Pipe-sizing-basic-principles

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Pipe Modelling讲义

Pipe Modelling讲义

管系建模Pipe Modelling1 简介1.6.2管系建模工具栏Pipe功能激活,保存,取消,删除,ReadyPipe Material功能1.单线变双线,双线变单线,管路材料生成,直管材料生成,弯头材料生成Pipe Model功能布管,添加附件,插入附件,旋转附件,删除附件管路对齐Pipe Model功能生成短管,自动短管命名显示短管界限2弯头处理功能Pipe Model>Bends菜单中的选项允许用户对已存在的管路进行有效的修改,不需要通过删除管路再步管。

这些处理功能通常都是在管路生成材料前进行的。

仍然存在某些约束。

例如:系统不支持导致一个已存在的内部连接点或外部连接点发生变化的修改操作。

所以,用户首先要取消连接才可以进行操作。

这些功能的应用如下所示:2.1显示,生成以及删除弯头2.1.1怎样显示0-弯头打开图纸PADV2.1.1管路必须处于激活状态选择Pipe Model>Bends>Display bends✧所激活管路中所有已存在的弯头用‘O’符号显示。

2.1.2怎样在直管中生成弯头⏹选择Pipe Model>Bends>Create指示附件…指示位置⏹完成后选择Operation Complete!这个位置可以通过各种2D,3D点定义来给出。

弯头用‘O’符号显示并被作为是一个0-弯头2.1.3怎样删除0-弯头⏹选择Pipe Model>Bends>Delete 0-bends⏹然后指示0-弯头或…⏹选择(Options)删除被激活管路上所有的已存在的0-弯头。

2.2移动弯头现在我们将了解移动弯头中使用到的各种方法。

2.2.1怎样移动弯头(自由)首先用Create功能生成如左图所示的弯头。

⏹选择Pipe Model>Bends>Move free⏹指示弯头,然后选择接着⏹指示左边的0-弯头⏹选择OK⏹为dx,dy,dz键入‘0,0,2000’2.3改变弯头角度⏹选择Pipe Model>Bends>Move angle⏹指示弯头⏹指示要改变长度的附件⏹键入‘90’3组合功能组合功能允许用户通过一个操作控制多个附件。

