Thumb for Mechanical Engineers 2011 Part 8 pptx

200 Rules of Thumb for Mechanical Engineers I I 1,000 ohms-cm, the ground bed resistivity is 3,0001 1,000 x 0.55 or 1.65 ohms. The resistance of multiple anodes installed vertically and connected in parallel may be calculated with the following equation: R = 0.00521PINL x (2.3L0g 8L1d - 1 + 2L1SLog 0.656N) (1) where R = ground bed resistance, ohms P = soil resistivity, ohm-cm N = number of anodes d = diameter of anode, ft L = length of anode, ft S = anode spacing, ft If the anode is installed with backfill such as coke breeze, use the diameter and length of the hole in which the anode is installed. If the anode is installed bare, use the actual dimensions of the anode. Figure 5 is based on Equation 1 and does not include the internal resistivity of the anode. The resistivity of a single vertical anode may be calculated with Equation 2. R = 0.00521P1L x (2.3L0g 8L1d - 1) (2) If the anode is installed with backfill, calculate the resistivity using the length and diameter of the hole in which the anode is installed. Calculate the resistivity using the actual anode dimensions. The difference between these two values is the internal resistance of the anode. Use the value of F’, typically about 50 ohm-cm, for the backfill medium. Figure 5 is based on 1,000 ohm-cm soil and a 7-ft x 8-in. hole with a 2-in. x 60-in. anode. Example. Determine the resistivity of 20 anodes installed vertically in 1,500 ohm-cm soil with a spacing of 20 ft. Read the ground bed resistivity from Figure 5. Spacing io-f t . itf t * 20-tt. =-it. io 15 2Q Number of Anodes 25 Figure 5. Anode bed resistance. Piping and Pressure Vessels 201 R = 0.202 ohm Since the anodes are to be installed in 1,500 ohm-cm soil and Figure 5 is based on 1,OOO ohm-cm soil, multiply R by the ratio of the actual soil resistivity to 1,OOO ohm-cm. R = 0.202 x 1,50O/l,OOO R = 0.303 ohm The internal resistivity for a single %in. x 60-in. vertical anode installed in 50 ohm-cm backfill (7 ft x &in. hole) is 0.106 ohm. Since 20 anodes will be installed in parallel, divide the resitivity for one anode by the number of anodes to obtain the internal resistivity of the anode bank. O.l06/u) = 0.005 ohm The total resistivity of the 20 anodes insta€led vertidly will therefore be 0.308 ohm (0.303 + 0.005). Galvanic Anodes Zinc and magnesium are the most commonly used materials for galvanic anodes. Magnesium is available either in standard alloy or high purity alloy. Galvanic anodes are usually pre-packaged with backfill to facilitate their installation. They may also be ordered bare if desired. Galvanic anodes offer the advantage of more uniformly distributing the cathodic protection current along the pipe line and it may be possible to protect the pipe line with a smaller amount of current than would be required with an im- pressed current system but not necessarily at a lower cost. Another advantage is that interference with other structures is minimized when galvanic anodes are used. Galvanic anodes are not an economical source of cathodic protection current in areas of high soil resistivity. Their use is generally limited to soils of 3,000 ohm-cm except where small amounts of current are needed. Magnesium is the most-used material for galvanic anodes for pipe line protection. Magnesium offers a higher solution potential than zinc and may therefore be used in areas of higher soil resistivity. A smaller amount of magnesium will generally be required for a comparable amount of current. Refer to Figure 6 for typical magnesium anode performance data. These curves are based on driving potentials of - 0.70 volts for H-1 alloy and - 0.90 volts for Galvomag working against a structure potential of - 0.85 volts referenced to copper sulfate. The driving potential with respect to steel for zinc is less than for magnesium. The efficiency of zinc at low current levels does not decrease as rapidly as the efficiency for magnesium. The solution potential for zinc referenced to a cop- 102 103 Anode Current - Milliamperes 104 Figure 6. Magnesium anode current. 202 Rules of Thumb for Mechanical Engineers 102 Current Output Milliamperes Figure 7a. Current output zinc anodes. Figure 7b. Current output zinc anodes. Piping and Pressure Vessels 203 Figure 8a. Current output zinc anodes. Figure 8b. Current output zinc anodes. 204 Rules of Thumb for Mechanical Engineers per sulfate cell is - 1.1 volts; standard magnesium has a solution potential of - 1.55 volts; and high purity magnesium has a solution potential of - 1.8 volts. If, for example, a pipe line is protected with zinc anodes at a polarization potential of - 0.9 volts, the driving potential will be - 1.1 - (-0.9) or -0.2 volts. If standard magnesium is used, the driving potential will be - 1.55 - ( - 0.9) or - 0.65 volts. The circuit resistance for magnesium will be approximately three times as great as for zinc. This would be handled by using fewer magnesium anodes, smaller anodes, or using series resistors. If the current demands for the system are increased due to coating deterioration, contact with foreign structures, or by oxygen reaching the pipe and causing depolarization, the potential drop will be less for zinc than for magnesium anodes. With zinc anodes, the current needs could increase by as much as 50% and the pipe polarization potential would still be about 0.8 volts. The polarization potential would drop to about 0.8 volts with only a 15% increase in current needs if magnesium were used. The current efficiency for zinc is 90% and this value holds over a wide range of current densities. Magnesium anodes have an efficiency of 50% at normal current densities. Magnesium anodes may be consumed by self corrosion if operated at very low current densities. Refer to Figures 7a, 7b, Sa, and 8b for zinc anode performance data. The data in Figures 7a and 7b are based on the anodes being installed in a gypsum-clay backfill and having a driving potential of - 0.2 volts. Figures 8a and 8b are based on the anodes being installed in water and having a driving potential of -0.2 volts. [from data prepared for the American Zinc Institute]. Example. Estimate the number of packaged anodes required to protect a pipe line. What is the anode resistance of a packaged magnesium anode installation consisting of nine 32 lb anodes spaced 7 ft apart in 2,000 ohm-cm soil? Refer to Figure 9. This chart is based on 17# packaged anodes in 1,000 ohm-cm soil. For nine 32 lb anodes, the resistivity will be 1 x 2,000/1,000 x 0.9 = 1.8 ohm See Figure 10 for a table of multiplying factors for other size anodes. 1 2 3 4 5 670910 20 30 40 50 Number of Anodes Figure 9. Anode bed resistance vs. number of anodes. 17# packaged magnesium anodes. Piping and Pressure Vessels 205 Chart based on 17-lb. magnesium anodes installed in 1000 ohm-cm soil in groups of For other conditions multiply number of anodes by the following multiplying factors: For soil resistivity: MF = For conventional magnesium: MF = 1.3 10 spaced on 10-ft. centers. For 9-lb. anodes: MF = 1.25 For 32-lb. anodes: MF = 0.9 1000 ln U 0 2 .I- O 1 2 3 4 5 10 20 304050 100 200300400 1000 Coating Conductivity (micromhoslsq ft) Figure 10. Number of anodes required for coated line protection. Example. A coated pipe line has a coating conductivity of 100 micromhoslsq ft and is 10,000 ft long, and the diameter is 103/4-in. How many 17 1b magnesium anodes will be required to protect 1,000 ft? Refer to Figure 7 and read 2 anodes per 1,000 ft. A total of twenty 17# anodes will be required for the entire line. Sources 1. Parker, M. E. and Peattie, E. G., Pipe Line Corrosion and Cathodic Protection, 3rd Ed. Houston: Gulf Publishing Co., 1984. 2. McAllister, E. W. (Ed.), Pipe Line Rules of Thiiinb Hurzdbook, 3rd Ed. Houston: Gulf Publishing Co., 1993. 206 Rules of Thumb for Mechanical Engineers Stress Analysis Stress analysis is the determination of the relationship be tween external forces applied to a vessel and the corresponding stress. The emphasis of this discussion is not how to do stress analysis in particular, but rather how to analyze vessels and their component parts in an effort to arrive at an economical and safe design-the difference being that we analyze stresses where necessary to determine thickness of material and sizes of members. We are not so concerned with building mathematical models as with providing a step- by-step approach to the design of ASME Code vessels. It is not necessary to find every stress but rather to know the governing stresses and how they relate to the vessel or its respective parts, attachments, and supports. The starting place for stress analysis is to determine all the design conditions for a given problem and then determine all the related external forces. We must then relate these external forces to the vessel parts which must resist them to find the corresponding stresses. By isolating the causes (loadings), the effects (stress) can be more accurately determined. The designer must also be keenly aware of the types of loads and how they relate to the vessel as a whole. Are the effects long or short term? Do they apply to a localized portion of the vessel or are they uniform throughout? How these stresses are interpreted and combined, what significance they have to the overall safety of the vessel, and what allowable stresses are applied will be determined by three things: 1. The StrengWfailure theory utilized. 2. The types and categories of loadings. 3. The hazard the stress represents to the vessel. Membrane Stress Analysis Pressure vessels commonly have the form of spheres, cylinders, cones, ellipsoids, tori, or composites of these. When the thickness is small in comparison with other dimensions (RJt > lo), vessels are referred to as mem- branes and the associated stresses resulting from the con- tained pressure are called membrane stresses. These membrane stresses are average tension or compression stresses. They are assumed to be uniform across the vessel wall and act tangentially to its surface. The membrane or wall is assumed to offer no resistance to bending. When the wall offers resistance to bending, bending stresses occur in addition to membrane stresses. In a vessel of complicated shape subjected to internal pressure, the simple membrane-stress concepts do not suf- fice to give an adequate idea of the true stress situation. The types of heads closing the vessel, effects of supports, vari- ation in thickness and cross section, nozzles, external attachments, and overall bending due to weight, wind, and seismic all cause varying stress distributions in the vessel. Deviations from a true membrane shape set up bending in the vessel wall and cause the direct loading to vary from point to point. The direct loading is diverted from the more flexible to the more rigid portions of the vessel. This effect is called “stress redistribution.” In any pressure vessel subjected to internal or external pressure, stresses are set up in the shell wall. The state of stress is triaxial and the three principal stresses are: ox = 1ongitudinaUmeridional stress q, = CircumferentiaVlatituudinal stress or = radial stress In addition, there may be bending and shear stresses. The radial stress is a direct stress, which is a result of the pressure acting directly on the wall, and causes a compressive stress equal to the pressure. In thin-walled vessels this stress is so small compared to the other “principal” stresses that it is generally ignored. Thus we assume for purposes of analysis that the state of stress is biaxial. This greatly simplifies the method of combining stresses in comparison to triaxial stress states. For thick-walled vessels (RJt c lo), the radial stress cannot be ignored and formulas are quite different from those used in finding “membrane stresses” in thin shells. Since ASME Code, Section VIII, Division 1, is basically for design by rules, a higher factor of safety is used to allow for the “unknown” stresses in the vessel. This higher safety factor, which allows for these unknown stresses, can impose a penalty on design but requires much less analysis. The design techniques outlined in this text are a compromise between finding all stresses and utilizing minimum code formulas. This additional knowl- Piping and Pressure Vessels 207 edge of stresses warrants the use of higher allowable stresses in some cases, while meeting the requirements that all loadings be considered. In conclusion, “membrane stress analysis” is not com- pletely accurate but allows certain simplifying assumptions to be made while maintaining a fair degree of accuracy. The main simplifying assumptions are that the stress is biaxial and that the stresses are uniform across the shell wall. For thin-walled vessels these assumptions have proven themselves to be reliable. No vessel meets the criteria of being a true membrane, but we can use this tool within a reasonable degree of accuracy. Failures in Pressure Vessels Vessel failures can be grouped into four major categories¶ which describe why a vessel fail= occurs. Failures can also be grouped into types of failures, which describe how the failure occurs. Each failure has a why and how to its history. It may have failed through corrosion fatigue be- cause the wrong material was selected! The designer must be as familiar with categories and types of failure as with categories and types of stress and loadings. Ultimately they are all related. Categories of Failures 1. Material-Improper selection of material; defects in material. 2. Design-Incorrect design data; inaccurate or incorrect design methods; inadequate shop testing. 3. Fabrication-Poor quality control; improper or in- sufficient fabrication procedures including welding; heat treatment or forming methods. 4. Service-Change of service condition by the user; in- experienced operations or maintenance personnel; upset conditions. Some types of service which require special attention both for selection of material, design details, and fabrication methods are as follows: a. Lethal b. Fatigue (cyclic) c. Brittle (low temperature) d. High temperature e. High shock or vibration f. Vessel contents Hydrogen Ammonia Compressed air Caustic Chlorides Types of Failures 1. Elastic deformation-Elastic instability or elastic buckling, vessel geometry, and stiffness as well as properties of materials are protection against buckling. 2. Brittle fracturexan occur at low or intermediate temperatures. Brittle fractures have occurred in vessels made of low carbon steel in the 40”-50”F range during hydrotest where minor flaws exist. 3. Excessive plastic deformation-The primary and secondary stress limits as outlined in ASME Section Wr, Division 2, are intended to prevent excessive plastic deformation and incremental collapse. 4. Stress rupture4reep deformation as a result of fatigue or cyclic loading, i.e., progressive fracture. Creep is a time-dependent phenomenon, whereas fatigue is a cycle-dependent phenomenon. 5. Plastic instability-Incremental collapse; incremental collapse is cyclic strain accumulation or cumulative cyclic deformation. Cumulative damage leads to instability of vessel by plastic deformation. 6. High strain-Low cycle fatigue is strain-governed and occurs mainly in lower-strengthhgh-ductile materials. 7. Stress corrosion-It is well known that chlorides cause stress corrosion cracking in stainless steels, likewise caustic service can cause stress corrosion cracking in carbon steels. Material selection is criti- cal in these services. 8. Corrosion fatigudccurs when corrosive and fatigue effects occur simultaneously. Corrosion can reduce fatigue life by pitting the surface and propagating cracks. Material selection and fatigue properties are the major considerations. In dealing with these various modes of failure, the designer must have at his disposal a picture of the state of stress 208 Rules of Thumb for Mechanical Engineers in the various parts. It is against these failure modes that the designer must compare and interpret stress values. But setting allowable stresses is not enough! For elastic instability one must consider geometry, stiffness, and the properties of the material. Material selection is a major con- sideration when related to the type of service. Design details and fabrication methods are as important as “allowable stress” in design of vessels for cyclic service. The designer and all those persons who ultimately affect the design must have a clear picture of the conditions under which the vessel will operate. ~ ~~ loadings Loadings or forces are the “causes” of stresses in pressure vessels. These forces and moments must be isolated both to determine where they apply to the vessel and when they apply to a vessel. Categories of loadings define where these forces are applied. Loadings may be applied over a large portion (general area) of the vessel or over a local area of the vessel. Remember both general and local loads can produce membrane and bending stresses. These stresses are additive and define the overall state of stress in the vessel or component. Stresses from local loads must be added to stresses from general loadings. These combined stresses are then compared to an allowable stress. Consider a pressurized, vertical vessel bending due to wind, which has an inward radial force applied locally. The effects of the pressure loading are longitudinal and circumferential tension. The effects of the wind loading are longitudinal tension on the windward side and longitudinal compression on the leeward side. The effect of the local inward radial load is some local membrane stresses and local bending stresses. The local stresses would be both circumferential and longitudinal, tension on the inside surface of the vessel, and compressive on the outside. Of course the steel at any given point only sees a certain level of stress or the combined effect. It is the designer’s job to combine the stresses from the various loadings to arrive at the worst pb able combination of stresses, combine them using some failure theory, and compare the results to an acceptable stress level to obtain an economical and safe design. This hypothetical problem serves to illustrate how categories and types of loadings are related to the stresses they produce. The stresses applied more or less continuously and uniformly across an entire section of the vessel are primary stresses. The stresses due to pressure and wind are primary membrane stresses. These stresses should be limited to the Code allowable. These stresses would cause the bursting or collapse of the vessel if allowed to reach an unaccept- ably high level. On the other hand, the stresses from the inward radial load could be either a primary local stress or secondary stress. It is a primary local stress if it is produced from an unre lenting load or a secondary stress if produced by a relent- ing load. Either stress may cause local deformation but will not in and of itself cause the vessel to fail. If it is a primary stress, the stress will be redisttibuted; if it is a secondary stress, the load will relax once slight deformation occurs. Also be aware that this is only true for ductile materials. In brittle materials, there would be no difference between primary and secondary stresses. If the material cannot yield to reduce the load, then the definition of secondary stress does not apply! Fortunately current pressure vessel codes require the use of ductile materials. This should make it obvious that the type and category of loading will determine the type and category of stress. This will be expanded upon later, but basically each combination of stresses (stress categories) will have different allowables, i.e.: . Primary stress: P, e SE . Primary membrane local (PL): PL=Pm+PL<1.5SE PL=Pm+Qm< 1.5 SE Primary membrane + secondary (Q): P,+Q<3SE But what if the loading was of relatively short duration? This describes the “type” of loading. Whether a loading is steady, more or less continuous, or nonsteady, variable, or temporary will also have an effect on what level of stress will be acceptable. If in our hypothetical problem the loading had been pressure + seismic + local load, we would have a different case. Due to the relatively short duration of seismic loading, a higher “temporary” allowable stress would be acceptable. The vessel doesn’t have to operate in an earthquake all the time. On the other hand, it also shouldn’t fall down in the event of an earthquake! Struc- Piping and Pressure Vessels 209 tural designs allow a one-third increase in allowable stress for seismic loadings for this reason. For steacfy loads, the