{"id":364,"date":"2017-10-15T14:34:46","date_gmt":"2017-10-15T14:34:46","guid":{"rendered":"http:\/\/www.mcmalchimia.com\/?p=364"},"modified":"2020-10-28T11:47:11","modified_gmt":"2020-10-28T11:47:11","slug":"first-project-step-2-c-final-model","status":"publish","type":"post","link":"https:\/\/www.mcm-alchimia.com\/en\/first-project-step-2-c-final-model\/","title":{"rendered":"First project &#8211; Step 2-C: Final model"},"content":{"rendered":"<p>Determination of the final mathematical model for the test.<\/p>\n<p>In the previous article we saw that our flask calibration test could be represented by the following diagram;<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-360\" src=\"http:\/\/www.mcmalchimia.com\/wp-content\/uploads\/2018\/10\/ishikawa_en.gif\" alt=\"\" width=\"600 \"height=\"246 \"\/><\/p>\n<p>Breaking down the input magnitudes in their contributions we would get:<\/p>\n<ul>\n<li> Ml = Ml_cal + SMl_res + SMl_rep, where the suffixes &#8220;cal&#8221;, &#8220;res&#8221; and &#8220;rep&#8221; will be by calibration, instrument resolution and repeatability respectively. The prefixes &#8220;S&#8221; indicate that this component will have zero value since it is added only for the purpose of evaluation of uncertainties. <\/Li>\n<li> Mv = Mv_cal + SMv_res <\/li>\n<li> The temperature, as we said before will be obtained from an average, so we can break down the equation in this average of readings. On the other hand, this thermometer has corrections. We could add this correction value (corr_t) to the average as a constant value without uncertainty, since this will be associated to the original values \u200b\u200bof temperature.<br \/>\nt = (ti + tf) \/ 2 + corr_t <\/li>\n<li> but each one of these values \u200b\u200bwill be affected by the calibration and resolution of the thermometer. So:<br \/>\nti = ti_cal + Sti_res<br \/>\ntf = tf_cal + Stf_res <\/li>\n<\/ul>\n<p>Therefore to conclude this step 2:<\/p>\n<ol>\n<li> We write the complete model in the text area for the Set of equations:<br \/>\n<em> V20 = ((Ml-Mv) \/ (Dens_w-Dens_a)) * (1- (Dens_a \/ Dens_b)) * (1-CDT * (t-20)) <\/em><br \/>\n<em> Ml = Ml_cal + SMl_res + SMl_rep <\/em><br \/>\n<em> Mv = Mv_cal + SMv_res <\/em><br \/>\n<em> t = (ti + tf) \/ 2 + corr_t <\/em><br \/>\n<em> ti = ti_cal + Sti_res <\/em><br \/>\n<em> tf = tf_cal + Stf_res <\/em> <\/li>\n<li> We fill the parameters grid with the following data: <\/li>\n<\/ol>\n<table style=\"height: 521px;\" border=\"0\" width=\"772\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<th scope=\"row\" width=\"107\"> V20 <\/th>\n<td width=\"114\">\n<div align=\"center\"> ml <\/div>\n<\/td>\n<td width=\"429\"> Volume contained at 20 \u00baC <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> Ml <\/th>\n<td>\n<div align=\"center\"> ml <\/div>\n<\/td>\n<td> Mass of the flask full with water up to calibration mark <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> Mv <\/th>\n<td>\n<div align=\"center\"> ml <\/div>\n<\/td>\n<td> Mass of empty flask <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> Dens_w <\/th>\n<td>\n<div align=\"center\"> g \/ ml <\/div>\n<\/td>\n<td> Filling water density <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> Dens_a <\/th>\n<td>\n<div align=\"center\"> g \/ ml <\/div>\n<\/td>\n<td> Density of the air <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> Dens_b <\/th>\n<td>\n<div align=\"center\"> g \/ ml <\/div>\n<\/td>\n<td> Density of weighing scale adjustment masses <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> CDT <\/th>\n<td>\n<div align=\"center\"> 1 \/ \u00baC <\/div>\n<\/td>\n<td> Coefficient of thermal deformation <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> t <\/th>\n<td>\n<div align=\"center\"> \u00baC <\/div>\n<\/td>\n<td> Average temperature along the test <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> Ml_cal <\/th>\n<td>\n<div align=\"center\"> ml <\/div>\n<\/td>\n<td> Flask mass including calibration uncertainty <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> SM_res <\/th>\n<td>\n<div align=\"center\"> ml <\/div>\n<\/td>\n<td> Contribution of uncertainty of Ml due resolution of the weighing scale <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> SM_rep <\/th>\n<td>\n<div align=\"center\"> ml <\/div>\n<\/td>\n<td> Contribution of uncertainty of Ml due repeatability <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> Mv_cal <\/th>\n<td>\n<div align=\"center\"> ml <\/div>\n<\/td>\n<td> Empty flask mass including calibration uncertainty <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> SMv_res <\/th>\n<td>\n<div align=\"center\"> ml <\/div>\n<\/td>\n<td> Contribution of uncertainty of Mv due resolution of the weighing scale <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> ti <\/th>\n<td>\n<div align=\"center\"> \u00baC <\/div>\n<\/td>\n<td> Initial temperature of the test <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> tf <\/th>\n<td>\n<div align=\"center\"> \u00baC <\/div>\n<\/td>\n<td> Final temperature of the test <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> corr_t <\/th>\n<td>\n<div align=\"center\"> \u00baC <\/div>\n<\/td>\n<td> Temperature correction <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> ti_cal <\/th>\n<td>\n<div align=\"center\"> \u00baC <\/div>\n<\/td>\n<td> Initial temperature with calibration uncertainty of the termometer <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> Sti_res <\/th>\n<td>\n<div align=\"center\"> \u00baC <\/div>\n<\/td>\n<td> Contribution of uncertainty of ti due thermometer resolution <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> tf_cal <\/th>\n<td>\n<div align=\"center\"> \u00baC <\/div>\n<\/td>\n<td> Final temperature with calibration uncertainty of the termometer <\/td>\n<\/tr>\n<tr>\n<th scope=\"row\"> Stf_res <\/th>\n<td>\n<div align=\"center\"> \u00baC <\/div>\n<\/td>\n<td> Contribution of uncertainty of tf due thermometer resolution <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.mcm-alchimia.com\/en\/wp-content\/uploads\/2018\/10\/step_2-1024x566.jpg\" alt=\"\" width=\"1024\" height=\"566\" class=\"alignnone size-large wp-image-9072\" srcset=\"https:\/\/www.mcm-alchimia.com\/en\/wp-content\/uploads\/2018\/10\/step_2-1024x566.jpg 1024w, https:\/\/www.mcm-alchimia.com\/en\/wp-content\/uploads\/2018\/10\/step_2-300x166.jpg 300w, https:\/\/www.mcm-alchimia.com\/en\/wp-content\/uploads\/2018\/10\/step_2-768x425.jpg 768w, https:\/\/www.mcm-alchimia.com\/en\/wp-content\/uploads\/2018\/10\/step_2.jpg 1096w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<hr \/>\n<p>More help<\/p>\n<ul>\n<li><a href=\"http:\/\/www.mcm-alchimia.com\/en\/first-project-step-1\/\">First project &#8211; Step 1<\/a><\/li>\n<li><a href=\"http:\/\/www.mcm-alchimia.com\/en\/first-project-step-2-a-basic-model\">First project &#8211; Step 2-A: Basic model<\/a><\/li>\n<li><a href=\"http:\/\/www.mcm-alchimia.com\/en\/first-project-step-2-b-input-uncertainties\">First project &#8211; Step 2-B: Input uncertainties<\/a><\/li>\n<li><span style=\"color: #aaaa00;\">First project &#8211; Step 2-C: Final model<\/span><\/li>\n<li><a href=\"http:\/\/www.mcm-alchimia.com\/en\/first-project-step-3\">First project &#8211; Step 3<\/a>.<\/li>\n<li><a href=\"http:\/\/www.mcm-alchimia.com\/en\/first-project-results\">First project &#8211; Results<\/a>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Determination of the final mathematical model for the test. In the previous article we saw that our flask calibration test could be represented by the following diagram; Breaking down the input magnitudes in their contributions we would get: Ml = Ml_cal + SMl_res + SMl_rep, where the suffixes &#8220;cal&#8221;, &#8220;res&#8221; and &#8220;rep&#8221; will be by [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-364","post","type-post","status-publish","format-standard","hentry","category-soporte-tecnico"],"_links":{"self":[{"href":"https:\/\/www.mcm-alchimia.com\/en\/wp-json\/wp\/v2\/posts\/364","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mcm-alchimia.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mcm-alchimia.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mcm-alchimia.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mcm-alchimia.com\/en\/wp-json\/wp\/v2\/comments?post=364"}],"version-history":[{"count":24,"href":"https:\/\/www.mcm-alchimia.com\/en\/wp-json\/wp\/v2\/posts\/364\/revisions"}],"predecessor-version":[{"id":9237,"href":"https:\/\/www.mcm-alchimia.com\/en\/wp-json\/wp\/v2\/posts\/364\/revisions\/9237"}],"wp:attachment":[{"href":"https:\/\/www.mcm-alchimia.com\/en\/wp-json\/wp\/v2\/media?parent=364"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mcm-alchimia.com\/en\/wp-json\/wp\/v2\/categories?post=364"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mcm-alchimia.com\/en\/wp-json\/wp\/v2\/tags?post=364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}