{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 4.11 – Practice Problem 2\n", "\n", "\n", "## Saturated Steam table B.6\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Pressure (bar)Temperature (C)Volume (l, m3/kg)Volume (v, m3/kg)Internal Energy (l, kJ/kg)Internal Energy (v, kJ/kg)Enthalpy (l, kJ/kg)Enthalpy (v, kJ/kg)
255.5155.460.0010970.34260655.162563.9655.762752.3
266.0158.830.0011010.31558669.722566.8670.382756.1
276.5161.980.0011040.29259683.362569.4684.082759.6
287.0164.950.0011080.27277696.232571.8697.002762.8
297.5167.750.0011110.25551708.402574.0709.242765.6
308.0170.410.0011150.24034719.972576.0720.862768.3
318.5172.940.0011180.22689731.002577.9731.952770.8
329.0175.350.0011210.21489741.552579.6742.562773.0
339.5177.660.0011240.20410751.672581.2752.742775.1
3410.0179.880.0011270.19436761.392582.7762.522777.1
3510.5182.010.0011300.18552770.752584.1771.942778.9
3611.0184.060.0011330.17745779.782585.5781.032780.6
3711.5186.040.0011360.17006788.512586.7789.822782.2
3812.0187.960.0011380.16326796.962587.8798.332783.7
\n", "
" ], "text/plain": [ " Pressure (bar) Temperature (C) Volume (l, m3/kg) Volume (v, m3/kg) \\\n", "25 5.5 155.46 0.001097 0.34260 \n", "26 6.0 158.83 0.001101 0.31558 \n", "27 6.5 161.98 0.001104 0.29259 \n", "28 7.0 164.95 0.001108 0.27277 \n", "29 7.5 167.75 0.001111 0.25551 \n", "30 8.0 170.41 0.001115 0.24034 \n", "31 8.5 172.94 0.001118 0.22689 \n", "32 9.0 175.35 0.001121 0.21489 \n", "33 9.5 177.66 0.001124 0.20410 \n", "34 10.0 179.88 0.001127 0.19436 \n", "35 10.5 182.01 0.001130 0.18552 \n", "36 11.0 184.06 0.001133 0.17745 \n", "37 11.5 186.04 0.001136 0.17006 \n", "38 12.0 187.96 0.001138 0.16326 \n", "\n", " Internal Energy (l, kJ/kg) Internal Energy (v, kJ/kg) \\\n", "25 655.16 2563.9 \n", "26 669.72 2566.8 \n", "27 683.36 2569.4 \n", "28 696.23 2571.8 \n", "29 708.40 2574.0 \n", "30 719.97 2576.0 \n", "31 731.00 2577.9 \n", "32 741.55 2579.6 \n", "33 751.67 2581.2 \n", "34 761.39 2582.7 \n", "35 770.75 2584.1 \n", "36 779.78 2585.5 \n", "37 788.51 2586.7 \n", "38 796.96 2587.8 \n", "\n", " Enthalpy (l, kJ/kg) Enthalpy (v, kJ/kg) \n", "25 655.76 2752.3 \n", "26 670.38 2756.1 \n", "27 684.08 2759.6 \n", "28 697.00 2762.8 \n", "29 709.24 2765.6 \n", "30 720.86 2768.3 \n", "31 731.95 2770.8 \n", "32 742.56 2773.0 \n", "33 752.74 2775.1 \n", "34 762.52 2777.1 \n", "35 771.94 2778.9 \n", "36 781.03 2780.6 \n", "37 789.82 2782.2 \n", "38 798.33 2783.7 " ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "df = pd.read_excel('../figures/Module-4/Sat-steam-p-int1.xlsx', sheet_name='Sheet2', index_col=None, na_values=['NA'])\n", "df.truncate(before = 25, after = 38)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Excerpt off steam table of B.7" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Temperature (C)Pressure (bar)Volume (m3/kg)Internal Energy (kJ/kg)Enthalpy (kJ/kg)Entropy (J/g*K)
050.00100.001012209.18210.190.70335
1100.00100.001043418.80419.841.30650
2150.00100.001090631.41632.501.84120
3179.88100.001127761.39762.522.13810
4179.88100.1943602582.702777.106.58500
5200.00100.2060202622.202828.306.69550
6250.00100.2327502710.402943.106.92650
7300.00100.2579902793.603051.607.12460
8350.00100.2825002875.703158.207.30290
\n", "
" ], "text/plain": [ " Temperature (C) Pressure (bar) Volume (m3/kg) Internal Energy (kJ/kg) \\\n", "0 50.00 10 0.001012 209.18 \n", "1 100.00 10 0.001043 418.80 \n", "2 150.00 10 0.001090 631.41 \n", "3 179.88 10 0.001127 761.39 \n", "4 179.88 10 0.194360 2582.70 \n", "5 200.00 10 0.206020 2622.20 \n", "6 250.00 10 0.232750 2710.40 \n", "7 300.00 10 0.257990 2793.60 \n", "8 350.00 10 0.282500 2875.70 \n", "\n", " Enthalpy (kJ/kg) Entropy (J/g*K) \n", "0 210.19 0.70335 \n", "1 419.84 1.30650 \n", "2 632.50 1.84120 \n", "3 762.52 2.13810 \n", "4 2777.10 6.58500 \n", "5 2828.30 6.69550 \n", "6 2943.10 6.92650 \n", "7 3051.60 7.12460 \n", "8 3158.20 7.30290 " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "df = pd.read_excel('../figures/Module-4/superheated-team-p10.xlsx', sheet_name='Sheet2', index_col=None, na_values=['NA'])\n", "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Modified question of 7.35\n", "\n", "\n", "Problem Statement\n", "\n", "A turbine discharges 200 kg/h of saturated steam at 10.0 bar absolute. It is desired to generate steam at 300 C and 10.0 bar by mixing the turbine discharge with a second stream of superheated steam of 350 C and 10.0 bar.\n", "\n", "- If 300 kg/h of the product steam is to be generated, how much heat must be added to the mixer?\n", "- If instead the mixing is carried out adiabatically, at what rate is the product steam generated?\n", "\n", "Preamble: This question is relatively basic and engages you on how to use the steam tables. Heat is covered in-depth in the next module but for now, you can consider the question as, how much more __enthalpy__ is needed to be added to the mixer.\n", "\n", "1. Draw a diagram of the process taking place and write the relevant equation:\n", " \n", " \n", "![](../figures/Module-4/question1.svg)\n", "\n", "\n", "$$\\dot{m_1}H_1 + \\dot{m_2}H_2 = \\dot{m_3}H_3$$\n", "\n", "$$ H = Q -W \\space or \\space H_{total} = \\sum {H} $$\n", "\n", "2. List simplifications and assumptions\n", " - As mentioned above, treat heat as enthalpy.\n", " - If you have read into module 5; then assume work is negligable.\n", "\n", "3. List known values \n", " - Input Stream 1: \n", " - $\\dot{m_1} = 200\\frac{kg}{hr}$\n", " - $H_1 = 762.5 \\frac{kj}{kg}$\n", " - Input Stream 2: \n", " - $\\dot{m_2} = ?$\n", " - $H_2 = 3051.6 \\frac{kj}{kg}$ From steam table B.6\n", " - Output Stream 3: \n", " - $\\dot{m_3} = ?$\n", " - $H_3 = 3158.2 \\frac{kj}{kg}$ From steam table B.7\n", " \n", "4. Solve the equations.\n", " In part i) we are given the total mass flow rate $\\dot{m_3}$ So we can solve for $\\dot{m_2}$ using conservation of mass. \n", " \n", " $$ 300 = 200 + \\dot {m_2} $$ \n", " \n", " Using this value we plug into the __first half__ of the energy balance\n", " \n", " $$200\\frac{kg}{hr} \\cdot 762.5 \\frac{kj}{kg} + 100\\frac{kg}{hr} \\cdot 3051.6 \\frac{kj}{kg} = 457660 \\frac{kj}{hr}$$ \n", " \n", " Since we want the exit stream at 350 C we need to check to see if the enthalpy we obtained corresponds with the desired enthalpy in the exit stream.\n", " \n", " $$ \\dot{m_3}\\cdot H_3 = 300\\frac{kg}{hr} \\cdot 3158.2 \\frac{kj}{kg} = 947460 \\frac{kj}{hr} $$\n", " \n", " It Doesn't correspond. There is missing energy that needs to be added. This is simple addition: \n", " \n", " $$ Energy\\space Needed = 947460 \\frac{kj}{hr} - 457660 \\frac{kj}{hr} = 489800 \\frac {kj}{hr}$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }