Nozzle Design

Updated: 2016-12-20th MCT

The ASME nozzle area replacement rules cannot be taken on their own. The sample vessel below is not modeled after a real vessel. Instead it is a collection of difficult to design features and obscure code requirements: large nozzles, swing bolt covers, cone discontinuities, use of bark stock for nozzles (code case 2148) and the use of sanitary ferrules in vessels. ASME code book rules outline how one can cut a hole in a vessel as long as the nozzle attached to it replaces the lost area. Below you will find guidance on code rules and issues surrounding the attachment of round and non-round nozzles to the vessel

Quick links (to topics on this page)

Designing Trouble-free Large Obround Nozzles

PVE-11110 Ben Vanderloo and Laurence Brundrett July 2017

Treater vessels separate oil, water and solids from an oil well. A firetube heats the liquid mixture lowering the viscosity allowing better gravity separation of the oil.   Horizontal treater vessels locate one or more firetubes in the head.  Vertical vessels locate it in the shell.  Either way a large opening is cut into the vessel to provide removable access for the firetube.

Fig 1 – Flanged obround nozzle with firetube and gasket

Large obround nozzles like those used on treater vessels can be a regular source of field trouble. The nozzle and flange can be subject to high stresses and deflections that interfere with adequate gasket seating.  This can show up as a flange that cannot be kept leak free without difficulty. 

The design of an ASME compliant obround nozzle is a combination of many mandatory inter-relating code passages.  In our practice we are regularly asked to redesign obround nozzles that either do not meet all the required code rules, or do but still leak. To be certain our obround nozzles will be trouble free we first make sure that all applicable code rules are met.  Second we use Finite Element Analysis (FEA) to check for excess stresses, flange rotation and displacement. This combination has helped us design reliable firetube nozzles. 

This article follows the design of a sample firetube nozzle through first the code design and then the FEA stages.  The specifications:

  • Materials: SA-516 70 for plate, SA-106 Gr B for pipe and SA-193 B7 for bolting
  • 100% RT is assumed (all weld efficiencies are 1.00).  
  • 72″ vessel outside diameter with a 2:1 semi elliptical head
  • 14″ firetube in a 16 x 32″ opening with a full face gasket
  • Operating conditions: 125 psi at 500°F
  • 0″ corrosion allowance
  • Design to ASME VIII-1 code rules where available

This is typical for firetube vessels we design.  Click for the full Code Calculations set.  The calculations are discussed below.

Semi Elliptical Head

Typically 2:1 semi elliptical heads are used on treater vessels.  As calculated:

  • 72″ outside diameter
  • 2:1 ratio
  • 0.224 calculated required thickness
  • 0.390 specified minimum thickness after forming (MAF)
  • (see calculations page 3)

The difference between the required thickness (0.224″) and the specified thickness (0.390″) will be used later to help the nozzle calculations.

Fig 2 – The semi elliptical head


The U shaped firetube needs to be removable, so it has to pass through one large flanged opening instead of two smaller nozzles. A single large obround nozzle that minimizes the size of the flat cover on the firetube is the standard solution.  

ASME VIII-1 allows obround nozzles to be designed to code rules when the large to small opening dimensions make a ratio of 2:1 or less. When the long dimension is more than 2 times the short dimension, alternate methods such as FEA analysis from VIII-2 or burst testing must be used. The 16 x 32″ opening in this sample is on the 2:1 ratio limit so the VIII-1 code rules can be used.  Many obround firetube nozzles meet this criteria.  The ASME VIII-1 method calculates the oblong opening as round.  The calculation results:

  • 0.5″ nozzle thickness
  • 0.5″ weld leg size
  • 2.881″ minimum external projection
  • 0.820″ minimum internal projection
  • (see calculations page 5)

Fig 3 – The nozzle has been calculated as a round opening per VIII-1 rules

Explanation: the ASME VIII-1 nozzle rules start simply. Material lost in the head due to the cut out opening must be replaced. Acceptable sources of this replacement material are excess material in the head (the head was designed thicker than required), excess material in the nozzle wall, all material in a reinforcing pad if one is used, material found in nozzle welds and the internal projection of the nozzle neck.  For this example the majority of the material comes from the extra head thickness:

  • 7.160 required area (required, but lost to the design because of the opening)
  • 5.320 excess area of shell (from difference between required and actual thickness)
  • 0.779 excess area in nozzle neck (the nozzle neck is thicker than required)
  • 0.820 area of internal nozzle projection (the internal projection is only used to provide strength to the nozzle)
  • 0.25 area of the nozzle to shell welds
  • 7.170 actual area of nozzle (sum of the above areas which is greater than the required area so area replacement rules pass
  • (see calculations page 6)

Additional rules apply, but basically this calculation is based on “area replacement” where all required material in the head cut out opening is replaced. It is an 18th century naval calculation method for cutting openings in ship bulkheads.  It predates our modern understanding of stress concentrations, but is still the core of ASME VIII-1 nozzle calculations.  In spite of its age and simplicity, the calculation method has a long history of successful services for simple round nozzles in most vessel locations.

Obround Neck

The nozzle calculation was simplified by assuming a round opening as allowed by code rules. However, under pressure the obround shape will attempt to become round. The obround nozzle shape is not as strong as a round pipe of the same thickness. The wall can be made thicker or stiffeners added.  ASME VIII-1 Appendix 13 provides rules to design a safe pressurized obround shape.

This obround nozzle is reinforced with stiffeners – in this sample the obround flange acts as the stiffener. The flange is made large enough until it can support the straight sides of the obround nozzle.  The extra head material has already been used for nozzle calculations, and is not considered here as additional support material.  


  • 16 x 32″ inside dimension (17 x 33″ outside dimension)
  • 0.5″ wall thickness (same as nozzle calculation)
  • 2.125″ high x 1.1875″ thick reinforcing ring
  • 5.0″ maximum pitch distance between reinforcing ring and the head (dimension will vary around the opening)
  • (see calculations page 10)

Fig 4 – The obround nozzle as calculated by Appendix 13.  The calculated distance between stiffeners cannot be less than the maximum head to flange distance at any point around the nozzle.  Only one section of the shape is used for the nozzle.

Obround Flange

The flange also has bending loads transmitted through the cover bolts. ASME code calculations exist for the round end portions of the flange.  No ASME VIII-1 code rules exist for the straight sides so it is customary to also use BS PD 5500. This is an iterative design process also involving the previous Appendix 13 and nozzle area replacement calculations.  The results:

  • 0.5″ nozzle thickness (as used in all previous calculations)
  • 21.25″ short direction outside flange dimension (as used for App 13 above) 
  • 16″ straight side length (as above)
  • 52 bolts @ 5/8″ UNC-11 located on a 20″ bolt circle with 16″ straight sides
  • 0.5″ flange weld size
  • (see calculations page 20 for the ASME flange, last 2 pages of calculations for the BS PD 5500)

Fig 5 – ASME and BS PD 5500 has been used to calculate the flange bending and bolt loads.  Flange dimensions match the reinforcing dimensions from the previously step.


The firetube experiences the internal pressure of the vessel as a 125 psi exterior crushing load. The pressure from the burner fan is negligible. The calculated requirements:

  • 14″ nominal pipe size (14″ OD)
  • 0.375″ nominal thickness (0.321″ after undertolerance has been removed)
  • 120″ maximum length inside the vessel
  • (See calculations page 24)

Fig 6 – The firetube

Cover and openings

The cover is calculated as a non-round plate according to ASME rules.  The results:

  • 20″ x 36″ bolt pattern (20″ round with 16″ straight sides) same as above
  • 1.1875″ thick
  • (see calculations page 27)

Fig 7 – The cover calculated on its own

The cover has two closely spaced openings into which the 14″ diameter firetube is welded.  The openings are too close together to use area replacement rules, but it is possible to calculate the round ends of the cover as reducing flanges.  No allowable code rules are available for the design of the area between the two nozzles. The results for the flange calculations on the round ends:

  • 20″ bolt circle (same as above)
  • 1.1875″ thickness (same as above)
  • 34 x 5/8″ UNC-11 located on a 20″ bolt circle (52 bolts – bolts on the straight sides)
  • full face soft rubber gasket
  • (see calculations page 29)

Fig 8 – The round end of the cover is calculated as a reducing flange. No code calculation is available for the area between nozzles.

Drawing of the Nozzle As Code Calculated

Finite Element Analysis (FEA)

Many of the above code calculations are in isolation, and the nozzle calculations are for a round not an obround shape. This is the largest limitation of the VIII-1 approach. Also no rules are available for the space between the two nozzles on the cover plate. This is a practical limit for design by rules as found in VIII-1 and other sources. FEA is used for the remainder of the analysis.

This is what we are looking for from the FEA analysis:

  1. Excess deflection: The code calculations do not check deflections. Do excess deflections exist, especially in the flange area that can lead to excess bolt bending and/or interfere with gasket operation and seating?
  2. Gasket contact stress: Is the gasket adequately compressed all the way around every bolt hole?  Lack of contact stress greater than the operating pressure is a predictor of gasket leakage through bolt holes.
  3. Excess stress: The calculations passed when examined individually, but is this assembly including its fasteners overstressed once component interactions are considered?

The first two questions ask if the design is reliable.  The last asks if the design has an adequate factor of safety. The FEA analysis shows that all three are issues for this sample in the AS Code Calculated condition:

  • Excess deflection is found in the head along the straight sides of the oblong opening, and on the straight length of the flange.  (See Fig 9)
  • Excess rotation of the flange and cover reduces the chance of a good gasket seating. FEA predicts a lack of gasket contact stress on the inside of the bolt holes leading to difficulty in obtaining or maintaining a leak free condition. (See Fig 10)
  • Excess bending stress exists in the nozzle to shell junction and in some of the flange bolts. (See Figs 11 and 12)

This predicts poor serviceability.  A Revised Design resolves these issues. The changes made are:

  • A 0.5″ thick by 4″ wide repad is added to the nozzle.  The maximum nozzle projection remains at 5″, but now measured from the repad, not the head.  Effectively the nozzle is 0.5″ longer.
  • The nozzle wall thickness is increased from 0.500 to 0.750″ (code rules also require the matching increase in the nozzle to flange weld size from 0.5 to 0.75″)
  • The nozzle inside projection is increased from 0.820 to 2.137″
  • The flange OD increases from 21.25 to 24″ (the straight side length remains at 16″)
  • The flange Bolt circle increases from 20″ to 21″ (the straight side length remains at 16″)

The reasons for the changes and their effects are explained below.  Click for a drawing of the Revised Design.

Deflection Check

In the As Code Calculated design, both the straight and curved sections of the obround flange show areas of high deflection. No guidelines exist for acceptable deflection limits, but excess displacements can result in high stresses.  Increasing the interior projection, nozzle thickness and adding a repad reduces the deflection. Making the nozzle longer reduces the amount of flange rotation caused by the remaining displacement. Increasing the flange width reduces the straight side deflection and rotation.  Refer to the drawings of the As Calculated Design and the Revised Design to see all of the changes.

Fig 9 – Deflections in the As Code Calculated design (left illustrations) are compared with the Revised Design (right illustrations). The revised design reduces deflections and flange rotation. The closeup section views are taken from the locations indicated by the arrows.  The same deflection scale is used for all images, all displacements are shown magnified 80x.

Gasket Seating

Large flange deflections and rotations lead to difficulties getting gaskets to seat and operate leak free. To be leak free, this full face gasket has to have operating compressive gasket stress greater than the operating pressure on all sides of all bolts. The As Code Calculated design has areas around the bolt holes with no seating load which predict a leakage path and field service difficulties. The Revised Design has reduced flange rotation resulting in adequate compressive loads on all sides of all bolt holes.

Fig 10 – Gasket contact stress in the As Code Calculated and Revised Design.  The As Code Calculated has areas indicated by the arrows where the contact pressure is less than the operating pressure indicating a likely leakage path around the bolt holes.  The Revised Design shows a desired seating stress on all sides of all bolts.

