{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "*This notebook contains course material from [CBE20255](https://jckantor.github.io/CBE20255)\n", "by Jeffrey Kantor (jeff at nd.edu); the content is available [on Github](https://github.com/jckantor/CBE20255.git).\n", "The text is released under the [CC-BY-NC-ND-4.0 license](https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode),\n", "and code is released under the [MIT license](https://opensource.org/licenses/MIT).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Energy Balances for a Steam Turbine](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/08.04-Energy-Balances-for-a-Steam-Turbine.ipynb) | [Contents](toc.ipynb) | [Adiabatic Flame Temperature](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/08.06-Adiabatic-Flame-Temperature.ipynb) >
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Humidity and Psychrometrics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "Psychrometrics is the study of the physical and thermodynamic properties of air and water vapor mixtures. Psychrometrics has a wide range of drying, humidification, weather, and environmental applications. The same principles, however, apply to any mixture of a condensable vapor mixed with non-condensable gase." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![20160618_090132.jpg](https://raw.githubusercontent.com/jckantor/CBE20255/master/notebooks/figures/20160618_090132.jpg?raw=true)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Definitions of Humidity\n", "\n", "The familiar definitions of mass and mole fraction, of course, apply to a mixture of a vapor and condensable gas. But there are also additional methods for expressing composition and the relative amount of the condensable component.\n", "\n", "For the definitions below, we will use $A$ to represent the non-condensable component (typically air), and $W$ to denote the condensable component (typically water)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Relative Humidity\n", "\n", "Relative humidity (symbol RH or $\\phi$) is the ratio of the partial pressure of water vapor to the equilibrium saturation pressure. \n", "\n", "$$\\mbox{Relative Humidity} = RH = \\phi = \\frac{p_W}{p^{sat}_W(T)}$$\n", "\n", "Relative humidity depends on temperature and, for mixtures of fixed composition, pressure. It is commonly expressed as a percentage." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Absolute Humidity\n", "\n", "Absolute humidity (symbol AH) is the total mass of water vapor per unit volume of humid air. \n", "\n", "$$\\mbox{Absolute Humidity} = AH = \\frac{m_W}{V}$$\n", "\n", "Typical units are $kg/m^3$ or $g/m^3$. Absolute humidity is useful for expressing how much water is present in a given volume at a particular pressure and temperature. However, because volume varies with temperature and pressure, volumetric measures are generally not used directly in mass and energy balances.\n", "\n", "Assuming the ideal gas law holds, the mass of water in a given volume is\n", "\n", "$$AH = \\frac{m_W}{V} \\approx \\frac{M_W p_W}{RT} \\approx \\frac{M_W y_W P}{RT}$$\n", "\n", "where $M_W$ is the molar mass of water, $p_W$ is the partial pressure, and $y_W$ is mole fraction. For a given mixture, increasing pressure compresses the mixture into a smaller volume and therefore increases absolute humidity. Conversely, increasing temperature expands the volume and therefore descreases absolute humidity. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Specific Humidity\n", "\n", "Specific Humidity (symbol SH) is the mass of water divided by total mass of moist air. \n", "\n", "$$\\mbox{Specific Humidity} = SH = \\frac{m_W}{m_A + m_W}$$\n", "\n", "This is equivalent to mass fraction. While this would work for a variety of applications, the resulting calculations are more complicated than necessay for the majority of cases where the mass flow of dry air is often constant. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mixing Ratio (or Moisture Content, or Humidity Ratio)\n", "\n", "Mixing Ratio (or Moisture Content) (symbol $w$) is ratio of the mass of water vapor to the mass of dry air.\n", "\n", "$$\\mbox{Mixing Ratio} = w = \\frac{m_W}{m_A}$$\n", "\n", "Typical units are kg of water per kg of dry air. (Older literature will sometimes show units of grains of water per pound of dry air. There are 7000 grains per pound.)\n", "\n", "Mixing ratio is the most commonly encountered measure of humidity because of it's computational utility in humidifciation and drying applications.\n", "\n", "From the ideal gas law\n", "\n", "$$m_W = \\frac{M_W p_W v}{RT}$$\n", "\n", "and\n", "\n", "$$m_A = \\frac{M_A p_A v}{RT} = \\frac{M_A (P-p_W) v}{RT}$$\n", "\n", "Taking the ratio\n", "\n", "$$w = \\frac{m_W}{m_A} = \\frac{M_W}{M_A} \\frac{p_W}{P - p_W} = \\frac{\\omega p_W}{P - p_W}$$\n", "\n", "where $\\omega = \\frac{M_W}{M_A} = 0.622$ is the ratio of molar masses. At saturation the mixing ratio is\n", "\n", "$$w_{sat}(T,P) = \\frac{\\omega p_W^{sat}(T)}{P - p_W^{sat}(T)}$$\n", "\n", "For a relative humidity $\\phi$, the mixing ratio is\n", "\n", "$$w(T,P,\\phi) = \\frac{\\omega \\phi p_W^{sat}(T)}{P - \\phi p_W^{sat}(T)}$$\n", "\n", "This expression demonstrates that the mixing ratio depends on temperature, pressure, and relative humidity." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dew Point\n", "\n", "The dew point (symbol $T_{dew}$) is the temperature at which the first drop of dew is formed when air is cooled at constant pressure. It is an indirect measure of moisture content." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data Sources" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Molar Masses of Air and Water" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Molar Mass of Air = 28.97\n", "Molar Mass of Water = 18.02\n", "Ratio Mw/Ma = 0.6219\n" ] } ], "source": [ "Ma = 0.78*(2*14.00675) + 0.21*(2*15.994) + 0.01*39.948\n", "print(\"Molar Mass of Air = {0:0.2f}\".format(Ma))\n", "\n", "Mw = 2*1.00794 + 15.9994\n", "print(\"Molar Mass of Water = {0:0.2f}\".format(Mw))\n", "\n", "print(\"Ratio Mw/Ma = {0:0.4f}\".format(Mw/Ma))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Vapor Pressure of Water\n", "\n", "There are a number of widely used correlations for the vapor pressure of water, among them Antoine's equation, Goff-Gratch equation, and the Arden Buck equation. The following cell implements correlations recommended by [Wagner and Pruß](http://thermophysics.ru/pdf_doc/IAPWS_1995.pdf) for the IAPWS 1995 Steam Tables.\n", "\n", "For the range 0 $^\\circ$C to 373 $^\\circ$C, the vapor pressure of liquid water is given by\n", "\n", "$$\\ln\\frac{p^{sat}_w}{p_c} = \\frac{T_c}{T}\\left(a_1\\vartheta + a_2\\vartheta^{1.5}\n", "+ a_3\\vartheta^3 + a_4\\vartheta^{3.5} + a_5\\vartheta^4 + a_6\\vartheta^{7.5}\\right)$$\n", "\n", "where \n", "\n", "$$\\vartheta = 1 - \\frac{T}{T_c}$$\n", "\n", "and $T_c = 647.096\\,K$ and $P_c = 220.640$ bar are the temperature and pressure at the critical point. For the range -100 $^\\circ$C to 0.01 $^\\circ$C, the vapor pressure of ice is calculated using \n", "\n", "$$\\ln\\frac{p^{sat}_w}{p_n} = b_0(1 - \\theta^{-1.5}) + b_1(1-\\theta^{-1.25})$$\n", "\n", "where\n", "\n", "$$\\theta = \\frac{T}{T_n}$$\n", "\n", "and $T_n = 0.01 ^\\circ$C and $p_n = 0.00611657\\,bar$ are the triple point temperature and pressure. These correlations assume temperature in Kelvin, and returns pressure in the same units at $p_c$ and $p_n$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", 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