Geometry

VESSEL GEOMENTRICAL RELATIONS CIRCULAR GEOMENTRY Ah h INPUTS Area Diameter

Ah D

15.70796 m2 5 m

A - Ah D

OUTPUT

CALCULATE

Height ratio h* Height h Ah

0.7459 3.73

m

h

CIRCULAR GEOMENTRY h Ah

HORIZONTAL CYLINDRICAL VESSELS V H

INPUTS

INPUTS Diameter D 1.35 m Length t-t L 4.64 m m3 Volume V 5 Dished end type HEMIELLIPSOIDAL Depth of dished end 'b' 0.5 m

Height h Diameter D OUTPUT

8 8

m m

CALCULATE

Area ratio A* Ah Area

1.0000 50.27

OUTPUT

CALCULATE

m2 Height

H

SPHERICAL VESSEL V H INPUTS Diameter D Volume V OUTPUT Height

5.3 550

m m3

CALCULATE

H

5.30

m

Legend: 1. h or H denotes partial height occupied by the fluid inside the vessel 2. Ah denotes partial area occupied by the fluid inside the vessel 3. V denotes volume of liquid inside the vessel 4. A* denotes partial area over total area of the vessel 5. h* denotes partial height of liquid over actual diameter of the vessel 6. b denotes depth of dished end applicable only for Hemiellipsoidal head

0.84

m

D h

PARTIAL VOLUMES FOR DIFFERENT VESSEL GEOMENTRY WITH CIRCULAR CROSS SECTION DIAMETER M 3.8 HEAD DEPTH 'b' M 0.95 LENGTH M 1.89 PARTIAL VOLUME OF VESSELS IN M3

PHI (h/D)

K1

K2

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48

0.1329 0.1874 0.2288 0.2634 0.2936 0.3206 0.3452 0.3679 0.389 0.4088 0.4273 0.4447 0.4615 0.4774 0.4925 0.507 0.5208 0.5341 0.5468 0.5591 0.5709 0.5823 0.5933 0.6039 0.6142 0.6241 0.6337 0.6429 0.6519 0.6606 0.669 0.6771 0.685 0.6926 0.6999 0.7071 0.714 0.7207 0.7272 0.7334 0.7395 0.7453 0.751 0.7565 0.7617 0.7668 0.7717 0.7765

156.03 77.493 51.313 38.223 30.369 25.133 21.393 18.588 16.406 14.661 14.28 13.09 12.083 11.22 9.4248 8.7703 8.1928 7.6794 7.2015 6.8068 6.4328 6.0928 5.7824 5.4978 5.236 4.4943 4.7706 4.5628 4.3693 4.1888 4.0199 3.8615 3.7128 3.5728 3.4408 3.3161 3.1982 3.0865 2.9805 2.8798 2.784 2.6928 2.6058 2.5228 2.4435 2.3676 2.2949 2.2253

PARTIALLY FILLED HEIGHT(h) M

0.038 0.076 0.114 0.152 0.19 0.228 0.266 0.304 0.342 0.38 0.418 0.456 0.494 0.532 0.57 0.608 0.646 0.684 0.722 0.76 0.798 0.836 0.874 0.912 0.95 0.988 1.026 1.064 1.102 1.14 1.178 1.216 1.254 1.292 1.33 1.368 1.406 1.444 1.482 1.52 1.558 1.596 1.634 1.672 1.71 1.748 1.786 1.824

Horizontal cylinder. vessel with flat ends 0.036 0.102 0.187 0.288 0.401 0.525 0.659 0.803 0.955 1.116 1.283 1.456 1.637 1.824 2.016 2.214 2.416 2.624 2.835 3.052 3.272 3.496 3.724 3.956 4.191 4.428 4.670 4.913 5.160 5.409 5.660 5.913 6.169 6.427 6.685 6.947 7.210 7.474 7.740 8.006 8.275 8.543 8.813 9.084 9.355 9.627 9.899 10.172

