i hate thermo xD
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cb16acdc67
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@ -14,7 +14,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"execution_count": 1,
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"id": "b1dedc02-4383-4c83-b91e-80f4e8a52165",
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"metadata": {},
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"outputs": [],
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@ -290,7 +290,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"execution_count": 2,
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"id": "05f73bb9-30ef-4fce-98ef-ef1db81f393d",
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"metadata": {},
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"outputs": [
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@ -365,7 +365,7 @@
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"| Stage | Temperature | Pressure | Quality | Enthalpy | Entropy |\n",
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"| ----- |----- | ----- | ----- | -----| ----- |\n",
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"| 1 - Condenser / P1 | |2.9 psi | 0 | 108.07 BTU/lbm | 0.19869 BTU/lbm-F|\n",
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"| 2 - P1/CFWH | |2000 psi|0| 671.797 BTU/lbm| 0.86284 BTU/lbm-F |\n",
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"| 2 - P1/CFWH | |2000 psi| | | $s_2$ = $s_1$ = 0.19869 BTU/lbm-F |\n",
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"| 3 - CFHW/P2 | |155 psi| 0 | 333.42 BTU/lbm| 0.51747 BTU/lbm-F|\n",
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"| 4 - Mix/Boiler | |2000 psi|0| 671.797 BTU/lbm | 0.86284 BTU/lbm-F|\n",
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"| 5 - Boiler/HPT |752 F| 2000 psi | |1293.1 BTU/lbm| 1.42335 BTU/lbm-F |\n",
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@ -373,12 +373,8 @@
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"| 7 - Boiler/LPT |700 F|680 psi| |1346.05 BTU/lbm| 1.57063 BTU/lbm-F|\n",
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"| 8 - LPT/CFWH | |155 psi| | |$s_8$ = $s_7$ = 1.57063 BTU/lbm-F |\n",
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"| 9 - LPT/Condenser | |2.9 psi| | |$s_9$ = $s_7$ = 1.57063 BTU/lbm-F|\n",
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"| 10 - CFWH/Mix | | 2000 psi |0| 671.797 BTU/lbm | 0.86284 BTU/lbm-F|\n",
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"| 11 - P2/Mix | | 2000 psi |0| 671.797 BTU/lbm| 0.86284 BTU/lbm-F|\n",
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"\n",
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"\n",
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"\n",
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"\n"
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"| 10 - CFWH/Mix | | 2000 psi || 671.797 BTU/lbm | 0.86284 BTU/lbm-F|\n",
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"| 11 - P2/Mix | | 2000 psi | | | $s_{11}$ = $s_3$ = 0.51747 BTU/lbm-F|"
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]
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},
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{
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@ -399,7 +395,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"execution_count": 3,
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"id": "085fa335-9198-4923-86d9-efb9ac397280",
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"metadata": {},
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"outputs": [
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@ -450,71 +446,92 @@
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"metadata": {},
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"source": [
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"$$y(h_8 - h_2 - h_3 + h_{10}) = h_{10}-h_2 $$\n",
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"$$y = \\frac{h_{10}-h_2}{h_8 - h_2 - h_3 + h_{10}} $$"
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"$$y = \\frac{h_{10}-h_2}{h_8 - h_2 - h_3 + h_{10}} $$\n",
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"\n",
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"Now, we don't know $y$, $h_{11}$, $h_{10}$, or $h_2$.\n",
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"\n",
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"But we know something about the mixing chamber!\n",
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"$$ \\dot m_4 h_4 = \\dot m_{11} h_{11} + \\dot m_{10} h_{10}$$\n",
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"$$ \\dot m_7 h_4 = \\dot m_{7} y h_{11} + \\dot m_{7} (1-y) h_{10}$$\n",
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"$$ h_4 = y h_{11} + (1-y) h_{10}$$\n",
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"$$ h_4 = y h_{11} + h_{10} -y h_{10}$$\n",
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"$$ y = \\frac{h_4 - h_{10}}{h_{11} - h_{10}}$$\n",
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"\n",
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"At this point we have 4 unknowns, 2 equations. Let's look at the boiler:\n",
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"$$ Q_{boiler} = \\dot m_4 h_4 - \\dot m_5 h_5 $$\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "5bed5dc9-34a9-4aa0-b0c7-c6637ab28774",
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"id": "92c15504-e768-4766-84f8-ae20010015b4",
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"id": "5bd7f9ab-f870-425d-9dd9-757ae992c3de",
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"metadata": {},
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"source": [
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"#Find h_2\n",
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"h_2 = givens.get(2000)['hf']\n",
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"###### Find h_2\n",
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"x_2 = (givens.get(2.9)['sf'] - givens.get(2000)['sf']) / (givens.get(2000)['sg'] - givens.get(2000)['sf'])\n",
