Pressure Vessel Simulator

このコンテンツはまだ日本語訳がありません。

Modified: Jun. 9, 2026

Published: Jun. 5, 2026

A pressurized cylinder carries two different stresses at once: a hoop stress around the circumference and a longitudinal stress along the axis, and the hoop stress is always exactly twice the longitudinal stress. That ratio is why a cylinder under pressure splits lengthwise rather than across, and it is the fact that governs every wall-thickness calculation. Too thin and the vessel yields; too thick and material is wasted. This simulator puts a 3D cylinder or sphere in your browser, ramps the internal pressure, and shows both stresses building on the wall in real time. Orbit the vessel, watch the color field shift with the von Mises stress, read the safety factor and required wall thickness, and check whether thin-wall theory even applies to your geometry. #PressureVessel #ThinWallStress #SolidMechanics

Open Simulator

What You Can Analyze

Hoop and longitudinal stress

Watch the hoop stress and the longitudinal stress build with pressure, and see the 2:1 ratio between them at every point in the sweep. For a sphere the two stresses are equal, so there is no preferred failure direction.

Cylinder vs sphere

Switch between vessel types and see how the stress state changes. A sphere carries the same membrane stress in every direction; a cylinder does not, and wall sizing follows the governing hoop stress.

Wall-thickness sizing

Read the minimum wall thickness required for a safety factor of one, compare it to your current wall, and get an immediate adequate or too-thin verdict. The r/t chart shows where thin-wall theory holds and where it breaks down.

Failure check

The von Mises equivalent stress is computed from the biaxial wall state and compared to the material yield strength. The safety factor and a Safe or Yields verdict update every time you drag a parameter.

Key Features

3D vessel with stress color field The cylinder or sphere renders in Three.js with the wall colored by von Mises stress. The hoop band is visually bolder than the longitudinal band, reflecting the 2:1 ratio. Drag to orbit, scroll to zoom.
Play to ramp pressure Press Pressurize and the internal pressure climbs from zero to the set value. A teal playhead tracks the operating point across every chart in real time.
Live stress and safety readouts Hoop stress, longitudinal stress, von Mises equivalent, maximum shear, safety factor, and a thin-wall validity flag all update as you drag any slider.
Four analysis charts in two tab groups The Stresses group shows stress versus pressure and stress versus wall thickness. The Sizing group shows required wall thickness versus pressure and the r/t validity ratio versus thickness. Each chart exports as PNG.
Five vessel presets Compressed-air tank, steam boiler, scuba cylinder, gas pipeline, and spherical storage tank, each a realistic starting point with real-world dimensions and material properties.
A/B vessel comparison Save the current vessel as Vessel A, change geometry or pressure, and overlay both datasets on every chart to compare two designs directly.
Downloadable resources A lab report with watermark-free vessel diagram and all four charts, a CSV dataset of stresses and required thickness across the pressure range, and a design-data package with a PNG and a pressurization video.

Preset Vessel Configurations

Preset	Vessel	p (MPa)	d (mm)	t (mm)	L (mm)	Yield (MPa)	Represents
Compressed-air tank	Cylinder	1.0	400	4	1200	250	Workshop or industrial air receiver
Steam boiler	Cylinder	2.0	1500	12	3000	250	Low-pressure steam drum
Scuba cylinder	Cylinder	23	170	6	600	500	High-pressure diving cylinder
Gas pipeline	Cylinder	8	600	10	4000	360	Medium-pressure transmission pipe
Spherical tank	Sphere	3	2000	15	2000	300	Large-volume storage sphere

Equations

Wall stresses for a thin-walled cylinder (hoop is twice longitudinal):

Hoop stress:         sh = p * r / t
Longitudinal stress: sl = p * r / (2 * t)

Wall stresses for a thin-walled sphere (equal membrane stress in all directions):

sh = sl = p * r / (2 * t)

Von Mises equivalent stress for the biaxial wall state (s3 = 0, thin wall):

svm = sqrt( sh^2 - sh*sl + sl^2 )

Maximum shear stress (absolute, versus the zero through-thickness principal):

tmax = max(sh, sl) / 2

Safety factor and failure verdict:

safety factor = yield / svm
yields when svm >= yield

Required wall thickness for a safety factor of one:

Cylinder: treq = sqrt(0.75) * p * r / yield
Sphere:   treq = 0.5 * p * r / yield

Thin-wall validity (theory assumes the ratio is at least 10):

r / t >= 10   (thin-wall theory applies)
r / t < 10    (thick-wall correction needed)

Guided Experiments

Work through the Pressure Vessel Experiments lesson for structured, Python-verified exercises that pair directly with this simulator:

Pressure Vessel Experiments: the hands-on lab lesson that pairs with this simulator.
Thin-Walled Pressure Vessels: the lesson that owns the underlying theory.
Solid Mechanics Analyzer: the full suite of stress-analysis simulators.
Axial Loading Simulator: normal stress and elongation in bars and stepped members.
Thermal Stress Simulator: temperature-driven stress in constrained members.

Comments

Loading comments...