玻璃纤维汉英词典

玻璃纤维汉英词典

玻璃纤维汉英词典《玻璃纤维汉英词典》编写组编写CQISAN吐血整理氰基树脂 amino resin安哥拉法 Angola process安山岩 andesite氨基硅烷 amino silane氦基聚酜胺 aminopolyamide氨基法氧基硅烷 aminoalkoxysilane氨水 ammonia water胺基硅烷 amine-functional silane胺类固化剂 amine curing agent八枚缎纹 eight harness satin巴拿马组织 Panama weave巴萨木 balsa (wood)钯依合金 palladium-iridium alloy白垩 chalk白棉[玻璃棉产品] white wool白泡石 white afrodite白砒 white arsenic,arsenic white白水 white water白水池 white water silo白水回收装置 save-all白水盘 save-all pan白炭黑 white carbon白云石 dolomite白云石灰石 dolomitic limestone摆锤法 pendulum process摆锤法铺毡机 pendulum felting machine摆锤机 pendulum unit摆锤式冲击试验 Charpy (impact) test摆动冲击板 oscillating impinge plate半导体玻璃纤维 semi-conducting glass fiber半干法[制吸声板] semidry process,paste process半管壳 half pipe section半硅砖 semi-silica brick半深度的流液洞 intermediate level throat半酸性耐火材料 semi-acid refractory半异形箱 semi-profile reed半硬棉板 semi-rigid (mineral wool) slab棒法[拉丝] rod process, rod-melting process棒法毛纱机 Angola process sliver machine棒管法[制光纤] rod-in-tube process棒磨 rod mill棒条筛 bar screen棒样弯曲强度 rod bending strength磅秤 weigher/ weighing scale包层光纤 cladded optical fiber包胶辊轮 rubber-coated roller包角[拉丝包角] Wraparound angle包芯纱 core-spun yarn宝塔纱 cone yarn饱和电抗供 saturable core reactor饱和聚脂树脂 saturated polyester resin保温带 lamella mat, reoriented insulation保温绳 heat insulating rope保温砖 insulating brick爆皮[球疵] chipped surface贝它纱 Beta yarn贝它纤维 Beta fiber备用料仓 stand-by bin苯酚 phenol苯磺酰气 benzene sulfochloride苯基三乙氧基硅烷 phenyltrie thoxysilane苯甲酸 benzonic acid苯甲酸钠 sodium benzoate苯醌 benzoquinone苯乙烯 styrene苯乙烯-丙烯鲭共聚物 styrene acrylonitrile copolymer, SAN苯乙烯-马来酐共聚物 styrene maleic anhydride copolymer,SMA 苯乙烯溶解度 styrene solubility bang绷带 bandage, casting tape比刚度 specific rigidity比较平板法[测导热系数]comparative plate method比模量 specific modulus比强度 specific strength比热 specific heat比热容 specific thermal capacity比容化效率 melting efficiency比值控制 ratio control比重 specific gravity闭口闪点 closed flash point, Abel flash point闭模成型 closed molding壁布 wall covering cloth壁纸 wall paper边壁吹风系统 air stripping system for sidewall边壁风机 sidewall blower边不良(织疵) poor selvedge边撑 temple, ditcher temple边撑台 temple table边剪 selvedge cutter边界元 boundary element边料 edge trims边纱 selvedge yarn边纱筒子 selvedge bobbin编链组织 pillar stitch编绳机 rope braiding machine, cord braiding machine编织 braiding编织袋 braided tape编织电缆外套braided cable jacket编织管 braided sleeve, braded tubing编织机 braiding machine, braider编织节距 braiding pitch编织拉挤工艺 braiding pultrusion process编织盘根 braided packing编织纱 braiding yarn编织绳 braided cord, braided rope, plaited rope编织筒子 braiding bobbin编织物 braided fabric编织预成型体 braided preform扁椭球封头曲面 oblated spheroid head contour变频调速 frequency-variable speed regulation变频器 inverter变速大卷装拉丝机 speed compensated winder变形 deformation变形纱 textured yarn标志纱 tracer yarn, identification yarn标准锆英石砖 standard zircon brick标准砖standard (size) brick表观松散密度 apparent bulk density表面处理 surface treatment, surface finish表面处理机组 finishing machine, finishing range表面电陌率 surface resistivity表面光洁度 surface finish表面化学处理finishing表面活性剂 surfactant,surface-active agent表面能 surface energy表面涂层 surface coating表面性质 surface properties表面修饰 surface finish表面毡 surfacing mat, surfacing tissue, surfacing veil表面着色 surface coloring丙阶树脂C-stage resin丙三醇环氧树脂glycerol epoxy resin丙烯请-丁二烯一苯乙烯共聚物acrylonitrile-butadiene-styrene copolymer, ABS 丙烯酸类树酯 acrylic resin, acrylics丙烯酸酯处理剂 acrylate finish丙烯酰硅烷 acrylyl silane并捻, , 并线 doubling, folding, secondary twisting并捻机 doubler, doubling machine, secondary twister并捻纱 doubled yarn, folded yarn并轴 beaming, rebeaming并轴辊 beaming roller并轴机 beaming machine并轴上浆 sizing and rebeaming process波特兰水泥 Portland cement波歇炉, 波歇窑 Pochet furnace波形瓦 corrugated sheet, corrugated tile玻璃棒 glass rod玻璃表面结构 surface structure of glass玻璃布 glass (fiber) cloth, fiber glass cloth玻璃布层压板 glass cloth laminate玻璃布接头机 glass cloth jointing machine玻璃成形 glass forming玻璃粉 glass powder玻璃钢 glass fiber reinforced plastics, GRP, GFRP, FRP玻璃钢基布 glass cloth for reinforcing plastics玻璃钢筋 GRP rebar玻璃光纤 glass optical fiber, optical glass fiber玻璃态转变 glass transition玻璃鳞片 glass flake玻璃棉 glass wool玻璃棉板 glass wool board, glass wool slab玻璃棉管壳 glass wool pipe section玻璃棉毡 glass wool batt, glass wool felt, glass wool blanket玻璃漆布 varnished glass cloth玻璃球 glass marble玻璃球二次冒泡温度 reboiling temperature of glass marbles玻璃球均匀性 homogeneity of glass marbles玻璃球缺陷 defects of glass marbles玻璃球网带冷却机 glass marble cooling conveyor玻璃球窑 glass marble furnace玻璃球应力 stress in glass marbles玻璃熔化温度 glass melting temperature玻璃熔体 glass melt玻璃熔窑 glass melting furnace, glass melter玻璃熔制 glass melting, glass making玻璃/树脂比 glass/resin ratio玻璃丝包电磁线 fiberglass magnet wire玻璃丝包线 fiberglass covered [wrapped] wire玻璃丝编织电线 fiberglass braided wire玻璃微纤维 glass microfiber玻璃微珠 glass microsphere玻璃细珠 glass bead玻璃纤维 glass fiber, fiberglass, fiber glass, fibrous glass玻璃纤维布 glass (fiber) cloth, fiberglass cloth玻璃纤维带 glass (fiber) tape, fiberglass tape玻璃纤维纺织品 glass (fiber) textiles, fiberglass textiles玻璃纤锥含量 glass (fiber) content玻璃纤维纱 glass (fiber) yarn, fiberglass yarn玻璃纤维绳 glass (fiber) cord, fiberglass cord, fiberglass rope玻璃纤维套管 glass fiber sleeve, fiberglass sleeve玻璃纤维线 glass (fiber) thread, fiberglass thread玻璃纤维增强材料 glass fiber reinforcement, fiberglass reinforcement玻璃纤维增强硅酸钙 glass fiber [fiberglass] reinforced calcium silicate玻璃纤维增强混凝土 glass fiber [fiberglass] reinforced concrete玻璃纤雄增强胶凝材料 glass fiber [fiberglass] reinforced cementing material玻璃纤维增弹结构泡沬塑料 glass fiber [fiberglass] reinforced structural foam玻璃纤维增强金属 glass fiber [fiberglass] reinforced metal玻璃纤维增强沥青 glass fiber [fiberglass] reinforced asphalt玻璃纤锥增强菱苦土 glass fiber [fiberglass] reinforced magnesite玻璃纤维增强氯氧镁胶结料glass fiber [fiberglass] reinforced Sorel cement, glass fiber reinforced magnesium oxychloride cement玻璃纤维增强热塑性塑料 glass fiber [fiberglass] reinforced thermoplastics玻璃纤锥增强砂浆 glass fiber [fiberglass] reinforced mortar玻璃纤维增强砂轮 glass fiber [fiberglass] reinforced grinding wheel玻璃纤锥增强石膏 glass fiber [fiberglass] reinforced gypsum玻璃纤维增强石棉制品 glass fiber [fiberglass] reinforced asbestos products玻璃纤维增强水泥 glass fiber [fiberglass] reinforced cement, GRC玻璃纤锥增强塑料 glass fiber [fiberglass] reinforced plastics玻璃纤维增强陶瓷 glass fiber [fiberglass] reinforced ceramic玻璃纤维增强橡胶 glass fiber [fiberglass] reinforced rubber玻璃纤维毡 glass (fiber) mat, fiberglass mat玻璃纤雄织物 glass (fiber) fabric f fiberglass fabric玻璃纤维纸 glass fiber paper玻璃形成氧化物 glass forming oxide玻璃液 molten glass, liquid glass玻璃液流 glass flow, glass current斑璃液流股 glass streams玻璃液面(molten) glass level, metal level, flux level玻璃液面高度(molten) glass level玻璃液面控制 glass level control玻璃液面线 metal line, flux line玻璃液润湿角 wetting angle of molten glass玻璃液深度 glass depth玻璃液压头 head of glass玻璃硬化速度 solidification rate of glass玻璃原料 glass-making materials玻璃云母布 glass-mica cloth玻瑰云母带 glass-mica tape玻瑰置换率 rate of glass replacement玻瑰组成 glass composition玻褒组分 glass ingredient, glass component玻纤毡增强热塑性塑料片材glass mat reinforced thermoplastic sheet, GMT 铂坩埚 platinum crucible铂耗 platinum (alloy) loss铂合金回收 recovery of platinum alloy铂合金加工 platinum alloy fabrication铂合金提纯 purification of platinum alloy铂铑 10 合金 10% rhodium-platinum alloy铂铑发热体 Pt-Rh heating element铂铑合金 platinum-rhodium alloy铂铑合金电极 platinum-rhodium electrode铂铑合金漏板 platinum-rhodium bushing, platinum-rhodium nozzle plate铂铑金 3 合金 3% gold-rhodium-platinum alloy铂探针 platinum probe铂中毒 contamination of platinum, poisoning of platinum薄纱罗 leno-marquisette薄毡 tissue, veil (mat)捕纬边线 catch cord不饱和聚酯树脂 unsaturated polyester resin不定位光纤束 unaligned bundle不定形耐火材料bulk refractory不发光火焰 non-luminous flame不干胶带 self-adhesive tape不燃性 non-combustibility不烧砖 unburned brick, unfired brick不完全燃烧 incomplete combustion布边 selvedge, selvage布边成形 selvedge formation布卷 cloth roll布卷大卷装装置 batching