{"id":100179,"date":"2026-02-15T20:25:20","date_gmt":"2026-02-15T20:25:20","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100179"},"modified":"2026-07-13T01:29:52","modified_gmt":"2026-07-13T01:29:52","slug":"orifice-flow-calculator-iso5167","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/nb\/calculators\/orifice-flow-calculator-iso5167\/","title":{"rendered":"Documented-Coefficient Orifice Flow Arithmetic"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Documented-Coefficient Orifice Flow Arithmetic\",\"description\":\"Computes upstream volume and mass flow from documented orifice geometry,differential pressure,density,discharge coefficient and expansibility factor without inventing ISO 5167 coefficients.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/orifice-flow-calculator-iso5167\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2026-07-13\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Documented C and epsilon\",\"SI and inch pressure inputs\",\"Upstream volume flow\",\"Mass flow\",\"Explicit ISO scope gate\"],\"keywords\":\"orifice flow arithmetic,ISO 5167 scope,discharge coefficient,expansibility factor,differential pressure\"}<\/script>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Does this calculate the ISO 5167 discharge coefficient?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. C must come from the applicable current procedure or controlled calculation including the correct tapping arrangement,geometry and Reynolds-number treatment.\"}},{\"@type\":\"Question\",\"name\":\"Does this calculate gas expansibility?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Epsilon must be documented for the same operating point;the worksheet does not infer it without upstream pressure,pressure ratio and thermodynamic data.\"}},{\"@type\":\"Question\",\"name\":\"Is the output an ISO conformity result?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It is arithmetic using entered coefficients. Installation,geometry,flow regime,uncertainty and all current ISO requirements remain separate.\"}},{\"@type\":\"Question\",\"name\":\"What volume-flow basis is displayed?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"The displayed volume flow is on the same upstream density basis entered. It is not a standard or normal gas volume flow.\"}}]}<\/script>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Documented-Coefficient Orifice Flow Arithmetic\",\"item\":\"https:\/\/vibromera.eu\/calculators\/orifice-flow-calculator-iso5167\/\"}]}<\/script>\n<style>:root{--s:#fff;--sa:#f8f6f2;--i:#1a1a1a;--is:#5a5650;--im:#8a857e;--a:#c85a2a;--al:#fdf0ea;--b:#d9d4cc;--bl:#e8e4dd;--y:#8a6500;--yl:#fef9e8;--r:#a12b2b;--g:#2a7a4b;--gl:#eaf8ef;--sh:0 1px 3px rgba(26,26,26,.06),0 4px 12px rgba(26,26,26,.04);--f:'DM Sans',sans-serif;--m:'JetBrains 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class=\"vc-header\"><p class=\"vc-header-eyebrow\">Source-gated flow arithmetic<\/p><h1 class=\"vc-header-title\">Documented-Coefficient Orifice Flow<\/h1><p class=\"vc-header-subtitle\">Calculate flow only after C and \u03b5 have been established for the exact plate,tappings,flow regime and operating point by the controlling procedure.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">C not invented<\/span><span class=\"vc-badge\">\u03b5 not invented<\/span><span class=\"vc-badge\">Not ISO conformity<\/span><\/div><\/header>\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\" novalidate><div class=\"vc-grid\"><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-d\">Orifice bore d<\/label><input class=\"vc-input\" id=\"vc-d\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-D\">Upstream pipe inside diameter D<\/label><input class=\"vc-input\" id=\"vc-D\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-du\">Diameter unit<\/label><select class=\"vc-select\" id=\"vc-du\"><option value=\"mm\">millimetres<\/option><option