13. At the AQWA facility in Hillarys, patrons view the marine life while walking through a tunnel formed by a semi-cylinder transparent wall, as illustrated below. The aquarium contains sea water (Specific Gravity 1.025), and the highest point of the transparent wall lies 6 metres below the water surface. The water may be regarded as being stationary. The transparent wall is comprised of a series of 5 m long sections. If a section of the glass wall is 2.0 metres in radius (to the outer surface of the glass) and 5 metres long, determine (a) The maximum (absolute) pressure acting on the transparent wall (in Pa) (b) The magnitude (in N) and direction of the force exerted on each individual 5 metre long section of the transparent wall by the water (do not consider the vertical solid sections of wall at the sides of the tunnel). H=6.0 m R=2.0m Table E.1 Lennard-Jones (6-12) Potential Parameters and Critical Properties Lennard-Jones parameters Critical properties Molecular Weight E/K Substance M () (K) Ref. T (K) Pc V (atm) (cm/g-mole) MX 106 (g/cms) k, x 10% (cal/cm.s.K) Light gases: H 2.016 2.915 38.0 a 33.3 12.80 65.0 34.7 He 4.003 2.576 10.2 a 5.26 2.26 57.8 25.4 Noble gases: Ne 20.180 2.789 35.7 a 44.5 26.9. 41.7 156. 79.2 Ar 39.948 3.432 122.4 b 150.7 48.0 75.2 264. 71.0 Kr 83.80 3.675 170.0 b 209.4 54.3 92.2 396. 49.4 Xe 131.29 4.009 234.7 b 289.8 58.0 118.8 490. 40.2 Simple polyatomic gases: Air N 28.964' 3.617 97.0 a 132.4' 37.0' 86.7 193. 90.8 28.013 3.667 99.8 b 126.2 33.5 90.1 180. 86.8 31.999 3.433 113. a 154.4 49.7 74.4 250. 105.3 28.010 3.590 110. a 132.9 34.5 93.1 190. 86.5 44.010 3.996 190. a 304.2 72.8 94.1 343. 122. NO 30.006 3.470 119. a 180. 64. 57. 258. 118.2 NO 44.012 3.879 220. a 309.7 71.7 96.3 332. 131. SO 64.065 4.026 363. C 430.7 77.8 122. 411. 98.6 F 37.997 3.653 112. a - - - - Cl 70.905 4.115 357. a 417. 76.1 124. Br 159.808 4.268 520. a 584. 102. 144. 420. 97.0 I, 253.809 4.982 550. a 800. - Hydrocarbons: CH 16.04 3.780 154. b 191.1 45.8 98.7 159. CH=CH 26.04 4.114 212. d 308.7 61.6 112.9 237. CH2=CH2 28.05 4.228 216. b 282.4 50.0 124. 215. CH6 30.07 4.388 232. b 305.4 48.2 148. 210. CH,C=CH 40.06 4.742 261. d 394.8 CHCH=CH2 42.08 4.766 275. b 365.0 45.5 181. 233. CHB 44.10 4.934 273. b 369.8 41.9 200. 228. n-CH10 58.12 5.604 304. b 425.2 37.5 255. 239. | |g | | | | 158. i-C4H10 58.12 5.393 295. b 408.1 36.0 263. 63% 11-C5H12 72.15 5.850 326. b 469.5 33.2. 311. 238. i-C5H12 72.15 5.812 327. b 460.4 33.7 306. C(CH3)4 72.15 5.759 312. b 433.8 31.6 303. n-C6H14 86.18 6.264 342. b 507.3 29.7 370. 248. n-C7H16 100.20 6.663 352. b 540.1 27.0 432. 254. 11-C8H18 114.23 7.035 361. b 568.7 24.5 492 259. n-CH20 128.26 7.463 351. b 594.6 22.6 548. 265. Cyclohexane 84.16 6.143 313. d 553. 40.0 308. 284. Benzene 78.11 5.443 387. b 562.6 48.6 260. 312. Other organic compounds: CH 16.04 3.780 154. b 191.1 45.8 98.7 159. 158. CHCl 50.49 4.151 355. 416.3 65.9 143. 338. CH2Cl 84.93 4.748 398. 510. 60. - CHCl3 119.38 5.389 340. e 536.6 54. 240. 410. CC14 153.82 5.947 323. e 556.4 45.0 276. 413. CN 52.034 4.361 349. e 400. 59. 60.076 4.130 336. e 378. 61. CS 76.143 4.483 467. e 552. 78. 170. 404. CClF 120.91 5.116 280. b 384.7 39.6 218. *J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, corrected printing with notes added, Wiley, New York (1964). L. S. Tee, S. Gotoh, and W. E. Stewart, Ind. Eng. Chem. Fundamentals, 5, 356-363 (1966). The values for benzene are from viscosity data on that substance. The values for other substances are computed from Correlation (iii) of the paper. L. Monchick and E. A. Mason, J. Chem. Phys., 35, 1676-1697 (1961); parameters obtained from viscosity. d L. W. Flynn and G. Thodos, AIChE Journal, 8, 362-365 (1962); parameters obtained from