motion布纳橡胶[商名] Buna rubber布针 needle arrangement部分热淸洗 partial heat-cleaning, caramelizing采矿 mining can参比漏扳 reference bushing残碳值 carbon residue仓壁振动器 bin vibrator, bin activator槽路现象 channeling槽筒络纱机 grooved drum winder槽简排线器 scroll cam traverse槽芯织物 fluted core fabric侧墙 side wallgeodesic line winding测温孔 temperature-measuring hole测温孔转 block with temperature measuring hole测压孔 pressure-measuring hole层合板 laminated plate,laminate层合板弯曲强度 laminate bending strength层合结构 laminated structure层合壳 laminated shell层合理论 lamination theory层合梁 laminated beam层间混杂 interply hybrid层间剪切性能 interlaminar shear properties层间应力 interlaminar stress层内混杂 intraply hybrid层压 laminating层压板 laminated plate, laminated board,laminate层压布 woven cloth for electric laminate, laminating cloth 层压机 laminating press层状对流 Laminar convection插片冷却器 fin cooler, fin shield茶壶效应 teapot effect拆包机,拆袋机 bag slitter, bag breaker掺杂石英包层光纤 doped-silica cladded optical fiber掺杂石英光纤 doped silica optical fiber缠绕标准线型 basic winding pattern缠绕成型 filament winding缠绕成型机 filament winding machine缠绕封头包角 displacement angle at dome缠绕规律 principles of winding缠绕角 winding angle缠绕速比 winding factor缠绕简体进角 displacement angle at cylinder缠绕线型 winding pattern缠绕芯模转角 rotating angle of mandrel缝绕用无捻粗纱 roving for filament winding, winding roving 缠绕张力 winding tension缠绕中心角 displacement angle长度-重最比 length-weight ratio长径比 aspect ratio长棉薄毡 staple fibre mat长石 feldspar长网[造纸用]Fourdrinier wire, fourdrinier wire长网抄取法[制吸声扳]Four-drinier process长网成形机 Fourdrinier machine长网造纸机 Fourdrinier ( paper ) machine长纤维粒料 long fiber pellet长纤维增强热塑性塑料long fiber reinforced thermoplastics, LFT长纤维增强热塑性塑料粒料LFT pellet, LFT-G长纤维增强热塑性塑料直接成型法 LFT-D process长效增塑剂 permanent plasticizer敞模成型 open molding敞模接触成型 open contact molding抄纸法 paper-making technique超高分子量聚乙烯纤维ultrahigh molecular weight polyethylene fiber, UHMW polyethylene fiber超声波测厚仪 ultrasonic thickness gauge超声波探伤 ultrasonic detection of defects超细玻璃棉superfine glass wool超细玻璃纤维 superfine glass fiber车床式缠绕机 lathe type winding machine车头巻纬器 weft winder at loom沉降缝 subsidence gap沉降片[针织机件]sinker沉降片座 sinker bar沉降室[制短切毡]forming box, forming hood沉降室[制矿物棉] blowing chamber, fiber collection hood沉入式电极 submerged electrode沉式流液洞 submerged throat, sunken throat衬垫纱 laying-in thread衬经 laying-in衬纬 laying-in, weft insertion称量 weighing称量车 weighing car称量斗 weighing hopper, weighing bucket称量精度 weighing accuracy称量周期 weighing cycle成带性 tapability, ribbonization成滴温度 dripping temperature成棉喷嘴 fiberizing jet成膜剂 film former, film-forming agent成围 loop forming成围比 loop formation ratio成网[形成纤网]web forming, web formation成纤机 fiberizing machine成纤率 fiberizability, fiberization efficiency, fiber-forming efficiency成形段 forming section, forming zone成形室 forming hood, forming chamber, forming box成形速比 collect-traverse speed ratio成型[模塑成型] molding, moulding成型窗 processing window成型缺陷 molding defects, molding faults成型温度 molding temperature成型性 moldability成型压力 molding pressure成型粘度 molding viscosity成型周期 molding cycle称量误差 weighing error承力索 heavy-duty rope, load-bearing rope城市煤气 town gas澄清部 refining end, refining zone, refiner澄淸剂 refining agent, fining agent池壁 tank wall池壁顶丝 jack screw for tank Mock池壁砖 tank block, sidewall block池底 tank bottom池底砖 tank bottom block池窑 tank furnace池窑法[拉丝] direct-melt process, DM process池窑流量[出料量]furnace pull,furnace throughput 驰豫时间 relaxation time尺寸稳定性 dimensional stability齿轮卷曲变形纱 gear crimped yarn充纱罗 mock-leno weave冲击板法 impinge plate process冲击荷载 impact load冲击强度 impact strength冲击韧性 impact toughness冲击撕裂试验 ballistic tear test冲孔吸声板 punched acoustic board冲天炉 cupola冲压 stamping冲压成形转 stamped brick冲压机 stamping machine冲压漏嘴 stamped tip, pressed tip冲压片材 stampable sheet冲液抽吸施胶法 flood and extract method抽风机 suction fan抽风系统 air suction system抽风箱 air suction box稠度变量 consistency variables出料量[池窑出料量](furnace) pull出料率 pullrate出射 emergence出射光线 emergent ray出射角 exit angle, emergent angle初捻 primary twisting初捻机 primary twister初捻纱 primary yarn初始重量 initial weight冲击试验机 impact tester除泡报 defoamer, defoaming agent除铁 iron separation储布器[表面处理机组部件] fabric accumulator储能模量 energy storage modulus储纬管 weft storage tube储纬器 weft storage, weft accumulator储毡器[短切原丝机组部件]mat accumulator处理布 finished fabric, treated fabric处理剂 finish, finishing agent处理纱 treated yarn处理液 finishing liquid触变剂 thixotropic agent触变胶浸润剂 thixotropic size触变性树脂 thixotropic resin触压固化树脂 contact (pressure) resins impression resin穿刺织物 pierced fabric穿经 drawing-in, reaching-in穿经钩, 穿综钩 drawing-in hook, heald hook穿经机 drawing-in frame穿经图 drawing-in pattern穿筘denting, reeding穿筘刀 denter, reeding knife穿筘钩 reed hook穿筘机 reeding machine, reed drawing-in machine穿筘图 reed plan穿综 healding, heald draft穿综筘 drawing-in, entering传递成型机 transfer molding machine传递输送机 transfer conveyor传动带 transmission belt传光束 light guide (bundle)传热系数 thermal transmittance, heat transmission coefficient 传输损耗 transmission loss传像束 image guide (bundle), image-transmitting bundle船用油 bunker oil串级控制 cascade control窗帘 curtain窗纱 insect screening, window screening吹扫风管 purge ducting垂流[成型缺陷]sagging垂直百叶帘 vertical blind垂直喷吹法 vertical blowing process锤磨机 hammer mill穿箱刀 denter,reeding knife纯碱 soda ash纯石英光纤 pure silice optical fiber纯氧燃烧 oxy-fuel combustion, oxy-fuel firing纯氧燃供窑 oxy-fuel fired furnace醇酸树脂 alkyd resin瓷土 china clay磁分离器 magnetic separator磁选机 magnetic separator次梁 secondary beam刺针 barbed needle粗碎 rough crushing促进剂 promotor, accelerator催化剂 catalyst脆裂 brittle fracture脆性 brittleness脆性断裂 brittle fracture淬火法[测玻璃析晶温度] quenching method错缝砖 joint-staggering bricks打浆机[造纸用] beater打纬 beating-up打纬机构 beating-up mechanism大功率光纤 high-power optical fiber大梁 girder大气暴露试检 atmospheric exposure test大小式钢领 reduced ring大芯径大数值孔径光纤 large core and large numerical aperture fiber 大修 major repair大磁 crown, main arch大确碑 crown brick大直径光纤 large diameter optical fiber大砖 block代铂坩埚 platinum-substitute crucible单纱上浆 single-end sizing代铂炉 platinum-substitute crucible代铂率 platinum substitution ratio带斗式提升机 belt bucket elevator带式输送机 belt conveyor带式涂油器 belt-type size applicator袋压成塑, 袋塑 bag molding袋装料 bagged material单边钢领 single flanged ring单材料光纤 single material optical fiber单层作业线[拉丝]single level geometry单辑离心法 single wheel spinning process单剑杆织机 single rapier loom单进单出光缆 single-input and single-out put light cable单进多出光缆 single-input and multi-output light cable单晶纤维 single crystal fiber单螺杆挤出机 single screw extruder单模光纤 single mode optical fiber单纱 single yarn.单纱强力试验机 single yarn strength tester单丝 filament, single fiber单丝成形张力 filament attenuation tension单丝喷雾 water spray for filaments单丝涂油 filament sizing单丝毡 filament mat单丝直径 filament diameter单体 monomer单头拉丝机 single-collet winder单位长度质量 mass per unit length单位耗热量 specific heat con-sumption单位面积质量 mass per unit area单位面积重量 area weight单纤光缆 single-fiber cable单纤维强度试验仪 single fiber strength tester单向带 unidirectional tape单向铺层 unidirectional lamina单向应力 unidirectional stress单向预漫料 unidirectional prepreg单向织物, 单向布 unidirectional fabric单元窑 unit melter单重[单位面积重量]areal weight, basis weight旦, 旦尼尔 denier氮化硅纤维 silicon nitride fiber氮化铝晶须 aluminum nitride whisker氮氧玻璃纤维 oxynitride glass fiber当量直径 equivalent diameter挡砖 skimmer block刀辊cutter roller, cutter barrel刀口卷曲变形纱 edge crimped yarn刀片 cutter blade导布辊 twitch roller, cloth guide roller导布装置 cloth guide导电玻瑱纤维 electric conducting glass fiber导电复合材料 conductive com-posite导电纱 electrically-conductive yarn导风筒基布 base cloth for air ducting导钩扳[捻线机部件]lappet,balloon guide rail导钩板升降装置 lappet lifting motion导光棒 light guide rod, light conducting rod导辑 guide roller导热系数 thermal conductivity导热系数测试仪 thermal conduc-tivity tester导纱钩pigtails twizzle导纱辊(yarn) guide roller导纱器yarn guide导纱眼guide eye导丝器fiber guide导纬器weft guide倒刺针, 倒钩针 barbed needle倒火焰 inverse flame倒盘头rebeaming倒轴 rebeaming倒轴机rebeaming machine捣打料 ramming material, ram-ming mix捣打砖 rammed brick灯光检验台 illuminated inspec-tion table灯芯 wick等静压成形砖 isostatic-pressed brick等静压氧化铬 isostatic-pressed chrome oxide等离子体启动化学汽相沉积法 plasma-activated chemical vapor deposition process等张力封头曲面 isoteosion head contour低毒固化剂 low toxicity curing agent低分子量聚酰胺 low molecular weight polyamide低介电玻璃纤维D-glass fiber, low dielectric constant glass fiber低密度聚乙烯 low density polyethylene低密度模塑料 low density mold-ing compound低密度片状模塑料 low density SMC低熔玻璃 low melting glass低释苯乙烯树脂 low styrene emission resin低收缩树海 low shrink resin, low profile resin低收缩添加剂 low-shrink additive, low profile additive低损耗光纤 low-loss optical fiber低压(固化〉树脂 low pressure resin低压模塑料 low pressure molding compound地板毡 flooring mat地秤 ground scale地毯底布 carpet backing点火孔 firing hole点火燃烧器 pilot burner电磁振动器 electromagnetic vibrator电动葫芦 electric hoist电辅助加热 electric boosting电弧炉 arc furnace电绝缘布 electrical insulation cloth电绝缘带 electrical insulation tape电绝缘套管 electrical insulation sleeve电绝缘性能 electrical insulating properties电熔刚玉砖fused corundum brick电熔铬刚玉砖 fused chrome-corundum brick电熔式代铂炉 electric melting type Pt-substitute crucible电熔窑 electric (melting) furnace电熔再结合刚玉砖 fusion re-bonded corundum brick电熔再烧结锆刚玉砖 fused re-bonded AZS brick电熔再烧结莫来石砖 fused re-bonded mullite brick电助熔 electric boosting点火 firing up电子秤 electronic weigher, electronic scale电子级玻璃布[电子布] glass fabric for electronics [electronic fabric] 电阻加热 electric resistance heating电阻炉 electric resistance furnace电阻式代铂炉 electric resistance type Pt-substitute crucible淀粉 starch淀粉浆料 starch size淀粉油浸润剂 starch-oil size吊顶 suspended ceiling吊挂[输送丝饼用]overhead conveying system吊梁 suspended beam吊碹 suspended arch吊综 harness mounting钓鱼杆基布 fishing rod cloth叠边[丝筒疵点]overlaid edge叠氮型硅烷 azido silane丁苯树脂 butadiene-styrene resin丁苯橡胶 butadiene-styrene rubber, styrene-butadiene rubber丁吡胶乳 butadiene-pyridine latex丁二烯-苯乙烯-乙烯基吡啶三聚物butadiene-styrene-vinyl pyridine terpolymer 丁二烯橡胶 butadiene rubber丁腈橡胶橡胶 butadiene nitrile rubber, nitrile-butadiene rubber丁钠榇胶 butadiene sodium rubber丁砖层 header course丁砖砌合 header bond顶出机构 knockout mechanism顶破强力 bursting strength顶铁 pressure iron bar定长玻璃纤维staple glass fiber定长纤维布 staple fiber cloth, woven staple fiber fabric定长纤维毛纱 staple (fiber) sliver定长纤维纱 staple (fiber) yarn定长自停(装置)fixed length stop motion定位光纤束 aligned bundle定纹 weave set定纹处理剂 weaveset finish锭轨 spindle rail锭距 spindle gauge, spindle pitch锭位 spindle position锭子 spindle锭子油 spindle oil锭子制动器 spindle brake动态粘弹性 dynamic viscoelasticity动态粘弹仪 dynamic viscoelasticity tester冻融循环试验 freeze-thaw cycles test斗式提升机 bucket elevator毒重石 witherite独居石 monazite镀金属玻璃纤维 metallized glass fiber, metal-coated glass fiber教金属鳞片 metallized flake镀金属纤维 metallized fiber镀铝玻璃纤维 aluminum-coated glass fiber, alununized glass fiber镀镍玻璃纤维nickle-coated glass fiber镀锌玻璃纤维zinc-coated glass fiber镀银玻璃纤维silver-coated glass fiber端墙 end wall端子夹头[漏板附件]terminal clamp短梁剪切试验 short beam shear test短程线缠绕 geodesic line winding短切长度 chopped length, chop length短切机 chopper, chopping ma-chine短切性 choppability短切用无捻粗纱 roving for chopping短切原丝 chopped strands短切原丝干燥机 chopped strand dryer短切原丝机 chopped strand machine短切原丝毡 chopped strand mat,CSM短切原丝毡机组 chopped strand mat machine, CSM machine短切毡用无捻粗纱 roving for CSM短纤维增强热塑性塑料short fiber reinforced thermoplastics, SFT 短效增塑剂 fugitive plasticizer’ temporary plasticizer断经[织疵] broken warp, broken end断经停车杆 warp stop rod断经自停装置 warp stop motion断裂长度breaking length断裂力学 fracture mechanics断裂绕度deflection at break断裂强度 breaking strength断裂强力breaking force断裂韧性fracture toughness断裂伸长 breaking elongation, elongation at break断头 fiber break(age) , end break(age)断头飞丝 filament breakage and fan break-out断头率 fiber breakage rate, end breakage rate断头自停(装置)stop motion断纬[织疵]broken pick断纬自停装置 weft stop motion缎纹 satin (weave)煅烧白云石 burnt dolomite煅烧破酸calcined magnesium carbonate煅烧气化结 calcined alumina煅石灰 burnt lime堆场 stacking yard堆垛机 stacking machine, piling machine堆垛输送机 stacking conveyor对苯二酚 bydroquinone对苯二甲酸型聚酯树脂 terephtbalic polyester resin对流 convection,convection cur-rent对轮法 co-acting roller process对模 matched die对模成型 matched-die molding对位芳族聚酰胺纤维 para-aramid fiber多氨基硅烷 polyamino silane多臂机dobby多臂机构 dobby motion多臂机龙头dobby head多臂提花组织 dobby weave多层结构 multilayer structure多层压机 daylight press, multi-opening press多层织物 multilayer fabric, multiple fabric多次并捻 cabling多氮杂酰胺硅烷 polyazamide silane多管进浆口[造纸用] inlet header多辊离心法 multiwheel spinning process多胶区[模塑缺陷] resin-rich area多进多出光缆 multi-input and multi-output light cable多晶纤维 polycrystalline fiber多孔硅砖 porous silica brick多孔氧化铬砖 porous chrome oxide brick多孔砖 porous brick, perforated brick多模光纤 multimode optical fiber多束光缆 multiple bundle cable多维编织 multidimensional braiding多维织物 multidimensional fabric多纤光缆 multifiber cable多向铺层 multidirectional lamina多轴缠绕机 multi-axis filament winder多轴向经编机 multiaxial warp-knitting machine多轴向经编针织物 multiaxial warp-knitted fabric多轴向织物, 多轴向布 multiaxial fabric多组分玻璃光纤 compound-glass optical fiber, multicomponent glass optical fiber顺式破碎机 jaw crusher恩氏粘度 Engler viscosity二次起泡温度secondary seeding temperature二次气泡 secondary seed二丁脂 dibutyl ester二甲苯树脂 xylene resin二甲基氨基丙基胺/壬酸缩聚物 diraethylaminopropylamine/pelargonic acid condensate 二羧基化丁二烯-苯乙烯共聚物 dicarboxylated butadiene-styrene copolymer二缩水甘油醚 diglycidyl ether二维织物 two-dimensional fabric, 2D fabric二氧化锆 zirconia,zirconium dioxide二氧化硅 silica, silicon dioxide二氧化锰 manganesia,manganese dioxide二氧化钛 titania,titanium dioxide二乙基苯胺 diethyl aniline二乙烯三胺 diethylene triamine二异氰酸脂 diisocyanate二甲基苯胺 dimethyl aniline发光火焰 luminous flame发泡促进剂. foaming accelerator发泡剂 foaming agent发生炉煤气 producer gas发烟点 smoke point法向应力 normal stress凡士林 vaseline矾土 alumina clay, alumine反玻化 devitrification反吹风清灰过滤 reverse jet filter, reverse air filter反螺旋缠绕 reverse helical winding反射绝热层 reflective insulation反手捻, Z捻 Z twist反碴 invert arch反应釜 reaction vessel反应注射成型 reaction injection molding, RIM反应注射拉挤 reactive injection pultrusion范德华键 van der Waals bond范德华力 van der Waals force方格布[俗称] roving cloth方解石 calcite, limespar方镁石 periclase方平组织 basket weave芳纶纤维[芳族聚酰胺纤维]aramid fiber芳族胺 aromatic amine芳族聚酰胺纤维 aromatic polyamide fiber, aramid fiber 防尘油 dust binder oil防虫网 insect screening防弹衣 bulletproof clothing防辐射玻璃纤维 radiation-proof glass fiber, L-glass fiber 防腐衬布 anticorrosion lining cloth防腐剂 antiseptic, antiseptic agent防护服 protective clothing防护热板法[测导热性能]guarded hot plate method防护热箱法[测导热性能]guarded hot box method防回火装置 fire check, flame trap防火处理剂 flameproof finish, fireproof finish放铁水孔 iron tapping hole防火服 fire protection clothing,fireproof clothing防火帘 fire curtain防火毯 fire blanket防老剂 antiager, anti-ageing agent防霉剂 mildew inhibitor防燃剂 fire suppressant防水布 waterproof cloth防水材料 waterproof material防水处理剂 waterproof finish防水剂 water repellent防水巻材 waterproof roll, waterproof membrane防烟剂 smoke suppressant防烟帘 smoke curtain防晕带 anticorona tape防粘输送带 non-tacky conveyor belt仿形织物 contoured fabric纺织玻璃纤维textile glass fiber纺织型浸润剂 textile size, size for textiles纺织增强型浸润剂 textile plastic size放玻璃液池 glass draining tank放玻璃液孔 glass draining hole放料漏板 drain bushing放铁水 iron tapping飞锯 flying saw飞丝[拉丝故障] filament fan break-out, snap out非硅烷偶联剂 nonsilane coupling agent非活性稀释剂 non-active diluent非活性增韧剂 non-active toughener非均质性 heterogeneity非离子乳化剂 nonionic emulsifier非离子皂 nonionic soap非连续玻璃纤维 discontinuous glass fiber非迁移性润滑剂 non-migrating lubricant非通信光纤 noncommunication optical fiber非稳态法[测导热性能]non-steady state method非线性缠绕 non-linear winding非相关光纤束 incoherent bundle非约束流动 non-bounded flow非正交三维织物 unorthogonal 3D fabric非织造布 nonwoven fabric非织造网布 nonwoven mesh, nonwoven scrim废漏板 scrap bushing废气 waste gas, exhaust gas废丝 waste fiber废丝处理 waste fiber disposal废丝回炉 remelting of waste fibers废丝回收 recycling of