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Created October 23, 2015 03:40
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Esboço de um trabalho de Cálculo de Reatores
Raw
index.html
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<title>Cálculo de Reatores Químicos</title>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/css/bootstrap.min.css">
</head>
<body class="asciimath2jax_ignore">
<div class="container">
<h1>Beber e não dirigir</h1>
<div id="output"></div>
</div>
<script src="https://code.jquery.com/jquery-2.1.4.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery-scrollTo/2.1.0/jquery.scrollTo.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/flot/0.8.3/jquery.flot.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
showProcessingMessages: false,
tex2jax: { inlineMath: [['$','$'],['\\(','\\)']] },
"HTML-CSS": { webFont: "Asana-Math" },
TeX: { extensions: ["mhchem.js", "cancel.js"] }
});
</script>
<script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_HTMLorMML"></script>
<script>
'use strict';
var print, latex, asciimath, strong, plot;
$(function () {
var typesettingPool = $('<div>').css({
position: 'absolute',
visibility: 'hidden'
}).addClass('asciimath2jax_process').appendTo('#output');
function typeset(text, after) {
MathJax.Hub.Queue(function () {
typesettingPool.append(document.createTextNode(text));
});
MathJax.Hub.Queue(["Typeset", MathJax.Hub, typesettingPool.get(0)]);
MathJax.Hub.Queue(function () {
after(typesettingPool.contents().detach());
});
}
latex = function (code) {
return function (p) {
MathJax.Hub.Queue(function () {
typesettingPool.append(document.createTextNode('$' + code + '$'));
});
MathJax.Hub.Queue(["Typeset", MathJax.Hub]);
MathJax.Hub.Queue(function () {
p.append(typesettingPool.contents().detach());
});
};
};
asciimath = function (code) {
return function (p) {
MathJax.Hub.Queue(function () {
typesettingPool.append(document.createTextNode('`' + code + '`'));
});
MathJax.Hub.Queue(["Typeset", MathJax.Hub]);
MathJax.Hub.Queue(function () {
p.append(typesettingPool.contents().detach());
});
};
};
strong = function (text) {
return function (p) {
MathJax.Hub.Queue(function () {
$('<strong>').text(text).appendTo(p);
});
};
};
print = function () {
if (print.ignorePrint) {
return;
}
var p = $('<p>').addClass('print');
var getType = {};
Array.prototype.slice.call(arguments).forEach(function (arg) {
if (arg && getType.toString.call(arg) === '[object Function]') {
arg(p);
} else {
MathJax.Hub.Queue(function () {
$('<span>').text(arg).appendTo(p);
});
}
});
MathJax.Hub.Queue(function () {
p.appendTo('#output');
$('body').scrollTo('100%');
});
};
print.ignorePrint = false;
plot = function (series, options) {
var plot = $('<div>').addClass('plot').appendTo('#output');
plot.width('50%').height(plot.width() * 3 / 4);
$('body').scrollTo('100%');
$.plot(plot, series, options);
return new (function (plot) {
var that = this;
that.update = function (series) {
$.plot(plot, series);
};
})(plot);
};
});
</script>
<script src="programa.js"></script>
</body>
</html>
Raw
programa.js
$(function () {
print.ignorePrint = false;
var sexo = "masculino";
var idade = 25;
var massa = 125;
print(strong('Perfil da pessoa que irá beber'));
print('Sexo: ' + sexo);
print('Idade: ' + idade + ' anos');
print('Massa: ' + massa + ' kg');
print(strong('Variáveis descritas no problema'));
var x_fluido = 0;
if (idade <= 0.5) {
x_fluido = .74;
} else if (idade <= 1) {
x_fluido = .60;
} else if (idade <= 12) {
x_fluido = .60;
} else if (idade <= 18) {
x_fluido = sexo === "masculino" ? .59 : .56;
} else if (idade <= 50) {
x_fluido = sexo === "masculino" ? .59 : .50;
} else {
x_fluido = sexo === "masculino" ? .56 : .47;
}
print(latex('m = ' + massa + ' \\text{ kg}'));
print(latex('x_{fluido} = ' + x_fluido), ' (' + (x_fluido * 100).toFixed(0) + '%)');
var rho_fluido = 1.1;
print(latex('\\rho_{fluido} = ' + rho_fluido + ' \\text{ kg}\\text{ L}^{-1}'));
var V_lata = 350 / 1000.0;
print(latex('V_{\\text{lata}} = ' + V_lata + ' \\text{ L}'));
var x_alcool = 0.047;
print(latex('x_{\\text{álcool}} = ' + x_alcool), ' (' + (x_alcool * 100).toFixed(1) + '%)');
var rho_alcool = 0.789;
print(latex('\\rho_{\\text{álcool}} = ' + rho_alcool + ' \\text{ kg}\\text{ L}^{-1}'));
print(strong("Modelo proposto pelo problema"));
print(latex('$\\ce{Álcool -> Álcool\\ absorvido -> Produto}$'));
print(latex('$\\ce{A ->[k_\\text{absorção}] Ab ->[k_\\text{destruição}] P}$'));
print(latex('$(-r_{A}) = k_\\text{absorção} C_{A}$'));
print(latex('$(-r_{Ab}) = k_\\text{destruição}$'));
var k_absorcao = 10;
print(latex('k_\\text{absorção} = ' + k_absorcao + ' \\text{ h}^{-1}'));
var k_destruicao = 0.13;
print(latex('k_\\text{destruição} = ' + k_destruicao + ' \\text{ g} \\text{ L}^{-1} \\text{ h}^{-1}'));
print('Em ', latex('t = 0'), ',');
print(latex('$C_{A0} = \\frac{m_A}{V_\\text{fluido}}$'));
print(latex('$C_{Ab0} = \\frac{m_{Ab}}{V_\\text{fluido}}$'));
print(strong('Resolução do problema'));
var m_fluido = massa * x_fluido;
print(latex('$m_\\text{fluido} = m x_\\text{fluido} = ' + m_fluido + ' \\text{ kg}$'));
var V_fluido = m_fluido / rho_fluido;
print(latex('$V_\\text{fluido} = \\frac{m_\\text{fluido}}{\\rho_\\text{fluido}} = ' + V_fluido + ' \\text{ L}$'));
print(strong('a) '), 'Quanto tempo você deverá esperar para dirigir se beber duas latas de cerveja?');
print('Concentrações iniciais:');
var n_latas = 2;
print(latex('$n_\\text{latas} = ' + n_latas + '$'));
var m_A0 = n_latas * rho_alcool * V_lata;
print(latex('$m_A = n_\\text{latas} \\rho_{\\text{álcool}} V_{\\text{lata}} = ' + m_A0 + ' \\text{ kg}$'));
var C_A0 = m_A0 / V_fluido;
print(latex('$C_{A0} = \\frac{m_A}{V_\\text{fluido}} = ' + C_A0 + ' \\text{ kg}/ \\text{L}^{-1}$'));
var C_Ab0 = 0;
print(latex('$C_{Ab0} = ' + C_Ab0 + ' \\text{ kg}/ \\text{L}^{-1}$'));
var C_P0 = 0;
print(latex('$C_{P0} = ' + C_P0 + ' \\text{ kg}/ \\text{L}^{-1}$'));
print('Taxas de reação:');
var r_A = function (C_A, C_Ab) {
return -k_absorcao * C_A;
};
print(latex('$r_A = -k_\\text{absorção} C_A$'));
var r_Ab = function (C_A, C_Ab) {
return k_absorcao * C_A - (C_Ab > 0 ? k_destruicao : 0);
};
print(latex('$r_{Ab} = k_\\text{absorção} C_A - k_\\text{destruição} {C_{Ab}}^0$'));
var r_P = function (C_A, C_Ab) {
return (C_Ab > 0 ? k_destruicao : 0);
};
print(latex('$r_P = k_\\text{destruição} {C_{Ab}}^0$'));
print('Obs: ', latex('{C_{Ab}}^0 = 0'), ' quando ', latex('C_{Ab} = 0'), ', isto é, a função é descontínua apenas em ', latex('C_{Ab} = 0'), '.');
print('Balanço material:');
print('Não há gradiente de concentração de álcool no organismo ', latex('\\rightarrow'), ' tanque agitado');
print('Não há taxa de entrada ou saída de componentes ', latex('\\rightarrow'), ' regime de batelada');
print(latex('$\\frac{dm_i}{dt} = \\cancelto{0}{F_{i0}} - \\cancelto{0}{F_{i}} + \\cancelto{r_i\\int_{V_\\text{fluido}}{dV}}{\\int_{V_\\text{fluido}}{r_i dV}}$'));
print(latex('$\\frac{dm_i}{dt} = r_i V_\\text{fluido}$'));
print(latex(
'$\\frac{dm_i}{dt} = ' +
'\\frac{d}{dt}\\left[C_i V_\\text{fluido}\\right] = ' +
'C_i\\cancelto{0}{\\frac{dV_\\text{fluido}}{dt}} + V_\\text{fluido}\\frac{dC_i}{dt} = ' +
'V_\\text{fluido}\\frac{dC_i}{dt}$'
));
print(latex('$\\cancel{V_\\text{fluido}}\\frac{dC_i}{dt} = r_i \\cancel{V_\\text{fluido}}$'));
print(latex('$\\frac{dC_i}{dt} = r_i$'));
print(latex('$dC_i = r_i dt$'));
print(latex('$\\int_{C_{i0}}^{C_i}{dC_{i}} = \\int_{0}^{t}{r_i dt}$'));
print(latex('$C_i - C_{i0} = \\int_{0}^{t}{r_i dt}$'));
print(latex('$C_i = C_{i0} + \\int_{0}^{t}{r_i dt}$'));
print(latex('$C_A = C_{A0} - k_\\text{absorção} \\int_{0}^{t}{C_A dt}$'));
print(latex('$C_{Ab} = C_{Ab0} + k_\\text{absorção} \\int_{0}^{t}{C_A dt} - k_\\text{destruição}\\int_{0}^{t}{{C_{Ab}}^0 dt}$'));
print(latex('$C_P = C_{P0} + k_\\text{destruição}\\int_{0}^{t}{{C_{Ab}}^0 dt}$'));
print('Resolução pelo método de Euler:');
var dt = .0001;
print(latex('$dt \\approx \\Delta t = ' + dt + ' \\text{ h}$'));
print(latex('$t = k \\Delta t$'));
print(latex('$C_i(t) = C_i(k \\Delta t) \\approx {C_i}_k$'));
print(latex('$\\Delta {C_i}_k = {C_i}_{k + 1} - {C_i}_k = r_i \\Delta t$'));
print(latex('${C_i}_{k + 1} = {C_i}_k + \\Delta {C_i}_k$'));
print(latex('$\\Delta {C_A}_k = - k_\\text{absorção} {C_A}_k \\Delta t$'));
print(latex('$\\Delta {C_{Ab}}_k = k_\\text{absorção} {C_A}_k \\Delta t - k_\\text{destruição}{{C_{Ab}}_k}^0 \\Delta t$'));
print(latex('$\\Delta {C_P}_k = k_\\text{destruição}{{C_{Ab}}_k}^0 \\Delta t$'));
var C_Ak = C_A0;
var C_Abk = C_Ab0;
var C_Pk = C_P0;
print.ignorePrint = false;
var plotSeries = [ [[0, C_A0]], [[0, C_Ab0]], [[0, C_P0]] ];
var plotConcentracoes = plot(plotSeries);
var k = 0;
dt = .001;
var f = function () {
C_Ak_1 = C_Ak + r_A(C_Ak, C_Abk) * dt;
C_Abk_1 = C_Abk + r_Ab(C_Ak, C_Abk) * dt;
C_Pk_1 = C_Pk + r_P(C_Ak, C_Abk) * dt;
++k;
plotSeries[0].push([k * dt, C_Ak_1]);
plotSeries[1].push([k * dt, C_Abk_1]);
plotSeries[2].push([k * dt, C_Pk_1]);
plotConcentracoes.update(plotSeries);
if (C_Ak_1 > 1e-9) {
C_Ak = C_Ak_1;
C_Abk = C_Abk_1;
C_Pk = C_Pk_1;
setTimeout(f, 100);
}
};
f();
});
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