vessel must support these loads more or less continuously during its useful life. As a result, the stresses produced from these loads must be maintained to an acceptable level. For nonsted’ loads, the vessel may experience some or all of these loadings at various times but not all at once and not more or less continuously. Therefore a temporarily higher stress is acceptable. For general loads that apply more or less uniformly across an entire section, the corresponding stresses must be lower, since the entire vessel must support that loading. For bcd Zoads, the corresponding stresses are confined to a small portion of the vessel and normally fall off rapidly in distance from the applied load. As discussed previously, pressurizing a vessel causes bending in certain compo- nents. But it doesn’t cause the entire vessel to bend. The results are not as significant (except in cyclic service) as those caused by general loadings. Therefore a slightly higher allowable stress would be in order. Loadings can be outlined as follows: A. Categories of loadings 1. General loads-Applied more or less continuously across a vessel section. a. Pressure loads-Internal or external pressure (design, operating, hydrotest, and hydrostatic head of liquid). b. Moment loads-Due to wind, seismic, erection, transportation. c. Compressivdtensile loads-Due to dead weight, installed equipment, ladders, platforms, piping, and vessel contents. d. Thermal loads-Hot box design of skirt-head at- tachment. 2. Local loads-Due to reactions from supports, in- ternals, attached piping, attached equipment, i.e., platforms, mixers, etc. a. Radial load-Inward or outward. b. Shear load-Longitudinal or circumferential. c. Torsional load. d. Tangential load. e. Moment load-Longitudinal or circumferential. f. Thermal loads. B. Types of loadings 1. Steady loads-Long-term duration, continuous. a. InternaVexternal pressure. b. Dead weight. c. Vessel contents. d. Loadings due to attached piping and equipment. e. Loadings to and from vessel supports. f. Thermal loads. g. Wind loads. a. Shop and field hydrotests. b. Earthquake. c. Erection. d. Transportation. e. Upset, emergency. f. Thermal loads. g. Start up, shut down. 2. Nonsteady loads-Short-term duration; variable. Stress ASME Code, Section VIII, Division 1 vs. Divlslon 2 ASME Code, Section Vm, Division 1 does not explicitly consider the effects of combined stress. Neither does it give detailed methods on how stresses are combined. ASME Code, Section WI, Division 2, on the other hand, provides specific guidelines for stresses, how they are combined, and allowable stresses for categories of combined stresses. Divi- sion 2 is design by analysis whereas Division 1 is designed by rules. Although stress analysis as utilized by Division 2 is beyond the scope ofthis discussion, the use of stress Categories, definitions of stress, and allowable stresses is applicable. Division 2 stress analysis considers all stresses in a triaxial state combined in accordance with the maximum shear stress theory. Division 1 and the procedures outlined in this section consider a biaxial state of stress combined in accordance with the maximum stress theory. Just as you would not design a nuclear reactor to the rules of Division 1, you would not design an air receiver by the techniques of Division 2. Each has its place and applications. The following discussion on categories of stress and allowables will utilize information from Division 2, which can be applied in general to all vessels. [...]... 73 8 / 15/36 1 Ilh6 11 18 13/16 204 OD 42 1 68 313 280 48 142 264 235 437 3 58 54 122 2 28 203 377 306 60 104 200 1 78 330 2 68 499 381 66 91 174 157 293 2 38 442 336 626 4 58 72 79 152 1 38 263 213 396 302 561 4 08 78 70 136 124 237 193 359 273 5 08 369 686 483 84 63 123 110 212 175 327 249 462 336 625 4 38 816 559 90 57 112 99 190 157 300 2 28 424 3 08 573 402 7 48 510 96 52 103 90 173 143 274 210 391 284 5 28 370... 