FEA Stress

The As Code Calculated design shows stresses around the small end of the flange neck which are too high to pass VIII-2 rules at the allowable VIII-1 stress levels.  The multiple design changes in the Revised Design reduce this stress.  This is one of the many cases where design by VIII-2 FEA is more restrictive than by use of VIII-1 rules and it shows up in many code compliant nozzles, not just the oblong ones shown here. 

Fig 11 – Stress results for the As Code Calculated and the Revised Design.  Stresses are plotted from 0 (blue) to to the 30,000 psi local membrane stress limit (red). The red arrow shows an extensive area in the head to nozzle region where the membrane limit has been exceeded through the full shell thickness.  This region fails VIII-2 FEA stress requirements.  The Revised Design has acceptable stresses through all areas of the full model.

Bolt Stress

ASME VIII-1 code design rules cover allowable bolt tension loads, which when checked using VIII-2 FEA rules pass in both the As Calculated and the Revised Design (Refer to the blue lines in Fig 12 below).  VIII-1 design rules do not provide a way of checking bending stresses in bolts.  The red lines in Fig 12 shows that some bolt bending stress are excessive in the As Code Calculated design, but acceptable after the Revised Design.  Again design to VIII-2 FEA rules is often more conservative than the rules found in VIII-1.

Fig 12 – Flange bolt stresses for the As Code Calculated and the Revised Design.  All bolt tension stresses are acceptable.  The flange motions and rotations as seen in the displacement results (Fig 9) show up here as bolt bending stresses.  Some bolts in the As Code Calculated design have excessive stress.  The Revised Design is acceptable.

Clean Up

The design calculations for the As Code Calculated design initially used to prove the design to the ASME VIII-1 code rules no longer match the Revised Design that passed the VIII-2 FEA requirements.  For an Authorized Inspector or reviewer to check this design, the code calculations need to be updated to match the final Revised Design dimensions. For this sample the result will be code calculations that comply with the VIII-1 rules, but look conservative.

Two sets of documents now exist for code review.  Some reviewers and Authorized Inspectors require the FEA approach, some require the code calculations. Either way, the required documentation is available.

In our experience, using the both the code rules and FEA methods outlined in this article results in reliable obround nozzles.


Vessel with a Large Opening

File: Sample 5, Date: June 16, 2010, By: LB

A Collection of Unusual Design Features

Sample solid model of a pressure vessel with a large opening

This sample vessel is not modeled after a real vessel. It is a collection of difficult design features and obscure code requirements: large nozzles, swing bolt covers, cone discontinuities, use of bar stock for nozzles (code case 2148) and the use of sanitary ferrules in vessels. Refer to the calculation sets for more details.

Unusual Flanges

The swing bolt cover is analyzed as an appendix 2 flange. The bolt circle is outside of the flange, which is a length of increased wall thickness pipe. The bolt loads try to twist the pipe inside out – the Appendix 2 calculations check for this. Additional calculations are run for the attachment lug weld and shear pin stress. Flange C is also a custom flange calculated to Appendix 2.


Ferrules and sanitary connections can not be calculated by the rules provided by Appendix 24 which requires metal to metal contact outside the gasket. Typically, ferrules need to be proof tested, or calculated by Finite Element Analysis. For this vessel, the manufacturer of the 2″ ferrule has provided a CRN number covering the design. The CRN implies that either proof testing or some other calculation method was used to prove the design. The 8″ ferrule does not have a CRN, here a proof test is specified.

Large Nozzles

The side nozzle C is checked against the rules of Appendix 1-7 because it is larger than 1/2 of the vessel body diameter. The rules of Appendix 1-7 are confusing and very difficult to interpret, so in this case, all the conditions regarding moments of inertia and area replacement have been applied.

Bar Stock

The rules that allow the use of bar stock in pressure vessel bodies or nozzles have been changing. At the time this sample was made, bar stock could only be used with code case 2148. This code case has since been annuled and later reinstated as 2148-1. See UG-14 and App 2-2(d) for up to date information on the use of bar stock in pressure vessels.

Example calculation sets using Advanced Pressure Vessel (APV), PVElite, and PVEng Spreadsheets can be downloaded from the links to the left.


Origins of the ASME area replacement rules?

