appearance -> "Projected"],
Arrow[0, 0, 2, #2 Cos@#, #2 Sin@#, 2 & @@@ Transpose[0, - Pi/2, 2, 1]],
Arrow[Append[Reverse@#, 3] & /@ CirclePoints[0, 0, 1, 0, 100]],
Arrow[Append[#, -3] & /@ CirclePoints[0, 0, 2, 0, 100]],
Arrowheads[.03, 1, .03, 1/3, .03, 2/3, Appearance -> "Projected"] ,
Table[Arrow[Append[#, i] & /@ CirclePoints[0, 0, 1.5, Pi, 100]],
i, Subdivide[-1, 1, 2]]];
Show[u1u2, arrows, PlotRange -> All, Boxed -> False, Axes -> False, BoxRatios -> 1, 1, 2]
answered May 30 at 9:09
kglrkglr
198k10223449
$endgroup$
color = RGBColor[0.454, 0.695, 0.875];
u1u2 = ContourPlot3D[4 == x^2 + y^2, x^2 + y^2 == 1,
x, -3, 3, y, -3, 3, z, -2, 2,
Mesh -> None, PlotPoints -> 20, Lighting -> "Ambient", White,
ContourStyle -> FaceForm[Opacity[0], Opacity[1, color]],
Opacity[1, LightGray]];
arrows = Graphics3D[FaceForm[Opacity[1, color]],
Polygon[Append[#, -2] & /@ CirclePoints[0, 0, 2, Pi, 100]],
Arrowheads[Large, Appearance -> "Projected"],
Arrow[0, 0, 2, #2 Cos@#, #2 Sin@#, 2 & @@@ Transpose[0, - Pi/2, 2, 1]],
Arrow[Append[Reverse@#, 3] & /@ CirclePoints[0, 0, 1, 0, 100]],
Arrow[Append[#, -3] & /@ CirclePoints[0, 0, 2, 0, 100]],
Arrowheads[.03, 1, .03, 1/3, .03, 2/3, Appearance -> "Projected"] ,
Table[Arrow[Append[#, i] & /@ CirclePoints[0, 0, 1.5, Pi, 100]],
i, Subdivide[-1, 1, 2]]];
Show[u1u2, arrows, PlotRange -> All, Boxed -> False, Axes -> False, BoxRatios -> 1, 1, 2]
answered May 30 at 9:09
kglrkglr
198k10223449
edited May 30 at 13:19
answered May 30 at 9:09
kglrkglr
198k10223449
answered May 30 at 9:09
kglrkglr
198k10223449
answered May 30 at 9:09
kglrkglr
198k10223449
198k10223449
add a comment |
add a comment |
$begingroup$
You can do this with graphics primitives. The only real problem I encountered was the size of the arrowheads. For some reason, they blow up randomly...
polygonPts =
Table[Cos[th], Sin[th], z, z, 0, 3, th, 0, Pi, Pi/50];
polygons =
MapThread[Polygon@Join[#, Reverse[#2]] &,
Partition[#, 2, 1] & /@ polygonPts];
arrowPts =
Transpose@
Table[((1 + r)/2) Cos[th], ((1 + r)/2) Sin[th], z, th, 0, 2 Pi,
Pi/50, z, 0.8, 1.6, 2.4];
cylinderOutlinePts =
Table[Cos[th], Sin[th], 3, th, 0, Pi, Pi/50];
lowerArrowPts =
Table[0.9 Cos[th], 0.9 Sin[th], -0.5, th, -Pi/2, 2 Pi - Pi/2,
Pi/50];
upperArrowPts =
Table[0.5 Cos[th], 0.5 Sin[th], 3.25, th, -Pi/2, 2 Pi - Pi/2,
Pi/50];
r = 0.6;
Graphics3D[
Line[-r, 0, 0, -r, 0, 3],
Line[r, 0, 0, r, 0, 3],
Line[-1, 0, 0, -1, 0, 3],
Line[1, 0, 0, 1, 0, 3],
Line[cylinderOutlinePts],
Arrow[lowerArrowPts],
Arrow[upperArrowPts],
Arrowheads[Automatic, 0, Automatic, 0.5,
Appearance -> "Projected"],
Arrow[arrowPts],
LightGray,
Cylinder[0, 0, 0, 0, 0, 3, r],
LightBlue,
Cylinder[0, 0, 0, 0, 0, 0.001],
EdgeForm[None],
polygons
, Lighting -> "Ambient", White, Boxed -> False]
answered May 30 at 9:58
C. E.C. E.
52.4k3102209
$endgroup$
add a comment |
$begingroup$
You can do this with graphics primitives. The only real problem I encountered was the size of the arrowheads. For some reason, they blow up randomly...
