Thickness/Diameter Ratio (Thin Wall)
Calculate a pressure vessel's thickness/diameter ratio, t/D, from the wall thickness t and the diameter D (same unit). This ratio is the criterion deciding whether a vessel can be treated as THIN-walled or needs THICK-walled (Lamé) theory. The distinction is fundamental because the formulas change: in THIN walls (rule of thumb t/D < 0.05, or t/r < 0.1), stress is practically UNIFORM across the thickness, and the simple membrane formulas hold (σ = P·r/t for hoop) — the case of the vast majority of vessels, pipes and tanks. In THICK walls (larger t/D, as in very-high-pressure vessels — hydrogenation reactors, gun barrels, high-pressure hydraulic tubing), stress VARIES strongly across the thickness (maximum at the inner surface, decreasing outward), and the simple formulas dangerously underestimate the inner peak stress — Lamé's equations must be used. Checking the t/D ratio is thus the first step in choosing the correct calculation theory. Vessels with t/D above ~0.1 require thick-wall analysis. This simple check avoids the serious error of applying thin-wall formulas to a thick vessel. Enter the thickness and the diameter.
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Relação espessura/diâmetro (parede fina)
A relação espessura/diâmetro de um vaso de pressão é t/D, a partir da espessura da parede t e do diâmetro D (na mesma unidade). Essa relação é o critério que determina se um vaso pode ser tratado como de parede fina (thin-walled) ou se precisa da teoria de parede espessa (thick-walled, de Lamé). A distinção é fundamental porque as fórmulas mudam: na parede fina (regra prática t/D < 0,05, ou t/r < 0,1), a tensão é praticamente uniforme ao longo da espessura, e valem as fórmulas simples de membrana (σ = P·r/t para hoop) — é o caso da grande maioria dos vasos, tubos e tanques. Na parede espessa (t/D maior, como em vasos de altíssima pressão — reatores de hidrogenação, canhões, tubulações hidráulicas), a tensão varia fortemente ao longo da espessura (máxima na superfície interna, decrescendo para fora), e as fórmulas simples subestimam perigosamente a tensão de pico interna — é preciso usar as equações de Lamé. Verificar a relação t/D é, portanto, o primeiro passo para escolher a teoria correta de cálculo. Vasos com t/D acima de ~0,1 exigem análise de parede espessa. Esta verificação simples evita o erro grave de aplicar fórmulas de parede fina a um vaso espesso. Informe a espessura e o diâmetro.
Related Tools
Thickness with Corrosion Allowance
Calculate the total thickness to specify for a pressure-vessel component including the corrosion allowance, t_total = t_calculated + CA, from the minimum pressure-calculated thickness t_calculated (mm) and the corrosion allowance CA (mm). The thickness from the ASME formulas is the MINIMUM needed to resist pressure — but the vessel will operate for DECADES, and corrosion (and erosion) will consume wall material over time. If the vessel were made exactly at the minimum thickness, the first corrosion would already leave it below safe. So a CORROSION ALLOWANCE (CA) is added — a 'sacrificial' over-thickness, typically 1.5 to 6 mm, sized for the expected corrosion rate times the design life (e.g., 0.1 mm/year × 25 years = 2.5 mm). Thus the thickness specified for fabrication is the structural minimum plus the corrosion allowance. Over life, inspection (by ultrasound) measures the REMAINING thickness; when corrosion consumes the whole allowance and the thickness approaches the structural minimum, the vessel must be repaired or retired. The corrosion allowance is like a 'life reserve' built into the wall. Enter the calculated thickness and the corrosion allowance.
Cylindrical Shell Thickness (ASME)
Calculate the minimum wall thickness of a pressure-vessel cylindrical shell by the ASME Section VIII Division 1 formula, t = (P·r) ÷ (S·E − 0.6·P), from the internal design pressure P (MPa), the internal radius r (mm), the material allowable stress S (MPa) and the welded-joint efficiency E (0-1). The pressure vessel — used in boilers, chemical reactors, heat exchangers, compressed-air and LPG tanks, autoclaves — is a CRITICAL safety component: a failure under pressure can be explosive and catastrophic. So its design is rigorously codified, the ASME BPVC (Boiler and Pressure Vessel Code) being the world's most used. This formula gives the minimum cylindrical-shell thickness to safely resist the circumferential (hoop) stress. The '−0.6·P' term refines the thin-wall formula for moderately thick walls. The joint efficiency E (0.70 to 1.0, per weld type and radiographic-inspection degree) penalizes strength at the welded region — fully radiographed welds have E=1.0, uninspected welds lower E. The corrosion allowance is added to the calculated thickness. This is the central pressure-vessel design calculation, and underestimating is inadmissible. Enter the design pressure, internal radius, allowable stress and joint efficiency.
Torispherical Head Thickness (ASME)
Calculate the minimum thickness of a torispherical (standard flanged-and-dished) pressure-vessel head, t = (0.885·P·L) ÷ (S·E − 0.1·P), from the internal pressure P (MPa), the spherical crown radius L (mm), the allowable stress S (MPa) and the joint efficiency E. The TORISPHERICAL head is the most COMMON and economical head type in medium-pressure vessels (and universal in shallow tanks): it combines a central spherical crown (radius L) with a toroidal knuckle transition at the edge, joining the cylindrical shell — a form easier and cheaper to stamp than the hemispherical, and more compact (lower height). The 0.885 factor and formula hold for the standard ASME geometry with L ≈ D (crown radius equal to diameter) and the knuckle radius of 6% of the diameter. The price of the economy is a GREATER thickness than the hemispherical (the toroidal transition concentrates stress) and a critical knuckle region, where high bending stresses can arise. The torispherical head is the practical 'middle ground' between the costly hemispherical and the flat (which needs enormous thicknesses). This formula is essential in designing vessels with this head type. Enter the pressure, crown radius, allowable stress and joint efficiency.
Hemispherical Head Thickness (ASME)
Calculate the minimum thickness of a pressure-vessel hemispherical head by the ASME Section VIII formula, t = (P·r) ÷ (2·S·E − 0.2·P), from the internal pressure P (MPa), internal radius r (mm), allowable stress S (MPa) and joint efficiency E. Heads close the ends of a pressure vessel's cylindrical shell, and their shape is decisive for structural efficiency. The HEMISPHERICAL (half-sphere) head is the MOST EFFICIENT of all: since the sphere distributes pressure equally in all directions (uniform membrane stress), the hemispherical head needs only about HALF the thickness of the cylindrical shell of the same radius and pressure (compare the '2·S·E' in the denominator with the shell's 'S·E'). So it is the choice for high-pressure vessels. The drawbacks are costlier fabrication and greater height (more space). For moderate pressures and costs, elliptical (2:1) or torispherical heads, intermediate, are used. The head-type choice is a trade-off among thickness/material (cost), space and fabrication ease. This formula is fundamental in the complete vessel design, combining shell and heads. Enter the pressure, internal radius, allowable stress and joint efficiency.
Vessel Head Axial Force
Calculate the total axial force the internal pressure exerts on a pressure vessel's cover (or head), F = P · (π·D²/4), from the internal pressure P (MPa) and the internal diameter D (mm); the result is in N. A vessel's internal pressure acts on the ENTIRE internal surface, and on the cover (or closure flange) it generates an axial force tending to PUSH the cover outward — equal to pressure times the cross-sectional area. This force can be ENORMOUS: a modest 1 MPa (10 bar) pressure in a 1-metre-diameter vessel generates a force of nearly 800 kN (80 tonnes!) trying to blow off the cover. This force is what the closure-flange BOLTS (or the head weld) must resist — so flanged pressure vessels have many robust bolts, and computing this force is the starting point of sizing the flange, bolts and gasket. The force also explains why one must NEVER open a still-pressurized vessel: the cover can be hurled with lethal force (serious accidents happen this way, especially with autoclaves and filters). Knowing the cover force is essential for safe closure design and operating procedures. Enter the internal pressure and the diameter.
Vessel Allowable Stress (ASME)
Calculate the design allowable stress of a pressure-vessel material by the ASME criterion, S = σ_uts ÷ n, from the material minimum tensile strength σ_uts (MPa) and the safety factor n (3.5 in the current ASME VIII Div. 1 edition for tensile strength). The allowable stress S is the MAXIMUM stress permitted in the vessel material in service, and is the basis of all thickness and MAWP calculations — it embeds the safety margin against failure. The ASME code sets the allowable stress as the SMALLEST among several criteria: a fraction of the TENSILE strength (σ_uts/3.5 in the current edition — formerly /4.0, reduced as materials and inspection advanced), a fraction of the YIELD strength (2/3 of σ_yield), and, at high temperatures, criteria based on CREEP and creep rupture (since at high temperature the material deforms slowly under constant load). For each material and temperature, the code TABULATES the S value — this formula shows the tensile-strength criterion, often governing at moderate temperatures. Using the correct allowable stress (from the code, for the right material and temperature) is absolutely essential: it is the safety margin protecting against vessel explosion. Enter the tensile strength and the safety factor.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.