value=\"in\">inches<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-dp\">Differential pressure \u0394p<\/label><input class=\"vc-input\" id=\"vc-dp\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-pu\">\u0394p unit<\/label><select class=\"vc-select\" id=\"vc-pu\"><option value=\"kpa\">kPa<\/option><option value=\"bar\">bar<\/option><option value=\"psi\">psi<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-rho\">Upstream density \u03c11 <span class=\"vc-hint\">(kg\/m\u00b3)<\/span><\/label><input class=\"vc-input\" id=\"vc-rho\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-c\">Documented discharge coefficient C<\/label><input class=\"vc-input\" id=\"vc-c\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-eps\">Documented expansibility factor \u03b5<\/label><input class=\"vc-input\" id=\"vc-eps\" inputmode=\"decimal\"><\/div><div class=\"vc-field vc-full\"><label class=\"vc-label\" for=\"vc-source\">Coefficient and installation record<\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" placeholder=\"procedure\/edition;plate;tap type;dimensions;Re;operating point;C;epsilon;uncertainty\"><\/div><div class=\"vc-field vc-full\"><label class=\"vc-check\" for=\"vc-gate\"><input id=\"vc-gate\" type=\"checkbox\"><span>The circular conduit runs full;flow is single-phase,subsonic and non-pulsating.D is50\u20131000mm.Reynolds number is at least5000.The plate,tappings,geometry,installation,pressure\/density reference,uncertainty,C and \u03b5 satisfy the controlling current procedure for this operating point.<\/span><\/label><\/div><\/div><div class=\"vc-validation\" id=\"vc-validation\" role=\"status\" aria-live=\"polite\"><\/div><\/form><div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Coefficient-based arithmetic<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div><div class=\"vc-result-grid\"><div class=\"vc-rcard vc-primary\"><div class=\"vc-rcard-label\">Upstream-basis volume flow qv<\/div><div class=\"vc-rcard-value\" id=\"vc-r-q\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Mass flow qm<\/div><div class=\"vc-rcard-value\" id=\"vc-r-m\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Diameter ratio \u03b2<\/div><div class=\"vc-rcard-value\" id=\"vc-r-beta\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Orifice area<\/div><div class=\"vc-rcard-value\" id=\"vc-r-area\">\u2014<\/div><\/div><div class=\"vc-status\" id=\"vc-r-note\">Entered-coefficient arithmetic only.<\/div><\/div><\/div><\/div>\n<div class=\"vc-section vc-open\"><button class=\"vc-section-toggle\" type=\"button\" aria-expanded=\"true\"><span class=\"vc-section-title\">Equation and ISO scope boundary<\/span><span>\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><h3>Implemented arithmetic<\/h3><div class=\"vc-formula\">qv = [C\u00b7\u03b5 \/ \u221a(1\u2212\u03b2\u2074)] \u00b7 (\u03c0d\u00b2\/4) \u00b7 \u221a(2\u0394p\/\u03c11); \u03b2=d\/D; qm=\u03c11qv<\/div><p>All quantities are converted to SI before calculation.qv is volume flow on the entered upstream-density basis;it is not standard\/normal gas volume.C and \u03b5 are inputs,not results.<\/p><h3>Current standards<\/h3><p>ISO5167-1:2022,edition3,sets general principles,installation and uncertainty requirements.The public scope requires a full circular conduit,single-phase subsonic non-pulsating flow.ISO5167-2:2022,edition2,covers qualifying orifice plates with flange,corner,or D andD\/2 tappings in conjunction with Part1;its public scope excludes D below50mm or above1000mm and pipe Reynolds number below5000.<\/p><div class=\"vc-warning\"><strong>Not an ISO calculator:<\/strong> exact C,\u03b5,beta\/Reynolds limits,tap corrections,geometry,straight lengths and uncertainty rules remain <strong>NEEDS_LICENSED_SOURCE<\/strong>.Passing this input gate does not establish ISO conformity,custody-transfer suitability or fitness for service.<\/div><h3>Removed unsafe model<\/h3><p>The previous page called `0.5959+0.0312\u03b2^2.1\u22120.184\u03b2^8` a simplified Reader-Harris coefficient while omitting Reynolds and tapping terms.It also accepted arbitrary \u03b5 without upstream pressure or thermodynamic inputs.That model is not retained.<\/p><h3>Sources<\/h3><p><a href=\"https:\/\/www.iso.org\/standard\/79179.html\" target=\"_blank\" rel=\"noopener\">ISO5167-1:2022 official record<\/a>; <a href=\"https:\/\/www.iso.org\/standard\/79180.html\" target=\"_blank\" rel=\"noopener\">ISO5167-2:2022 official record<\/a>; <a href=\"https:\/\/www.iso.org\/standard\/85584.html\" target=\"_blank\" rel=\"noopener\">ISO\/TR12767:2023 official record<\/a>.<\/p><\/div><\/div><\/div>\n<div class=\"vc-section\"><button class=\"vc-section-toggle\" type=\"button\" aria-expanded=\"false\"><span class=\"vc-section-title\">Frequently asked questions<\/span><span>\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div id=\"vc-faq-list\"><\/div><\/div><\/div><\/div><footer class=\"vc-footer\">\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u2014 reviewed 13 July 2026<\/footer><\/div>\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}function read(raw){var t=String(raw||'').trim();if(!t||(t.includes(',')&&t.includes('.')))return null;t=t.replace(',','.');if(!\/^(?:\\d+(?:\\.\\d*)?|\\.\\d+)$\/.test(t))return null;var v=Number(t);return Number.isFinite(v)&&v>0?v:null}function fmt(v){if(Math.abs(v)>=1e7||Math.abs(v)<1e-5)return v.toExponential(6);return Number(v.toPrecision(10)).toString()}function hide(m){$('vc-results').classList.remove('vc-visible');$('vc-validation').textContent=m||''}function calc(){if(!$('vc-source').value.trim())return hide('Enter the coefficient and installation record.');if(!$('vc-gate').checked)return hide('Confirm the full ISO scope and coefficient basis.');var d=read($('vc-d').value),D=read($('vc-D').value),dp=read($('vc-dp').value),rho=read($('vc-rho').value),c=read($('vc-c').value),eps=read($('vc-eps').value);if([d,D,dp,rho,c,eps].some(function(x){return x===null}))return hide('Enter positive complete numbers using a decimal point or comma.');var dm=d*($('vc-du').value==='in'?.0254:.001),Dm=D*($('vc-du').value==='in'?.0254:.001),dmm=Dm*1000,pa=dp*($('vc-pu').value==='bar'?100000:$('vc-pu').value==='psi'?6894.757293168:1000);if(!(dm<Dm))return hide('Require d < D.');if(dmm<50||dmm>1000)return hide('The public ISO 5167-2 scope requires D from50mm through1000mm.');if(c>1||eps>1)return hide('Require 0 < C \u22641 and 0 < \u03b5 \u22641;use the documented values.');var beta=dm\/Dm,area=Math.PI*dm*dm\/4,q=c*eps*area\/Math.sqrt(1-Math.pow(beta,4))*Math.sqrt(2*pa\/rho),m=q*rho;if(![q,m,beta,area].every(Number.isFinite))return hide('The arithmetic did not produce finite results.');$('vc-r-q').textContent=fmt(q)+' m\u00b3\/s \/ '+fmt(q*3600)+' m\u00b3\/h';$('vc-r-m').textContent=fmt(m)+' kg\/s \/ '+fmt(m*3600)+' kg\/h';$('vc-r-beta').textContent=fmt(beta);$('vc-r-area').textContent=fmt(area)+' m\u00b2';$('vc-r-note').textContent='Uses entered C='+fmt(c)+' and \u03b5='+fmt(eps)+'.Volume flow is on the entered upstream-density basis.No ISO conformity or uncertainty result is calculated.';$('vc-validation').textContent='';$('vc-results').classList.add('vc-visible')}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);$('vc-copy-btn').addEventListener('click',function(){var t='Documented-coefficient orifice flow\\nqv: '+$('vc-r-q').textContent+'\\nqm: '+$('vc-r-m').textContent+'\\nbeta: '+$('vc-r-beta').textContent+'\\n'+$('vc-r-note').textContent+'\\nSource: '+$('vc-source').value.trim();if(navigator.clipboard)navigator.clipboard.writeText(t)});document.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',String(s.classList.contains('vc-open')))})});var faq=[['Does this calculate C?','No.Enter C from the applicable controlled procedure for the exact tapping arrangement,geometry and Reynolds number.'],['Does this calculate epsilon?','No.Enter the documented expansibility factor for 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