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"print(f'x_2 = {x_2:.3f}')\n",
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"h_2 = x_2 * (givens.get(2000)['hg'] - givens.get(2000)['hf']) + givens.get(2000)['hf']\n",
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"print(f'h_2 = {h_2:.3f} BTU/lbm')\n",
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"\n",
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"#Find h_10\n",
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"h_10 = givens.get(2000)['hf']\n",
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"print(f'h_2 = {h_2:.3f} BTU/lbm')\n",
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"print(f'h_10 = {h_10:.3f} BTU/lbm')\n",
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"\n",
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"#Find h_3\n",
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"h_10 = givens.get(155)['hf']\n",
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"print(f'h_2 = {h_2:.3f} BTU/lbm')\n",
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"\n"
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"h_3 = givens.get(155)['hf']\n",
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"print(f'h_3 = {h_3:.3f} BTU/lbm')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "df89be07-8172-44bf-900a-46e2108cdd9a",
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"id": "7b295ed8-207f-445b-8a60-51dbaaa7012f",
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"metadata": {},
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"source": [
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"Now we also don't know $W_{LPT}$. We need a second equation to find $y$. We get it from the closed water heater, which conserves energy between the two streams:\n",
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"\n",
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"$$ \\dot m_3 h_3 + \\dot m_{10} h_{10} = \\dot m_2 h_2 + \\dot m_8 h_8 $$\n",
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"\n",
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"But THIS equation has us going further down the rabbit hole. Must find pump works, then HPT work, then finally we can take the LPT work from that. THEN! We can find y. Things we know though:\n",
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"$$\\dot m_3 = \\dot m_7 = \\dot m_{11}$$\n",
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"$$\\dot m_{10} = \\dot m_2 = \\dot m_1 = m_9$$\n",
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"$$\\dot m_4 = \\dot m_5 = \\dot m_6 = m_7$$\n",
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"and also when looking at pumps, we can find the work done by each pump, and work done by the high pressure turbine. We find all of these, and then we can figure out what that LPT work is.\n",
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"\n",
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"**P1 Work**:\n",
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"$$W_{P1} = \\dot m_7 (1-y) (h_2 - h_1)$$\n",
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"**P2 Work**:\n",
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"$$W_{P2} = \\dot m_7 y (h_{11} - h_3)$$\n",
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"\n",
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"**Boiler Heat**:\n",
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"$$Q_{Boiler} = \\dot m_7 (h_{4} - h_5)$$\n",
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"\n",
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"**Condenser Heat**:\n",
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"$$Q_{Condenser} = \\dot m_7 (1-y) (h_9 - h_1)$$\n",
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"\n",
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"**CFWH Balance**:\n",
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"$$\\dot m_7 y (h_3 - h_7) = \\dot m_7 (1-y) (h_{10} - h_2)$$\n",
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"$$y (h_3 - h_7) = (1-y) (h_{10} - h_2)$$\n",
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"\n",
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"**HPT Work**:\n",
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"$$W_{HPT} = \\dot m_7 (h_6 - h_5)$$\n"
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"**Part B**\n",
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"$$ W_{HPT} = \\dot m_5 h_5 - \\dot m_6 h_6$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "c7c46329-0ea4-40c5-b0d8-6fd87ce57673",
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"execution_count": 17,
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"id": "4ce1da3b-82c9-492a-ae75-62bef90d9bae",
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"metadata": {},
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"outputs": [],
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"source": []
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"x_6 = 0.986\n",
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"h_6 = 1192.609 BTU/lbm\n",
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"\n",
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"=========FINAL ANSWER=========\n",
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"8b:\n",
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"W_HPT = 2.605e+07 BTU/hr\n",
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"=========FINAL ANSWER=========\n",
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"\n"
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]
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}
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],
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"source": [
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"# Find quality at 8\n",
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"x_6 = (1.42335 - givens.get(680)['sf']) / (givens.get(680)['sg'] - givens.get(680)['sf'])\n",
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"print(f'x_6 = {x_6:.3f}')\n",
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"\n",
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"# Find enthalpy at 8\n",
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"h_6 = x_6 * (givens.get(680)['hg'] - givens.get(680)['hf']) + givens.get(680)['hf']\n",
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"print(f'h_6 = {h_6:.3f} BTU/lbm')\n",
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"\n",
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"W_hpt = (72*60*60) *(1293.1 - h_6)\n",
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"answer_print('8b', f'W_HPT = {W_hpt:.3e} BTU/hr')\n",
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" "
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]
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},
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{
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"attachments": {
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@ -14,7 +14,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"execution_count": 1,
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"id": "b1dedc02-4383-4c83-b91e-80f4e8a52165",
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"metadata": {},
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"outputs": [],
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@ -290,7 +290,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"execution_count": 2,
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"id": "05f73bb9-30ef-4fce-98ef-ef1db81f393d",
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"metadata": {},
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"outputs": [
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@ -365,7 +365,7 @@
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"| Stage | Temperature | Pressure | Quality | Enthalpy | Entropy |\n",
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"| ----- |----- | ----- | ----- | -----| ----- |\n",
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"| 1 - Condenser / P1 | |2.9 psi | 0 | 108.07 BTU/lbm | 0.19869 BTU/lbm-F|\n",
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"| 2 - P1/CFWH | |2000 psi|0| 671.797 BTU/lbm| 0.86284 BTU/lbm-F |\n",
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"| 2 - P1/CFWH | |2000 psi| | | $s_2$ = $s_1$ = 0.19869 BTU/lbm-F |\n",
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"| 3 - CFHW/P2 | |155 psi| 0 | 333.42 BTU/lbm| 0.51747 BTU/lbm-F|\n",
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"| 4 - Mix/Boiler | |2000 psi|0| 671.797 BTU/lbm | 0.86284 BTU/lbm-F|\n",
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"| 5 - Boiler/HPT |752 F| 2000 psi | |1293.1 BTU/lbm| 1.42335 BTU/lbm-F |\n",
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@ -373,12 +373,8 @@
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"| 7 - Boiler/LPT |700 F|680 psi| |1346.05 BTU/lbm| 1.57063 BTU/lbm-F|\n",
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"| 8 - LPT/CFWH | |155 psi| | |$s_8$ = $s_7$ = 1.57063 BTU/lbm-F |\n",
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"| 9 - LPT/Condenser | |2.9 psi| | |$s_9$ = $s_7$ = 1.57063 BTU/lbm-F|\n",
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"| 10 - CFWH/Mix | | 2000 psi |0| 671.797 BTU/lbm | 0.86284 BTU/lbm-F|\n",
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"| 11 - P2/Mix | | 2000 psi |0| 671.797 BTU/lbm| 0.86284 BTU/lbm-F|\n",
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"\n",
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"\n",
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"\n",
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"\n"
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"| 10 - CFWH/Mix | | 2000 psi || 671.797 BTU/lbm | 0.86284 BTU/lbm-F|\n",
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"| 11 - P2/Mix | | 2000 psi | | | $s_{11}$ = $s_3$ = 0.51747 BTU/lbm-F|"
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]
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},
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{
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@ -399,7 +395,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"execution_count": 3,
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"id": "085fa335-9198-4923-86d9-efb9ac397280",
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"metadata": {},
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"outputs": [
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@ -450,71 +446,92 @@
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"metadata": {},
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"source": [
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"$$y(h_8 - h_2 - h_3 + h_{10}) = h_{10}-h_2 $$\n",
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"$$y = \\frac{h_{10}-h_2}{h_8 - h_2 - h_3 + h_{10}} $$"
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"$$y = \\frac{h_{10}-h_2}{h_8 - h_2 - h_3 + h_{10}} $$\n",
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"\n",
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"Now, we don't know $y$, $h_{11}$, $h_{10}$, or $h_2$.\n",
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"\n",
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"But we know something about the mixing chamber!\n",
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"$$ \\dot m_4 h_4 = \\dot m_{11} h_{11} + \\dot m_{10} h_{10}$$\n",
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"$$ \\dot m_7 h_4 = \\dot m_{7} y h_{11} + \\dot m_{7} (1-y) h_{10}$$\n",
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"$$ h_4 = y h_{11} + (1-y) h_{10}$$\n",
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"$$ h_4 = y h_{11} + h_{10} -y h_{10}$$\n",
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"$$ y = \\frac{h_4 - h_{10}}{h_{11} - h_{10}}$$\n",
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"\n",
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"At this point we have 4 unknowns, 2 equations. Let's look at the boiler:\n",
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"$$ Q_{boiler} = \\dot m_4 h_4 - \\dot m_5 h_5 $$\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "5bed5dc9-34a9-4aa0-b0c7-c6637ab28774",
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"id": "92c15504-e768-4766-84f8-ae20010015b4",