viscosity. R. A. Svehla, NASA Tech. Report R-132 (1962); parameters obtained from viscosity. This report provides extensive tables of Lennard-Jones parameters, heat capacities, and calculated transport properties. Values of the critical constants for the pure substances are selected from K. A. Kobe and R. E. Lynn, Jr., Chem. Rev., 52, 117-236 (1962); Amer. Petroleum Inst. Research Proj. 44, Thermodynamics Research Center, Texas A&M University, College Station, Texas (1966); and Thermodynamic Functions of Gases, F. Din (editor), Vols. 1-3, Butterworths, London (1956, 1961, 1962). Values of the critical viscosity are from O. A. Hougen and K. M. Watson, Chemical Process Principles, Vol. 3, Wiley, New York (1947), p. 873. "Values of the critical thermal conductivity are from E. J. Owens and G. Thodos, AIChE Journal, 3, 454-461 (1957). For air, the molecular weight M and the pseudocritical properties have been computed from the average composition of dry air as given in COESA, U.S. Standard Atmosphere 1976, U.S. Government Printing Office, Washington, D.C. (1976). Table E.2 Collision Integrals for Use with the Lennard-Jones (6-12) Potential for the Prediction of Transport Properties of Gases at Low Densities" 2 = 1 KT/B or (for viscosity and thermal KT/e (for or KT/BAB conductivity) diffusivity) KT/BAB (for viscosity and thermal conductivity) (for diffusivity) 0.30 2.840 2.649 2.7 1.0691 0.9782 0.35 2.676 2.468 2.8 1.0583 0.9682 0.40 2.531 2.314 2.9 1.0482 0.9588 0.45 2.401 2.182 3.0 1.0388 0.9500 0.50 2.284 2.066 3.1 1.0300 0.9418 0.55 2.178 1.965 3.2 1.0217 0.9340 0.60 2.084 1.877 3.3 1.0139 0.9267 0.65 1.999 1.799 3.4 1.0066 0.9197 0.70 1.922 1.729 3.5 0.9996 0.9131 0.75 1.853 1.667 3.6 0.9931 0.9068 0.80 1.790 1.612 3.7 0.9868 0.9008 0.85 1.734 1.562 3.8 0.9809 0.8952 0.90 1.682 1.517 3.9 0.9753 0.8897 0.95 1.636 1.477 4.0 0.9699 0.8845 1.00 1.593 1.440 4.1 0.9647 0.8796 1.05 1.554 1.406 4.2 0.9598 0.8748 1.10 1.518 1.375 4.3 0.9551 0.8703 1.15 1.485 1.347 4.4 0.9506 0.8659 1.20 1.455 1.320 4.5 0.9462 0.8617 1.25 1.427 1.296 4.6 0.9420 0.8576 1.30 1:401 1.274 4.7 0.9380 0.8537 1.35 1.377 1.253 4.8 0.9341 0.8499 1.40 1.355 1.234 4.9 0.9304 0.8463 1.45 1.334 1.216 5.0 0.9268 0.8428 1.50 1.315 1.199 6.0 0.8962 0.8129 1.55 1.297 1.183 7.0 0.8727 0.7898 1.60 1.280 1.168 8.0 0.8538 0.7711 1.65 1.264 1.154 9.0 0.8380 0.7555 1.70 1.249 1.141 10.0 0.8244 0.7422 1.75 1.235 1.128 12.0 0.8018 0.7202 1.80 1.222 1.117 14.0 0.7836 0.7025 1.85 1.209 1.105 16.0 0.7683 0.6878 1.90 1.198 1.095 18.0 0.7552 0.6751 198 1,186 1.085 20.0 0.7436 0.6640 2.00 1.176 1.075 25.0 0.7198 0.6414 2.10 1.156 1.058 30.0 0.7010 0.6235 2.20 1.138 1.042 35.0 0.6854 0.6088 2.30 1.122 1.027 40.0 0.6723 0.5964 2.40 1.107 1.013 50.0 0.6510 0.5763 2.50 1.0933 1.0006 75.0 0.6140 0.5415 2.60 1.0807 0.9890 100.0 0.5887 0.5180 "The values in this table, applicable for the Lennard-Jones (6-12) potential, are interpolated from the results of L. Monchick and E. A. Mason, J. Chem. Phys., 35, 1676-1697 (1961). The Monchick-Mason table is believed to be slightly better than the earlier table by J. O. Hirschfelder, R. B. Bird, and E. L. Spotz, J. Chem. Phys., 16, 968-981 (1948). This table has been extended to lower temperatures by C. F. Curtiss, J. Chem. Phys., 97, 7679-7686 (1992). Curtiss showed that at low temperatures, the Boltzmann equation needs to be modified to take into account "orbiting pairs" of molecules. Only by making this modification is it possible to get a smooth transition from quantum to classical behavior. The deviations are appreciable below dimensionless temperatures of 0.30. "The collision integrals have been curve-fitted by P. D. Neufeld, A. R. Janzen, and R. A. Aziz, J. Chem. Phys., 57, 1100-1102 (1972), as follows: