[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-665082-105":59,"doc-detail-665082-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","pressure-vessels-4-design-and-calculation","Pressure Vessels - 4 - Design and Calculation","","Material on pressure equipment design and calculation for “Pressure Vessels” under the PED-4 lecture series. Covers applicable standards including ČSN 690010, EN 13445-3, DIN, ASME BPVC, and GOST, and explains typical pressure vessel types such as reactors, autoclaves, heat exchangers, columns, boilers, and tanks. Details exclusions from the standards rules, common vessel geometries, thin-wall shell versus membrane theory validity ranges, and membrane-theory force balance for tangential and axial stresses, plus temperature limits for different steel classes.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/pressure-vessels-4-design-and-calculation/665082/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/pressure-vessels-4-design-and-calculation/665082.png","ImageObject",300,407,{"name":92,"@type":93},"Eliana","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Which standards are listed for designing pressure vessels?","Question",{"text":112,"@type":113},"The text lists ČSN 690010, EN 13445-3, DIN, ASME BPVC, and GOST as standards used for design and calculation.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What kinds of equipment are stated as not requiring the standard rules?",{"text":117,"@type":113},"Exemptions include pipes/tubes and vessels built in tubes produced to the given ČSN for a specified pressure, certain tube-derived vessels with limited diameter, liquid-filled non-aggressive/non-toxic/non-explosive vessels under specified temperature/overpressure limits, small-volume/low-pressure cases, and specific compact heat exchangers (tube-in-tube) with outside diameter under 100 mm.",{"name":119,"@type":110,"acceptedAnswer":120},"What are the key validity conditions for membrane theory in thin-walled cylinders?",{"text":121,"@type":113},"Membrane theory is given with validity ranges based on relative thickness, including scalc/Di ≤ 0.1 for Di ≥ 200 (with k up to about 1.2 and theoretical/tactical k values) and scalc/Di ≤ 0.3 for Di \u003C 200.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},665082,1793289003,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},4398048949847,"https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267","Processing Equipment  \nDesign  \n4. Pressure Vessels  \nPressure vessels must be designed according proper standards:  \nČSN 690010 – Czech State Standard  \nEN 13445-3 – European Standard; Unfired pressure vessels: Design and calculation DIN – Deutsche Industrie Norm  \nASME BPVC – American Society of Mechanical Engineers; Boiler and Pressure Vessel Code GOST – Gosudarstvennyj Standart  \nLecturer: Pavel Hoffman  \n[http://fsinet.fsid.cvut.cz/cz/U218/peoples/hoffman/index.htm](http://fsinet.fsid.cvut.cz/cz/U218/peoples/hoffman/index.htm)  \ne-mail: [pavel.hoffman@fs.cvut.cz](pavel.hoffman@fs.cvut.cz)  \nTypes of pressure vessels:  \nReactors, autoclaves, heat exchangers, columns, boilers, tanks etc. are usually pressure vessels.  \n(remember our first lectures with equipments examples)  \nAccording the Czech Standard for pressure vessels ČSN 690010-1.1 and European standard ES 13445-1 pressure vessels are not  \n(􀁯 rules of these standards need not be applied to these pressure vessels):  \n• Pipes, tubes and their parts and vessels built in tubes produced according the ČSN for a given pressure  \n(e.g. pipe PN6 is designed for working pressure 6 bars 􀁯 it is not necessary to check it again)  \n• Pressure vessels made from tubes produced according the ČSN for a given  \npressure with maximal inside diameter 100 mm  \n(e.g. a vessel welded from such tubes)  \n2  \nPED-4  \n• Pressure vessels filled with a liquid (non aggressive, non toxic, non explosive) if the highest working temperature is lower