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"id": "5bd7f9ab-f870-425d-9dd9-757ae992c3de",
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"metadata": {},
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"source": [
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"#Find h_2\n",
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"h_2 = givens.get(2000)['hf']\n",
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"###### Find h_2\n",
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"x_2 = (givens.get(2.9)['sf'] - givens.get(2000)['sf']) / (givens.get(2000)['sg'] - givens.get(2000)['sf'])\n",
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"print(f'x_2 = {x_2:.3f}')\n",
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"h_2 = x_2 * (givens.get(2000)['hg'] - givens.get(2000)['hf']) + givens.get(2000)['hf']\n",
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"print(f'h_2 = {h_2:.3f} BTU/lbm')\n",
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"\n",
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"#Find h_10\n",
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"h_10 = givens.get(2000)['hf']\n",
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"print(f'h_2 = {h_2:.3f} BTU/lbm')\n",
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"print(f'h_10 = {h_10:.3f} BTU/lbm')\n",
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"\n",
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"#Find h_3\n",
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"h_10 = givens.get(155)['hf']\n",
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"print(f'h_2 = {h_2:.3f} BTU/lbm')\n",
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"\n"
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"h_3 = givens.get(155)['hf']\n",
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"print(f'h_3 = {h_3:.3f} BTU/lbm')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "df89be07-8172-44bf-900a-46e2108cdd9a",
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"id": "7b295ed8-207f-445b-8a60-51dbaaa7012f",
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"metadata": {},
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"source": [
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"Now we also don't know $W_{LPT}$. We need a second equation to find $y$. We get it from the closed water heater, which conserves energy between the two streams:\n",
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"\n",
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"$$ \\dot m_3 h_3 + \\dot m_{10} h_{10} = \\dot m_2 h_2 + \\dot m_8 h_8 $$\n",
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"\n",
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"But THIS equation has us going further down the rabbit hole. Must find pump works, then HPT work, then finally we can take the LPT work from that. THEN! We can find y. Things we know though:\n",
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"$$\\dot m_3 = \\dot m_7 = \\dot m_{11}$$\n",
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"$$\\dot m_{10} = \\dot m_2 = \\dot m_1 = m_9$$\n",
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"$$\\dot m_4 = \\dot m_5 = \\dot m_6 = m_7$$\n",
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"and also when looking at pumps, we can find the work done by each pump, and work done by the high pressure turbine. We find all of these, and then we can figure out what that LPT work is.\n",
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"\n",
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"**P1 Work**:\n",
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"$$W_{P1} = \\dot m_7 (1-y) (h_2 - h_1)$$\n",
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"**P2 Work**:\n",
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"$$W_{P2} = \\dot m_7 y (h_{11} - h_3)$$\n",
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"\n",
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"**Boiler Heat**:\n",
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"$$Q_{Boiler} = \\dot m_7 (h_{4} - h_5)$$\n",
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"\n",
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"**Condenser Heat**:\n",
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"$$Q_{Condenser} = \\dot m_7 (1-y) (h_9 - h_1)$$\n",
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"\n",
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"**CFWH Balance**:\n",
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"$$\\dot m_7 y (h_3 - h_7) = \\dot m_7 (1-y) (h_{10} - h_2)$$\n",
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"$$y (h_3 - h_7) = (1-y) (h_{10} - h_2)$$\n",
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"\n",
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"**HPT Work**:\n",
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"$$W_{HPT} = \\dot m_7 (h_6 - h_5)$$\n"
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"**Part B**\n",
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"$$ W_{HPT} = \\dot m_5 h_5 - \\dot m_6 h_6$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "c7c46329-0ea4-40c5-b0d8-6fd87ce57673",
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"execution_count": 17,
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"id": "4ce1da3b-82c9-492a-ae75-62bef90d9bae",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"x_6 = 0.986\n",
|
||||
"h_6 = 1192.609 BTU/lbm\n",
|
||||
"\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"8b:\n",
|
||||
"W_HPT = 2.605e+07 BTU/hr\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# Find quality at 8\n",
|
||||
"x_6 = (1.42335 - givens.get(680)['sf']) / (givens.get(680)['sg'] - givens.get(680)['sf'])\n",
|
||||
"print(f'x_6 = {x_6:.3f}')\n",
|
||||
"\n",
|
||||
"# Find enthalpy at 8\n",
|
||||
"h_6 = x_6 * (givens.get(680)['hg'] - givens.get(680)['hf']) + givens.get(680)['hf']\n",
|
||||
"print(f'h_6 = {h_6:.3f} BTU/lbm')\n",
|
||||
"\n",
|
||||
"W_hpt = (72*60*60) *(1293.1 - h_6)\n",
|
||||
"answer_print('8b', f'W_HPT = {W_hpt:.3e} BTU/hr')\n",
|
||||
" "
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user