File: PVE-2461, Last Updated: Oct. 11, 2007, By: LB

The area replacement rules in the ASME code books have always interested me: You can cut a hole in a vessel as long as the nozzle attached to it replaces the lost area. How can this be a rational method of designing pressure vessels?


I was re-reading a fascinating book that I first encountered when I was a kid called “The new Science of Strong Materials or Why You Don’t Fall Through the Floor” by J. E. Gordon, 1968, Penguin Books. This interesting book is still in print. (The pictures in the latest paperback reprints are no longer viewable, try finding an original print.)   I came across the section quoted below (Page 60) dealing with tubular shapes like railway bridges and ships.

A ship is a long tube closed at both ends which happens to be afloat but is not otherwise structurally very different from Stephenson’s Menai bridge. [topic of the authors previous paragraph] The support which the water gives to the hull does not necessarily coincide with the weights of engines, cargo and fuel which are put into the ship and so there is a tendency for the hull to bend. It ought to be impossible to break a ship, floating alongside a quay, by careless and uneven loading of the holds and tanks, but this has happened often enough and will probably happen again. In dry-dock ships are supported with care upon keel-blocks arranged to give even support but there is not much even support at sea where a ship may be picked up by rude waves at each end, leaving her heavy middle unsustained, or else exposing a naked forefoot and propeller at the same moment. As ships tended to get longer and more lightly built, the Admiralty decided to make some practical experiments on the strength of ships. In 1903 a destroyer, H.M.S. Wolf, was specially prepared for the purpose. The ship was put into dry-dock and the water was pumped out while she was supported, in succession, amidships and at the ends. The stresses in various parts of the hull were measured with strain-gauges, which are sensitive means of measuring changes of length, and therefore of strain, in a material. The ship was then taken to sea to look for bad weather. It does not require very much imagination to visualize the observers, struggling with seasickness and with the old-fashioned temperamental strain-gauges, wedged into Plutonic compartments in the bottom of the ship, which was put through a sea which was described in the official report as ‘rough and especially steep with much force and vigor’. Her captain seems to have given the Wolf as bad a time as he could manage but, whatever they did, no stress greater than about 12,000 p.s.i. or 80 MN/m2 could be found in the ship’s hull.

As the tensile strength of the’ steel used in ships was about 60,000 p.s.i. or 400 MN/m2, and no stress anywhere near this figure could be measured, either at sea or during the bending trials in dry-dock, not only the Admiralty Constructors but Naval Architects in general concluded that the methods of calculating the strength of ships by simple beam theory, which had become standardized, were satisfactory and ensured an ample margin of safety. Sometimes nobody is quite as blind as the expert. Ships continued to break from time to time. A 300-foot (90 meters) ore-carrying steamer, for instance, broke in two and sank in a storm on one of the Great Lakes of America. The maximum calculated stress under the probable conditions was not more than a third of the breaking stress of the ship’s material. Even when major disasters did not actually happen, cracks appeared around hatchways and other openings in the hull and decks.* These openings are of course the key to the problem. Stephenson’s tubular bridge was eminently satisfactory because it is a continuous shell with no holes in it except the rivet holes. Ships have hatchways and all sorts of other openings. Naval Architects are not especially stupid and they made due allowance for the material which was cut away at the openings, increasing the calculated stresses around the holes pro rata. Professor Inglis, in a famous paper in 1913, showed however that ‘pro rata’ was not good enough and he introduced the concept of ‘stress-concentration’ which, as we shall see (Chapter 4), is of vital importance both in calculating the strength of structures and in understanding materials.

What Inglis was saying was that if we remove, say, a third of the cross-section of a member by cutting a hole in it then the stress at the edge of the hole is not 3/2 (or 1.5) of the average but it may, locally, be many times as high. The amount by which the stress is raised above the average by the hole – the stress-concentration factor – depends both upon the shape of the hole and upon the material, being worst for sharp re-entrants and for brittle materials. This conclusion, which Inglis arrived at by mathematical analysis, was regarded with the usual lack of respect by that curiously impractical tribe who call themselves ‘practical men’. This was largely because mild steel is, of all materials, perhaps the least susceptible to the effects of stress concentrations though it is by no means impervious (Plate 3). It is significant that, in the Wolf experiments, none of the strain gauges seems to have been put close to the edge of any important opening in the hull.


Is this really the origin of the Area replacement (or pro-rata) rules that we use in pressure vessels? Is it just a set of rules that failed when applied to ships but have been successfully applied to pressure vessels? Yes these pro rata rules are still in use in the ASME pressure vessel and piping codes. Basically, when we remove some material from a vessel in the form of a nozzle opening, we look for an equal amount of extra material to replace it, in both the surrounding shell, and in the nozzle pipe.

I have a mental picture that I use to explain the development process – I do not know how accurate it is but it goes like this: The stresses in vessels were too complicated to accurately understand at the time, so a rule like area replacement is adopted from another field like naval architecture. Or it is independently developed by the original pressure vessel designers (our rules UG-36 to 43). The designs work well most of the time but occasionally a pressure vessel blows up (this is after all an experience based code). With more experience, more restrictions like appendix 1-7 are added and our vessels fail less often. Are designers ignoring the intent of the code but purely following the rules – the more specific restrictions on the geometry are added – (like UW-14 to 16). And so it goes – we are still changing the pressure vessel code today. At no point is the problem fully understood but pressure vessels gradually get more reliable. We can expect more restrictions in the future…


The ASME nozzle area replacement rules cannot be taken on their own. There are a large number of code sections that need to be considered on each nozzle – UG-36 to 43, App 1-7, UW-14 to 16, UG-45 and others. The rules explicitly only apply to circular, obround and elliptical openings – for the last two, the length cannot be more than twice the width. In practice, these limits are commonly violated.

The amount by which the stress is raised above the average by the hole – the stress-concentration factor – depends both upon the shape of the hole and upon the material, being worst for sharp re-entrants and for brittle materials [J.E. Gordon, copied from the above quote].

Brittle materials are not much of an issue with modern pressure vessels; however the shape of opening issues still remains. Also we do not distinguish between nozzles attached to high stress areas of vessels like knuckles on heads, or lower stress areas like straight shells. I wonder if an enterprising (or luckless) engineer could design a nozzle for a pressure vessel that meets all code rules, but is unsafe. Have we closed all the loopholes?

Using the ASME VIII-1 Nozzle F Factor (UG-37)

File: PVE-3783 Jan. 24, 2013, LRB

The stresses around a nozzle located in a cylindrical shell are not the same in all directions. If a non-round nozzle is oriented in the correct direction, ASME allows us to take advantage of this.

Algor Model of two nozzles with different stresses.

A pressure vessel with two identical elliptical nozzles, but oriented in different directions

This is a FEA plot of a pressure vessel with two identical elliptical nozzles, but oriented in different directions. ASME says that the two nozzles have different stresses around them, as the FEA results confirm. A cylindrical shell circ stress is 2x the longitudinal stress. The nozzle that cuts more material in the long direction has higher stresses.

  • The default F factor is 1.0 – this effect can be ignored if desired.
  • F Factor can reduce the required amount of area replacement to 1/2 in certain directions – this allows less conservative nozzle designs if the non-round nozzle is oriented favorably.
  • F Factors other than 1.0 can only be used for integral (full penetration welded, no re-pad) nozzles.
  • The nozzle will need to be calculated twice – once in the longitudinal direction at F = 1.0 and once in the circ direction at F=0.5. Different d values will be used for the different directions.

An example follows:

F correction factor

F = correction factor that compensates for the variation in internal pressure stresses on different planes with respect to the axis of a vessel. A value of 1.00 shall be used for all configurations except that Figure UG-37 may be used for integrally reinforced openings in cylindrical shells and cones. [See UW-16(c)(1).]

ASME figure UG-37. At angle of 0 degrees, the maximum circ stress exists, F = 1.0. At angle 90 degrees, the maximum longitudinal stress exist, which is half the circ stress. F = 0.5

Companion Sample Problem and Calculation Set

The enclosed example shows an elliptical manway nozzle that takes advantage of the F factor to get a higher pressure rating than otherwise possible.

Calculation Set