{"id":3779,"date":"2018-02-09T08:21:49","date_gmt":"2018-02-09T13:21:49","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1013\/?p=3779"},"modified":"2026-04-05T21:03:20","modified_gmt":"2026-04-06T02:03:20","slug":"s3eva2017ti_t3-sustancia-en-lago","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-s3eva20\/s3eva2017ti_t3-sustancia-en-lago\/","title":{"rendered":"s3Eva2017TI_T3 Sustancia en lago"},"content":{"rendered":"\n<p><em><strong>Ejercicio<\/strong><\/em>: <a href=\"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-3eva20\/3eva2017ti_t3-sustancia-en-lago\/\" data-type=\"post\" data-id=\"968\">3Eva2017TI_T3 Sustancia en lago<\/a><\/p>\n\n\n\n<p>El ejercicio se divide en dos partes: secci\u00f3n transversal con la derivada y concentraci\u00f3n promedio con integrales.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Secci\u00f3n transversal<\/h4>\n\n\n\n<p>Se calcula la derivada con&nbsp; una aproximaci\u00f3n b\u00e1sica con error O(h)<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> f'(x_i) = \\frac{f(x_{i+1})-f(x_i)}{h} + O(h) <\/span>\n\n\n\n<p>repitiendo la f\u00f3rmula entre cada par de puntos consecutivos<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>dv\/dz: &#091;-1.1775  -0.7875  -0.39175 -0.09825  0.     ]<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"530\" height=\"415\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2017\/12\/SustanciaLago01.png\" alt=\"SustanciaLago01\" class=\"wp-image-17667\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Concentraci\u00f3n promedio<\/h2>\n\n\n\n<p>Para los integrales usamos la regla del trapecio:<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> I = (b-a) \\frac{f(a)+f(b)}{2}<\/span>\n\n\n\n<pre class=\"wp-block-code\"><code>numerador:  224.38960000000003\ndenominador:  29.852\nconcentracion promedio:  7.516735897092323<\/code><\/pre>\n\n\n\n<p>Aplicando los algoritmos en Python para todos los puntos:<\/p>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: plain; title: ; notranslate\" title=\"\">\n# 3Eva_IT2017_T3 Sustancia en lago\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n# INGRESO\nzi = np.array(&#x5B;0.  , 4   , 8   , 12    , 16])\nvi = np.array(&#x5B;9.82, 5.11, 1.96,  0.393,  0.])\nci = np.array(&#x5B;10.2, 8.5 , 7.4 ,  5.2  ,  4.1])\n\n# PROCEDIMIENTO\nn = len(zi)\n# primera derivada hacia adelante con error O(h)\ndv = np.zeros(n,dtype=float)\nfor i in range(0,n-1,1):\n    h = zi&#x5B;i+1]-zi&#x5B;i]\n    dv&#x5B;i]=(vi&#x5B;i+1]-vi&#x5B;i])\/h\n\nAs = -dv*zi\n\n# integrales por rect\u00e1ngulo\nnumerador = 0\nfor i in range(0,n-1,1):\n    altura = (ci&#x5B;i]*As&#x5B;i]+ci&#x5B;i+1]*As&#x5B;i+1])\/2\n    numerador = numerador +altura*(zi&#x5B;i+1]-zi&#x5B;i])\n\ndenominador = 0\nfor i in range(0,n-1,1):\n    altura = (As&#x5B;i]+As&#x5B;i+1])\/2\n    denominador = denominador +altura*(zi&#x5B;i+1]-zi&#x5B;i])\n\ncpromedio = numerador\/denominador\n\n# SALIDA\nprint('dv\/dz: ')\nprint(dv)\nprint('numerador: ',numerador)\nprint('denominador: ',denominador)\nprint('concentracion promedio: ',cpromedio)\n\n# Grafica\nplt.subplot(121)\nplt.plot(zi,vi)\nplt.plot(zi,vi,'bo')\nplt.xlabel('profundidad z')\nplt.ylabel('Volumen')\nplt.grid()\nplt.subplot(122)\nplt.plot(zi,ci, color = 'orange')\nplt.plot(zi,ci,'ro')\nplt.xlabel('profundidad z')\nplt.ylabel('concentraci\u00f3n')\nplt.grid()\nplt.show()\n<\/pre><\/div>\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2018\/02\/sustancialago02.png\" alt=\"sustancia lago 02\" class=\"wp-image-18585\" \/><\/figure>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ejercicio: 3Eva2017TI_T3 Sustancia en lago El ejercicio se divide en dos partes: secci\u00f3n transversal con la derivada y concentraci\u00f3n promedio con integrales. Secci\u00f3n transversal Se calcula la derivada con&nbsp; una aproximaci\u00f3n b\u00e1sica con error O(h) repitiendo la f\u00f3rmula entre cada par de puntos consecutivos Concentraci\u00f3n promedio Para los integrales usamos la regla del trapecio: Aplicando [&hellip;]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-mn-ejemplo","format":"standard","meta":{"footnotes":""},"categories":[51],"tags":[58,54],"class_list":["post-3779","post","type-post","status-publish","format-standard","hentry","category-mn-s3eva20","tag-ejemplos-python","tag-mnumericos"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/3779","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=3779"}],"version-history":[{"count":5,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/3779\/revisions"}],"predecessor-version":[{"id":23933,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/3779\/revisions\/23933"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=3779"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=3779"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=3779"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}