polygonPts =
Table[Cos[th], Sin[th], z, z, 0, 3, th, 0, Pi, Pi/50];
polygons =
MapThread[Polygon@Join[#, Reverse[#2]] &,
Partition[#, 2, 1] & /@ polygonPts];
arrowPts =
Transpose@
Table[((1 + r)/2) Cos[th], ((1 + r)/2) Sin[th], z, th, 0, 2 Pi,
Pi/50, z, 0.8, 1.6, 2.4];
cylinderOutlinePts =
Table[Cos[th], Sin[th], 3, th, 0, Pi, Pi/50];
lowerArrowPts =
Table[0.9 Cos[th], 0.9 Sin[th], -0.5, th, -Pi/2, 2 Pi - Pi/2,
Pi/50];
upperArrowPts =
Table[0.5 Cos[th], 0.5 Sin[th], 3.25, th, -Pi/2, 2 Pi - Pi/2,
Pi/50];
r = 0.6;
Graphics3D[
Line[-r, 0, 0, -r, 0, 3],
Line[r, 0, 0, r, 0, 3],
Line[-1, 0, 0, -1, 0, 3],
Line[1, 0, 0, 1, 0, 3],
Line[cylinderOutlinePts],
Arrow[lowerArrowPts],
Arrow[upperArrowPts],
Arrowheads[Automatic, 0, Automatic, 0.5,
Appearance -> "Projected"],
Arrow[arrowPts],
LightGray,
Cylinder[0, 0, 0, 0, 0, 3, r],
LightBlue,
Cylinder[0, 0, 0, 0, 0, 0.001],
EdgeForm[None],
polygons
, Lighting -> "Ambient", White, Boxed -> False]
answered May 30 at 9:58
C. E.C. E.
52.4k3102209
$endgroup$
add a comment |
$begingroup$
You can do this with graphics primitives. The only real problem I encountered was the size of the arrowheads. For some reason, they blow up randomly...
polygonPts =
Table[Cos[th], Sin[th], z, z, 0, 3, th, 0, Pi, Pi/50];
polygons =
MapThread[Polygon@Join[#, Reverse[#2]] &,
Partition[#, 2, 1] & /@ polygonPts];
arrowPts =
Transpose@
Table[((1 + r)/2) Cos[th], ((1 + r)/2) Sin[th], z, th, 0, 2 Pi,
Pi/50, z, 0.8, 1.6, 2.4];
cylinderOutlinePts =
Table[Cos[th], Sin[th], 3, th, 0, Pi, Pi/50];
lowerArrowPts =
Table[0.9 Cos[th], 0.9 Sin[th], -0.5, th, -Pi/2, 2 Pi - Pi/2,
Pi/50];
upperArrowPts =
Table[0.5 Cos[th], 0.5 Sin[th], 3.25, th, -Pi/2, 2 Pi - Pi/2,
Pi/50];
r = 0.6;
Graphics3D[
Line[-r, 0, 0, -r, 0, 3],
Line[r, 0, 0, r, 0, 3],
Line[-1, 0, 0, -1, 0, 3],
Line[1, 0, 0, 1, 0, 3],
Line[cylinderOutlinePts],
Arrow[lowerArrowPts],
Arrow[upperArrowPts],
Arrowheads[Automatic, 0, Automatic, 0.5,
Appearance -> "Projected"],
Arrow[arrowPts],
LightGray,
Cylinder[0, 0, 0, 0, 0, 3, r],
LightBlue,
Cylinder[0, 0, 0, 0, 0, 0.001],
EdgeForm[None],
polygons
, Lighting -> "Ambient", White, Boxed -> False]
answered May 30 at 9:58
C. E.C. E.
52.4k3102209
$endgroup$
You can do this with graphics primitives. The only real problem I encountered was the size of the arrowheads. For some reason, they blow up randomly...
polygonPts =
Table[Cos[th], Sin[th], z, z, 0, 3, th, 0, Pi, Pi/50];
polygons =
MapThread[Polygon@Join[#, Reverse[#2]] &,
Partition[#, 2, 1] & /@ polygonPts];
arrowPts =
Transpose@
Table[((1 + r)/2) Cos[th], ((1 + r)/2) Sin[th], z, th, 0, 2 Pi,
Pi/50, z, 0.8, 1.6, 2.4];
cylinderOutlinePts =
Table[Cos[th], Sin[th], 3, th, 0, Pi, Pi/50];
lowerArrowPts =
Table[0.9 Cos[th], 0.9 Sin[th], -0.5, th, -Pi/2, 2 Pi - Pi/2,
Pi/50];
upperArrowPts =
Table[0.5 Cos[th], 0.5 Sin[th], 3.25, th, -Pi/2, 2 Pi - Pi/2,
Pi/50];
r = 0.6;
Graphics3D[
Line[-r, 0, 0, -r, 0, 3],
Line[r, 0, 0, r, 0, 3],
Line[-1, 0, 0, -1, 0, 3],
Line[1, 0, 0, 1, 0, 3],
Line[cylinderOutlinePts],
Arrow[lowerArrowPts],
Arrow[upperArrowPts],
Arrowheads[Automatic, 0, Automatic, 0.5,
Appearance -> "Projected"],
Arrow[arrowPts],
LightGray,
Cylinder[0, 0, 0, 0, 0, 3, r],
LightBlue,
Cylinder[0, 0, 0, 0, 0, 0.001],
EdgeForm[None],
polygons
, Lighting -> "Ambient", White, Boxed -> False]
answered May 30 at 9:58
C. E.C. E.
52.4k3102209
edited May 30 at 12:00
answered May 30 at 9:58
C. E.C. E.
52.4k3102209
answered May 30 at 9:58
C. E.C. E.
52.4k3102209
answered May 30 at 9:58
C. E.C. E.
52.4k3102209
52.4k3102209
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1
$begingroup$
It's funny that I found a video just two days ago which is actually really nice and demonstrates this: Unmixing Color Machine (Ultra Laminar Reversible Flow)
$endgroup$
– halirutan♦
May 30 at 14:46
$begingroup$
@halirutan Same, that cannot be a coincidence!
$endgroup$
– IllidanS4
May 30 at 22:22