370 689 470 87 5 0 0 102 48 94 82 160 130 249 190 363 263 490 343 639 435 81 0 540 1.005 1 08 44 87 76 1 48 1 18 2 28 176 337 245 456 320 594 405 754 502 935 613 m 114 42 79 70 1 38 109 211 162 311 223 426 299 555 379 705 469 87 4 571 1,064 m 120 39 74 65 1 28 101 197 149 287 209 400 280 521 355 660 440 81 9 536 997 m 126 37 69 61 120 95 184 1 38 266 195 374 263 490 334 621 414 770 504 9 38 132 35 65 57 113 88 173... 1.0 1.0 1.0 100% 85 % 100% 80 % 1.0 1.0 1.0 1.0 100% 85 % 100% 80 % 1.0 1.0 1.0 1.0 100% 85 % 100% 80 % 1.0 85 85 7 1000/, 100% 100% 100% 1.0 85 1.0 7 100% 100% 100% 100% 1.0 1.0 1.0 1.0 100% 85 % 100940 80 % 1.0 85 1.0 7 100% 100% 100% 100% 1.0 85 85 7 100% 100% 100% 100% 2 18 Rules of Thumb for Mechanical Engineers Notes Table 2 Joint Efficiencies Full None 10 TYPes of Joints X-Ray Spot 85 7 65 Single and... Figure UCS 28. 2 of ASME Code, Section VIII, Div 00 5/16 00 437 1 W 3/e I OD 00 537 03 616 03 0 1 637 00 585 715 661 795 m 7 38 875 687 81 6 762 89 4 603 1,124 715 83 9 974 475 88 4 569 1,060 673 1,253 789 916 1,053 m 369 687 449 83 6 5 38 1,002 636 1, 185 86 4 994 m 275 526 350 652 426 793 510 950 603 1,123 705 1,312 81 7 940 1,073 201 385 261 499 332 619 405 753 485 902 573 1,066 669 1,246 774 1,442 89 1 1,017... 1,066 669 1,246 774 1,442 89 1 1,017 1,152 140 271 189 363 2 48 475 309 590 385 717 462 85 9 546 1,015 637 1, 186 737 1,373 966 1,095 a , 133 2 58 1 78 342 9/16 233 4 48 % 294 562 367 684 440 81 9 520 9 68 6 08 1.131 703 1.309 80 6 1,509 919 1,042 7/s 1%6 1 11/16 1% lk? 11h6 3/4 642 13/16 744 03 m 84 6 m 13/16 222 Rules of Thumb for Mechanical Engineers Useful Formulas for Vessels C2,61 1 Properties of a circle (See... 113 88 173 129 2 48 181 3 48 242 462 315 586 391 727 1 38 33 62 54 106 83 163 121 234 169 325 2 28 437 297 555 144 31 59 51 98 78 154 114 221 1 58 304 214 411 150 49 92 74 146 107 209 1 48 286 156 46 87 70 1 38 101 199 44 67 131 96 189 7/16 162 83 14 1 Motes: 1 All values are in in 2 Values are for temperatures up to 500OF 3 Top value is for full vacuum, lower value is half vacuum 4 Values are for carbon or... c for Partial Volumes of a Horizontal Cylinder hlD or V = uR2t'c Figure 1 Formulas for partial volumes of a horizontal cylinder .0524 0941 1424 1955 2523 3119 3735 A364 5 R-h 8 = arc cos R C 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 5636 6265 688 1 7477 b045 85 76 9059 85 9 9 480 95 981 3 Piping and Pressure Vessels 221 Maximum length of Unstiffened Shells Thickness (in.) Diameter fin.) 1/4 36 5/16 33 / 8. .. Pm R =- PRi 2SE 2P - PO R 2SE + 8P 2SEt Ri + 2t 2SEt Ro - 8t P(Ri + 2t) 2Et P(Ro- 8t) 2Et PDiK 2SE - 2P PDoK 2SE + 2P(K - -1) 2SEt KDi + 2t 2 1 S.E [Section UG-32d]* PDi 2SE 2P - PO D 2SE + 1.8P 2SEt Di + 2t 2SEt Do- 1.8t 100%-6% Torispherical [Section UG-32(e)]* 88 5PLi SE - lP 88 5PL, SE + 8P SEt 88 5Li + 1t SEt 88 5L, - 8t Torispherical < 16.66 [Section 1-4(d)]* PLiM 2SE - 2P PLM 2SE + P(M - 2) 2SEt... volume: VI + V2 + V3 2 Table 1 Partial Volumes Volume to Ht Type -[ u D2Ht 4 Hemi Volume to h Volume to Hb -9 3D4 u DHE 'K 2 [ 2 1 2:l S.E 'K rDH2 1 - - h2(l.5D - h) 6 h2(l.5D 12 - h) 100%-6% F & D D is in it Table 2 General Data -m Type Surface Area Volume C.G Empty Hemi u D2/2 u D3/12 287 8D 375D 1. 084 D! R DV24 1439D 187 5D 25D 084 7D3 100D Points on Heads 5D 2:l S.E 100%-6% F&D 9 286 D2 Depth of Head, d Full... flat plate (diameter) D.L.=2 - r r + 2 - nL+2f Go) (1;o) 2 For 2: 1 S.E heads the crown and knuckle radius may be approximated as follows: L = 9045 D r = 1727 D 220 Rules of Thumb for Mechanical Engineers 4.Depth of head 3 Conversion factors A=L-r B=R-r Multiply ft3 x 7. 48 to get gallons Multiply ft3 x 62.39 to get lb-water Multiply gallons x 8. 33 to get lb-water d = L - d m Volumes and Surface Areas . .2t 2SEt Do - 1.8t SEt .88 5L, - .8t PDO 2SE + 1.8P PDi 2SE - .2P 100%-6% Torispherical [Section UG-32(e)]* .88 5PL, SE + .8P SEt .88 5Li + .1 t .88 5PLi SE - .lP Torispherical. 85 % 1.0 85 % 1.0 85 % .85 100% .85 100% 1.0 85 % .85 100% .85 100% Combinationt 1.0 100% 1.0 100% 1.0 100% .85 100% 1.0 100% 1.0 100940 1.0 100% .85 100% None 1.0 80 %. 100% None 1.0 80 % 1.0 80 % 1.0 80 % .7 100% .7 100% 1.0 80 % .7 100% .7 100% *See Note 1. jSee Note 2. 2 18 Rules of Thumb for Mechanical Engineers Notes Table 2 Joint

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