---
jupyter:
  description: 'A slip-on pipe flange as a 3D CAD exercise: a dimensioned drawing with a full section to model in
    planex2d or any CAD system, a solution from a half section revolved and a circular pattern of bolt holes, and the
    exact volume, mass and center of mass to check a model against.'
---

# Pipe flange

A slip-on flange is pushed over the end of a pipe and welded to it, so that the pipe can be bolted to a valve or to the
next pipe. It is a turned part, a plate with a hub at the back and a raised face at the front, which takes the gasket,
revolved about the pipe's axis. The bolt holes are a circular pattern through the plate. Model the flange from the
drawing in planex2d or in any CAD system, then check its volume, mass and center of mass against the values at the end
of the page. A solution in planex2d follows.

![The pipe flange exercise: a dimensioned drawing of a slip-on flange with a hub, a raised face and four bolt holes, in a full section, a view onto the raised face and an isometric](../_static/gallery/pipe-flange.png){.result}

```python
import math
import netgen.occ as occ
import planex as px
```

```python nbsphinx="hidden"
from docs_figures import Row, Views
```

## The half section

The half section is sketched in the front plane, the plane with its normal toward the viewer, $-y$, with $x$ out from
the axis, $z$ along it and the origin on the axis at the hub's end. The outline runs out along the hub's end, up the
hub, out along the plate's back, up its rim, in along its front, up the raised face and in to the bore. Every line is
horizontal or vertical, and with the auto-constraint dict for level and plumb lines it stays so. The bore is 49 across,
for a pipe of 48.3. The hub is 70 across and 12 long, the plate 130 across and 16 thick, and the raised face 78 across
and 2 high, clear of the bolt holes (Figure 1):

```python
front = px.XZ
half = px.Sketch(front, auto_constraint={"horizontal": True, "vertical": True})
half.Move((24.5, 0)).Line(10.5, id="hub_end")
half.Turn(90).Line(12, id="hub")  # Turn(90) turns the pen left, Turn(-90) right
half.Turn(-90).Line(30, id="plate_back")
half.Turn(90).Line(16, id="rim")
half.Turn(90).Line(26, id="plate_front")
half.Turn(-90).Line(2, id="raised_side")
half.Turn(90).Line(14.5, id="raised_face")
half.Close(id="bore")
half.Constrain("hub_end.start", "H", px.Coincident)
half.Constrain("bore", "V", px.Distance, 49 / 2, id="bore_r")  # from the axis: half the diameter
half.Constrain("hub", "V", px.Distance, 70 / 2, id="hub_r")
half.Constrain("rim", "V", px.Distance, 130 / 2, id="plate_r")
half.Constrain("raised_side", "V", px.Distance, 78 / 2, id="raised_r")
half.Constrain("hub", px.Distance, 12, id="hub_l")
half.Constrain("rim", px.Distance, 16, id="plate_t")
half.Constrain("raised_side", px.Distance, 2, id="raised_h")
print("status", half.status, "| degrees of freedom", half.dof)
```

```python nbsphinx="hide-input"
Row((half, "Every dimension and tie of the half section", {"constraints": True}), caption="The half section")
```

The section's face, taken to OpenCASCADE with `ToOCCFace`, is revolved a full turn about the $z$ axis (Figure 2):

```python
flange = half.Face().ToOCCFace().Revolve(occ.Axis((0, 0, 0), occ.Z), 360)
```

```python nbsphinx="hide-input"
Views(("The half section revolved", [(flange, "shade"), (flange, "ink")]), angles=(-60, 0, 30), caption="The flange")
```

## The bolt holes

The four bolt holes of 18 lie on a bolt circle of 100, between the axes. The first one lies at 45°, where its center's
$h$ and $v$ are equal, which `Expression` states, and `CircularPattern` repeats it 90° apart. They are sketched on the
plate's front, the xy plane lifted to 28, and pocketed 16 down through the plate (Figure 3):

```python
holes = px.Sketch(px.Plane(px.XY, 28), auto_constraint=True)
holes.Circle(100 / 2, id="bolt_circle", construction=True)
holes.Constrain("bolt_circle.center", "origin", px.Coincident)
holes.Constrain("bolt_circle", px.Diameter, 100, id="bolt_circle_d")
holes.Circle(18 / 2, center=(36, 34), id="hole")
holes.Constrain("hole.center", "bolt_circle", px.Coincident)  # a point on a circle
holes.Expression("hole.center.h = hole.center.v", id="at_45")  # the first hole at 45°
holes.Constrain("hole", px.Diameter, 18, id="hole_d")
holes.CircularPattern(["hole"], "origin", 4, id="pattern")
print("status", holes.status, "| degrees of freedom", holes.dof)
flange = px.Pocket(flange, holes, 16)
```

```python nbsphinx="hide-input"
Row((holes, "The bolt holes on the plate's front", {"plot": {"show_parent": flange, "show_constraints": True}}),
    (flange, "Four holes through the plate", {"views": [(flange, "shade"), (flange, "ink")], "angles": (-60, 0, 30)}),
    caption="The bolt holes")
```

## The checks

These are the volume, the mass in steel P250GH (7.85 g/cm³) and the center of mass, with the origin on the axis at the
hub's end, to compare with your own model. The flange is three rings, each $\pi\,(R^2 - r^2)$ times its length around
the bore of 24.5, less the four holes through the plate. It is symmetric about its axis, so its center of mass lies on
it, at the height where the moments of the rings and the holes balance:

```python
parts = [(math.pi * (35**2 - 24.5**2) * 12, 6), (math.pi * (65**2 - 24.5**2) * 16, 20),
         (math.pi * (39**2 - 24.5**2) * 2, 29), (-4 * math.pi * 9**2 * 16, 20)]  # (volume, height of its middle)
exact = sum(v for v, z in parts)
c = flange.center
print("volume", round(flange.mass, 1), "mm³, exact", round(exact, 1))
print("mass", round(flange.mass * 7.85e-6, 4), "kg")
print("center of mass", round(c.z, 4), "above the hub's end, exact", round(sum(v * z for v, z in parts) / exact, 4),
      "| off the axis by", round(math.hypot(c.x, c.y), 6))
```

The flange as STEP, for another CAD system:

```python
flange.WriteStep("pipe_flange.step")
```

The flange as STEP: [pipe_flange.step](pipe_flange.step)

```python nbsphinx="hidden"
import sys
sys.path.insert(0, "..")
import matplotlib.pyplot as plt
from drawings import LANDSCAPE, Pictorial, SheetFigure, View
from gallery import save_figure

# first angle: the full section through the plane y = 0 in front (the part behind it seen from the front, its cut faces
# hatched), the view from above onto the raised face below it
behind = flange * occ.Box((-70, 0, -1), (70, 70, 31))
cut = [f for f in behind.faces if abs(f.center.y) < 1e-6 and f.bounding_box[1].y - f.bounding_box[0].y < 1e-6]
section = View([], solid=behind, plane=front, hidden_edges=False, hatch=cut, axes=[((0, -4), (0, 34))],
               measures=[((-65, 12), (65, 12), -24, "⌀130"), ((-35, 0), (35, 0), -12, "⌀70"),
                         ((-24.5, 30), (24.5, 30), 36, "⌀49"), ((-39, 30), (39, 30), 44, "⌀78"),
                         ((65, 0), (65, 12), 74, 12), ((65, 12), (65, 28), 74, 16), ((39, 0), (39, 30), 86, 30)])
top = View([(holes, {"bolt_circle_d": (120, "leader"), "hole_d": (45, "leader", 4)}, {"bolt_circle": "pitch"})],
           solid=flange, plane=px.XY, at=(0, -105), hidden_edges=False,
           axes=[((-70, 0), (70, 0)), ((0, -70), (0, 70))])
pictorial = Pictorial(flange, at=(125, -40), width=70, angles=(-60, 0, 30))
drawing = SheetFigure([section, top, pictorial], margin=16, notes=("planex2d.org", "3D exercise 27"), first_angle=True,
                      sheet=LANDSCAPE)
print("scale", drawing.planex_scale, "| paper", [round(v * 25.4) for v in drawing.get_size_inches()], "mm")
save_figure(drawing, "pipe-flange", dpi=200)
plt.close(drawing)
```