This partial calculator reports a nominal thin-wall OD-based hoop-stress benchmark, diameter/thickness ratio, clear-gap/OD ratio, and selected outside tube area per axial foot. It visibly flags selections whose inner-radius/thickness ratio is below 10. It is not a Stevens boiler design or allowable-pressure calculation.
Stevens Boiler - Selected Tube Benchmark
Explore a selected tube's nominal membrane benchmark, slenderness, spacing and outside-area arithmetic.
Equation Used
- Pressure is an entered gauge-pressure difference.
- The stress value is an OD-based nominal thin-wall benchmark, not an allowable stress.
- Thin-wall status requires the selected inner-radius/thickness ratio to be at least 10.
- Outside area is geometric lateral area for one axial foot only.
- Material, temperature, joints, headers, corrosion, code rules and safety are excluded.
The secondary figure uses a common scale for the entered tube OD, wall and clear gap and flags the thin-wall condition.
Selected tube benchmark
The nominal benchmark uses sigma=P D/(2t) with entered outside diameter as the stated diameter approximation. D/t identifies slenderness. The gap ratio is g/D. Outside lateral area for one axial foot is N pi D times 12 inches, divided by 144 square inches per square foot.
What the calculator determines
Use it to inspect selected tube arithmetic and whether the common introductory thin-wall condition r_i/t at least 10 is met. The cross-section figure uses the entered OD, wall and gap on one common scale.
Selected relationships
sigma_nom=P D/(2t); D/t=D/t; g/D=g/D; A_out=N pi D (12)/144.
Selected-input example
At 50 psi, 1 inch OD, 0.065 inch wall, 1 inch clear gap and 50 tubes, the OD-based nominal benchmark is 384.615 psi, D/t is 15.385, gap/OD is 1, and selected outside area is 13.09 square feet per axial foot. The inner r/t is only 6.692, so thin-wall use is flagged.
Not a pressure-vessel design
Actual inside or mean diameter convention, headers, ligaments, joints, material allowable stress, temperature, corrosion allowance, manufacturing tolerance, external loads, thermal stress, buckling, code factors, inspection and safety are excluded.
Questions
Is the benchmark an allowable stress or pressure?
No. It is only the elementary membrane expression evaluated with the entered OD approximation.
Why is there a thin-wall warning?
University of Illinois mechanics notes limit the introductory approximation to inner-radius/thickness ratios of at least 10. Several allowed input combinations do not meet that condition.
Is outside area heat-transfer area?
No. It is geometric outside lateral area only; fouling, fins, contact, coefficients and temperature differences are absent.
Authoritative references
- University of Illinois Introductory Solid Mechanics: Pressure Vessels — derives cylindrical thin-wall hoop stress and states the r/t applicability condition.
- Purdue Engineering: Measurement Uncertainty Reading — uses the thin-walled cylindrical hoop-stress estimate with pressure, diameter and thickness.
- NIST Guide to the SI, Appendix B.8 — gives the exact inch conversion used in unit documentation.
References & Further Reading
- Wikipedia contributors. Water-tube boiler. Wikipedia
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