Horizontal cylinder vessel with Hemiellipsoidal ends 0.041 0.119 0.225 0.355 0.505 0.674 0.861 1.064 1.284 1.518 1.804 2.077 2.366 2.669 2.889 3.199 3.521 3.853 4.191 4.546 4.906 5.276 5.654 6.041 6.435 6.596 7.246 7.661 8.083 8.512 8.946 9.385 9.830 10.279 10.733 11.192 11.654 12.121 12.591 13.063 13.539 14.017 14.497 14.980 15.464 15.949 16.436 16.924

4

Horizontal Horizontal cylinder with cylinder Spherical Torispherical vessel with Vessel ends hemispherical ends 0.045 0.009 0.040 0.136 0.034 0.116 0.263 0.076 0.219 0.422 0.134 0.343 0.609 0.208 0.486 0.823 0.298 0.647 1.062 0.403 0.825 1.325 0.522 1.018 1.612 0.656 1.225 1.920 0.804 1.446 2.326 1.043 1.711 2.698 1.241 1.966 3.094 1.457 2.235 3.513 1.689 2.518 3.762 1.745 2.733 4.185 1.971 3.023 4.625 2.209 3.323 5.081 2.458 3.633 5.546 2.710 3.948 6.040 2.988 4.279 6.541 3.269 4.614 7.056 3.560 4.958 7.585 3.860 5.309 8.126 4.170 5.668 8.680 4.489 6.034 8.763 4.334 6.208 9.822 5.152 6.785 10.409 5.496 7.170 11.007 5.847 7.561 11.615 6.206 7.957 12.231 6.571 8.358 12.856 6.943 8.764 13.491 7.321 9.176 14.132 7.705 9.591 14.780 8.095 10.009 15.437 8.490 10.433 16.099 8.889 10.860 16.767 9.293 11.290 17.442 9.701 11.724 18.120 10.113 12.159 18.803 10.529 12.598 19.490 10.947 13.038 20.182 11.368 13.481 20.876 11.792 13.926 21.573 12.218 14.372 22.272 12.645 14.819 22.973 13.074 15.267 23.676 13.504 15.717

D h

PARTIAL VOLUMES FOR DIFFERENT VESSEL GEOMENTRY WITH CIRCULAR CROSS SECTION DIAMETER M 3.8 HEAD DEPTH 'b' M 0.95 LENGTH M 1.89 PARTIAL VOLUME OF VESSELS IN M3

PHI (h/D)

K1

K2

0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1

0.781 0.7854 0.7896 0.7936 0.7975 0.8012 0.8048 0.8081 0.8119 0.8144 0.8173 0.82 0.8226 0.8251 0.8273 0.8294 0.8341 0.8333 0.8349 0.8364 0.8377 0.8389 0.8399 0.8408 0.8415 0.8421 0.8425 0.8427 0.8428 0.8429 0.8424 0.842 0.8414 0.8406 0.8396 0.8384 0.8371 0.8355 0.8338 0.8318 0.8296 0.8272 0.8246 0.8217 0.8185 0.8151 0.8113 0.8071 0.8026 0.7976 0.792 0.7854

2.1585 2.0944 2.0328 1.9736 1.9166 1.8617 1.8088 1.7578 1.7086 1.6611 1.6152 1.5708 1.5279 1.4863 1.4461 1.4072 1.3694 1.3328 1.2973 1.2628 1.2293 1.1968 1.1652 1.1345 1.1046 1.0755 1.0472 1.0196 0.9928 0.9666 0.9412 0.9163 0.892 0.8684 0.8453 0.8228 0.8008 0.7793 0.7583 0.7378 0.7177 0.6981 0.679 0.6602 0.6418 0.6239 0.6063 0.589 0.5722 0.5556 0.5395 0.5236

PARTIALLY FILLED HEIGHT(h) M

1.862 1.9 1.938 1.976 2.014 2.052 2.09 2.128 2.166 2.204 2.242 2.28 2.318 2.356 2.394 2.432 2.47 2.508 2.546 2.584 2.622 2.66 2.698 2.736 2.774 2.812 2.85 2.888 2.926 2.964 3.002 3.04 3.078 3.116 3.154 3.192 3.23 3.268 3.306 3.344 3.382 3.42 3.458 3.496 3.534 3.572 3.61 3.648 3.686 3.724 3.762 3.8

Horizontal cylinder. vessel with flat ends 10.444 10.717 10.990 11.262 11.535 11.808 12.080 12.350 12.630 12.891 13.160 13.427 13.695 13.961 14.224 14.487 14.797 15.010 15.266 15.522 15.775 16.026 16.275 16.522 16.765 17.007 17.245 17.479 17.711 17.943 18.162 18.384 18.600 18.812 19.019 19.220 19.419 19.610 19.797 19.977 20.151 20.318 20.479 20.631 20.775 20.911 21.035 21.146 21.247 21.332 21.399 21.435

Horizontal cylinder vessel with Hemiellipsoidal ends 17.411 17.900 18.388 18.876 19.364 19.851 20.337 20.820 21.311 21.783 22.261 22.736 23.209 23.680 24.145 24.608 25.114 25.523 25.971 26.416 26.855 27.289 27.717 28.139 28.555 28.964 29.366 29.759 30.146 30.528 30.894 31.255 31.606 31.948 32.279 32.600 32.912 33.209 33.497 33.772 34.032 34.281 34.518 34.736 34.938 35.128 35.297 35.443 35.575 35.679 35.761 35.800

4

Horizontal Horizontal cylinder with cylinder Spherical Torispherical vessel with Vessel ends hemispherical ends 24.379 13.934 16.166 25.083 14.365 16.616 25.787 14.796 17.066 26.490 15.227 17.515 27.193 15.657 17.965 27.893 16.086 18.413 28.593 16.513 18.861 29.289 16.939 19.306 29.993 17.363 19.760 30.675 17.784 20.194 31.363 18.203 20.635 32.045 18.618 21.072 32.724 19.030 21.509 33.398 19.437 21.943 34.066 19.841 22.372 34.728 20.242 22.799 35.432 20.636 23.270 36.035 21.026 23.643 36.676 21.410 24.058 37.310 21.788 24.469 37.934 22.159 24.874 38.552 22.525 25.276 39.158 22.884 25.671 39.757 23.236 26.063 40.344 23.579 26.447 40.921 23.914 26.827 41.487 24.242 27.199 42.039 24.560 27.564 42.582 24.871 27.924 43.113 25.170 28.279 43.626 25.463 28.618 44.127 25.743 28.954 44.612 26.012 29.281 45.085 26.273 29.600 45.540 26.521 29.909 45.980 26.760 30.209 46.405 26.986 30.500 46.809 27.199 30.778 47.197 27.400 31.049 47.566 27.589 31.306 47.913 27.763 31.551 48.243 27.925 31.785 48.556 28.077 32.008 48.841 28.209 32.215 49.101 28.327 32.406 49.345 28.435 32.587 49.559 28.524 32.747 49.740 28.594 32.888 49.903 28.656 33.014 50.026 28.694 33.115 50.123 28.724 33.194 50.166 28.731 33.233

D h

PHI (h/D)

K1

PARTIAL VOLUMES FOR DIFFERENT VESSEL GEOMENTRY WITH CIRCULAR CROSS SECTION DIAMETER M 3.8 HEAD DEPTH 'b' M 0.95 LENGTH M 1.89 PARTIAL VOLUME OF VESSELS IN M3 K2

PARTIALLY FILLED HEIGHT(h) M

Horizontal cylinder. vessel with flat ends

Horizontal cylinder vessel with Hemiellipsoidal ends

4

Horizontal Horizontal cylinder with cylinder Spherical Torispherical vessel with Vessel ends hemispherical ends

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