11.6 Qualitative questions
- Page ID
- 810
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Additional Questions
1. In the analysis of the maximum temperature in the shock tube, it was assumed that process is isentropic. If this assumption is not correct would the maximum temperature obtained is increased or decreased?
2. In the analysis of the maximum temperature in the shock wave it was assumed that process is isentropic. Clearly, this assumption is violated when there are shock waves. In that cases, what is the reasoning behind use this assumption any why?
Tables of Normal Shocks, \(k=1.4\) Ideal Gas
| \(M_x\) | 1.00 | 1.05 | 1.10 | 1.15 | 1.20 | 1.25 | 1.30 | 1.35 | 1.40 | 1.45 | 1.50 | 1.55 | 1.60 | 1.65 | 1.70 | 1.75 | 1.80 | 1.85 | 1.90 | 1.95 | 2.00 | 2.05 | 2.10 | 2.15 | 2.20 | 2.25 | 2.30 | 2.35 | 2.40 | 2.45 | 2.50 | 2.75 | 3.00 | 3.25 | 3.50 | 3.75 | 4.00 | 4.25 | 4.50 | 4.75 | 5.00 | 5.25 | 5.50 | 5.75 | 6.00 | 6.25 | 6.50 | 6.75 | 7.00 | 7.25 | 7.50 | 7.75 | 8.00 | 8.25 | 8.50 | 8.75 | 9.00 | 9.25 | 9.50 | 9.75 | 10.00 |
| \(M_y\) | 1.00000 | 0.95313 | 0.91177 | 0.87502 | 0.84217 | 0.81264 | 0.78596 | 0.76175 | 0.73971 | 0.71956 | 0.70109 | 0.68410 | 0.66844 | 0.65396 | 0.64054 | 0.62809 | 0.61650 | 0.60570 | 0.59562 | 0.58618 | 0.57735 | 0.56906 | 0.56128 | 0.55395 | 0.54706 | 0.54055 | 0.53441 | 0.52861 | 0.52312 | 0.51792 | 0.51299 | 0.49181 | 0.47519 | 0.46192 | 0.45115 | 0.44231 | 0.43496 | 0.42878 | 0.42355 | 0.41908 | 0.41523 | 0.41189 | 0.40897 | 0.40642 | 0.40416 | 0.40216 | 0.40038 | 0.39879 | 0.39736 | 0.39607 | 0.39491 | 0.39385 | 0.39289 | 0.39201 | 0.39121 | 0.39048 | 0.38980 | 0.38918 | 0.38860 | 0.38807 | 0.38758 |
| \(\dfrac{T_y}{T_x}\) | 1.00000 | 1.03284 | 1.06494 | 1.09658 | 1.12799 | 1.15938 | 1.19087 | 1.22261 | 1.25469 | 1.28720 | 1.32022 | 1.35379 | 1.38797 | 1.42280 | 1.45833 | 1.49458 | 1.53158 | 1.56935 | 1.60792 | 1.64729 | 1.68750 | 1.72855 | 1.77045 | 1.81322 | 1.85686 | 1.90138 | 1.94680 | 1.99311 | 2.04033 | 2.08846 | 2.13750 | 2.39657 | 2.67901 | 2.98511 | 3.31505 | 3.66894 | 4.04688 | 4.44891 | 4.87509 | 5.32544 | 5.80000 | 6.29878 | 6.82180 | 7.36906 | 7.94059 | 8.53637 | 9.15643 | 9.80077 | 10.46939 | 11.16229 | 11.87948 | 12.62095 | 13.38672 | 14.17678 | 14.99113 | 15.82978 | 16.69273 | 17.57997 | 18.49152 | 19.42736 | 20.38750 |
| \(\dfrac{\rho_y}{\rho_x}\) | 1.00000 | 1.08398 | 1.16908 | 1.25504 | 1.34161 | 1.42857 | 1.51570 | 1.60278 | 1.68966 | 1.77614 | 1.86207 | 1.94732 | 2.03175 | 2.11525 | 2.19772 | 2.27907 | 2.35922 | 2.43811 | 2.51568 | 2.59188 | 2.66667 | 2.74002 | 2.81190 | 2.88231 | 2.95122 | 3.01863 | 3.08455 | 3.14897 | 3.21190 | 3.27335 | 3.33333 | 3.61194 | 3.85714 | 4.07229 | 4.26087 | 4.42623 | 4.57143 | 4.69919 | 4.81188 | 4.91156 | 5.00000 | 5.07869 | 5.14894 | 5.21182 | 5.26829 | 5.31915 | 5.36508 | 5.40667 | 5.44444 | 5.47883 | 5.51020 | 5.53890 | 5.56522 | 5.58939 | 5.61165 | 5.63218 | 5.65116 | 5.66874 | 5.68504 | 5.70019 | 5.71429 |
| \(\dfrac{T_y}{T_x}\) | 1.00000 | 1.11958 | 1.24500 | 1.37625 | 1.51333 | 1.65625 | 1.80500 | 1.95958 | 2.12000 | 2.28625 | 2.45833 | 2.63625 | 2.82000 | 3.00958 | 3.20500 | 3.40625 | 3.61333 | 3.82625 | 4.04500 | 4.26958 | 4.50000 | 4.73625 | 4.97833 | 5.22625 | 5.48000 | 5.73958 | 6.00500 | 6.27625 | 6.55333 | 6.83625 | 7.12500 | 8.65625 | 10.33333 | 12.15625 | 14.12500 | 16.23958 | 18.50000 | 20.90625 | 23.45833 | 26.15625 | 29.00000 | 31.98958 | 35.12500 | 38.40625 | 41.83333 | 45.40625 | 49.12500 | 52.98958 | 57.00000 | 61.15625 | 65.45833 | 69.90625 | 74.50000 | 79.23958 | 84.12500 | 89.15625 | 94.33333 | 99.65625 | 105.12500 | 110.73958 | 116.50000 |
| \(\dfrac{\rho_y}{\rho_x}\) | 1.00000 | 0.99985 | 0.99893 | 0.99669 | 0.99280 | 0.98706 | 0.97937 | 0.96974 | 0.95819 | 0.94484 | 0.92979 | 0.91319 | 0.89520 | 0.87599 | 0.85572 | 0.83457 | 0.81268 | 0.79023 | 0.76736 | 0.74420 | 0.72087 | 0.69751 | 0.67420 | 0.65105 | 0.62814 | 0.60553 | 0.58329 | 0.56148 | 0.54014 | 0.51931 | 0.49901 | 0.40623 | 0.32834 | 0.26451 | 0.21295 | 0.17166 | 0.13876 | 0.11256 | 0.09170 | 0.07505 | 0.06172 | 0.05100 | 0.04236 | 0.03536 | 0.02965 | 0.02498 | 0.02115 | 0.01798 | 0.01535 | 0.01316 | 0.01133 | 0.00979 | 0.00849 | 0.00739 | 0.00645 | 0.00565 | 0.00496 | 0.00437 | 0.00387 | 0.00343 | 0.00304 |
Contributors and Attributions
Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.