than a boiling temperature corresponding to the overpressure 0.07 MPa (e.g. for water it is \u003C 115 ° C)  \n• Pressure vessels for that a product of volume (in dm 3 ) andoverpressure (in MPa) is less than 10 and the pressure is lower than 0.07 MPa  \n• Pressure vessels with volume less 1 dm 3 regardless of pressure  \n• Heat exchangers of type tube in tube with outside diameter  \n\u003C 100 mm  \n(Such vessels must be designed for these working parameters, but may not be approved by a relevant authority)  \nPED-4 3  \nCompressed vapor  \npCV 􀁼 0.31 MPa, t“CV 􀁼 135 °C  \nDiffuser  \nThermocompressor was installed in a normalized tube DN 250 and PN 10 􀁯 it was not a pressure vessel  \nPart with equal  \narea (cylindrical)  Part with const.  \npressure (conical)   \nLaval jet of driving steam (expansion nozzle)  \nVapor  PV 􀁼 0.23 MPa, t“V 􀁼 125 °C  \n Draining  \nMixing jet of vapor and exp. steam  \nDraining  \nDriving steam  \npDS 􀁤 10 bar, tDS 􀁼 195 °C  \nIt was not necessary to ask a relevant inspectorate for approval of the TC documentation (calculations and drawings) and the manufacturing authorization 􀁯 time and money saving.  \nPED-4 4  \nPressure vessels are usually designed from these geometrical shapes:  \n• Sphere  \n• Cylinder  \n• Cone  \n• Plate  \n• (Ellipsoid, torus ..)  \nBrief repetition of previous knowledge:  \n• Rotary symmetrical vessels are from the stress point of view better than these ones made from flat plates.  \n• The most advantageous is sphere (remember the previous part).  \n• Theory of shells and membranes is used for solution of thinwalled vessels. PED-4 5  \nThin-wall shell is for ratio  \nde  \nk 􀀠 ~~ ~~ 􀁤 1 . 1 or 􀁤 1 . 17  \ndi (with higher (according safety) theory)  \nMembrane – in wall are only tensile or compression forces (stresses); stresses are calculated only from balance of forces in a section  \nRigid shell – in wall are shear forces, bending and twist moments; for stresses calculation sometimes we need deformation conditions too.  \nExamples of shells whose dimensionless wall thickness  is on the boundary between thin-and thick-walled shells.  \nFor k = 1.1  \nFor k = 1.17  \nis wall thickness  \nis wall thickness  \ndi (mm) = 100 500 1000 3000  \n practical value  \ns = (de -di ) / 2 ≤ (1.1 di – di ) / 2 = 0.1 di / 2  \ns = (de -di ) / 2 ≤ (1.17 di – di ) / 2 = 0.17 di / 2  \ntheoretical value  \nk = 1.1 k = 1.17  \ns ≤ 5.0 mm 􀁯 11.7 MPa s ≤ 8.5 mm 􀁯 pimax = 22.7 MPa  \n25.0 􀁯 pimax = 14.1 MPa 42.5 50 85  \n150 􀁯 pimax = 15 MPa 255 pimax = 25.5 MPa  \n􀁯 A majority ","cbCaiq6OsX2QfM50","https://ap.wps.com/l/cbCaiq6OsX2QfM50","pdf",1906261,32,"English","# Pressure Vessels\n## Standards for design and calculation\n## Types and exemptions from standard rules\n## Geometrical shapes and shell theory\n## Membrane theory and calculation ranges\n## Force balance and stress relations","[{\"question\":\"Which standards are listed for designing pressure vessels?\",\"answer\":\"The text lists ČSN 690010, EN 13445-3, DIN, ASME BPVC, and GOST as standards used for design and calculation.\"},{\"question\":\"What kinds of equipment are stated as not requiring the standard rules?\",\"answer\":\"Exemptions include pipes/tubes and vessels built in tubes produced to the given ČSN for a specified pressure, certain tube-derived vessels with limited diameter, liquid-filled non-aggressive/non-toxic/non-explosive vessels under specified temperature/overpressure limits, small-volume/low-pressure cases, and specific compact heat exchangers (tube-in-tube) with outside diameter under 100 mm.\"},{\"question\":\"What are the key validity conditions for membrane theory in thin-walled cylinders?\",\"answer\":\"Membrane theory is given with validity ranges based on relative thickness, including scalc/Di ≤ 0.1 for Di ≥ 200 (with k up to about 1.2 and theoretical/tactical k values) and scalc/Di ≤ 0.3 for Di \\u003c 200.\"}]","Pressure Vessels - 4 - Design and Calculation | PDF",81]