waste fibers废丝通道 waste fiber collecting shoot沸水煮试验 boiling water test fen分辨率 resolution, resolving power分辨能力 resolving power, resolution分别称量 separate weighing分布式控制系统 distributed control system, DCS分层[层间开裂] delamination分隔式料仓 compartment silo分隔式燃烧器 separate burner分股集束器splitting comb分股集束原丝split strand分级燃烧 fractional combustion分绞 lease,leasingt splitting分绞棒 lease rod, lease bar分绞箱 lease reed, lease comb分绞线 lease cord分经棒 lease rod, lease bar分经箱 lease reed分经器 warp separator分拉 tandem (collet) winding分拉拉丝机 tandem collet winder分离式卷取 remote take-up分流阀 diverter valve分批式脱油炉 batch type desizing oven分批整经 back-beaming method分散剂 dispersing agent分散性 dispersity, dispersivity分束效率 splitting efficiency分束率 splitting ratio分条整经 sectional warping分条整经滚简 sectional warping drum分条整经机 sectional warper, sectional warping machine 分条整经机定幅箱 section space reed分支光纤 bifurcated optical fiber酚醛环氧树脂 phenolic epoxy resin酚醛树脂 phenolic resin焚烧器 incinerator粉剂短切原丝毡 powder-bound chopped strand mat粉煤灰 fly ash粉末沉积法 powder deposition process粉末回收盘 powder recovery tray粉末漫溃法 powder impregnation process粉末涂层 powder coating粉末粘结剂 powder binder粉碎 pulverizing,disintegrating粉碎机 pulverizer,disintegrator风刀 air knife, air cutter风环 air ring风套 air cabinet, air plenum风嘴 air nozzle, tuyere封闭辊 sealing roller封头 dome蜂窝夹层结构 honeycomb sandwich蜂窝芯 honeycomb core缝编 stitching, stitch-bonding缝编短切原丝毡 stitch-bonded chopped strand mat缝编复合轻 stitched combination mat缝编机 stitch-bonding machine,stitching machine缝编线 stitching thread, stitc-hing yarn缝编毡 stitched mat, knitted mat缝编织物 stitched fabric, stitch-bonded fabric缝纫线 sewing thread缝毡 mattress, sewn blanket缝毡机 sewing machine, stitc-hing machine呋喃树脂furan resin, furane resin弗雷泽织物透气性试验仪 Frazier permeometer氟化物玻璃光纤 fluoride glass optical fiber氟树脂 fluororesin氟碳树脂 fluorocarbon resin浮雕吸声板 embossed acoustic board浮球式液面传感器 floating level sensor浮选机 flotation machine浮砖 floater, boat辅助羊脚[导钩板升降杆] auxiliary poker腐蚀干涉法[测玻璃球均匀性] etching-interfering method 附壁效应 wall effect附模性 mold conformance复合材料 composite (material)复合材料力学 mechanics of composites复合绝热层 composite insulation复合滤纸 composite filter paper复合纱 commingled yarn,hybrid yarn, composite yarn复合纤维 commingled fiber, hy-brid fiber,composite fiber 复合敏 combination mat复合针 compound needle复抢纱 doubled yarn, folded yarn复数模量 complex modulus富树脂区 resin-rich area富氧燃烧 oxygen enriched com-bustion覆盖毡 overlay mat覆面毡 veil (mat)覆膜滤料 membrane laminated filter media。

pipes & pipe sizing

pipes & pipe sizing

Pipes and Pipe SizingPipe sizing is a crucial aspect of steam system design. This tutorial offers detailed advice on standards, schedules, materials and sizing for various saturated and superheated steam duties. Use the quick links below to take you to the main sections of this tutorial: The printable version of this page has now been replaced byThe Steam and Condensate Loop Book Try answering the Questions for this tutorial View the complete collection of Steam Engineering Tutorials Contact Us Top Standards and wall thickness There are a number of piping standards in existence around the world, but arguably the most global are those derived by the American Petroleum Institute (API), where pipes are categorised in schedule numbers. These schedule numbers bear a relation to the pressure rating of the piping. There are eleven Schedules ranging from the lowest at 5 through 10, 20, 30, 40, 60, 80, 100, 120, 140 to schedule No. 160. For nominal size piping 150 mm and smaller, Schedule 40 (sometimes called 'standard weight') is the lightest that would be specified for steam applications. Regardless of schedule number, pipes of a particular size all have the same outside diameter (not withstanding manufacturing tolerances). As the schedule number increases, the wall thickness increases, and the actual bore is reduced. For example:• •A 100 mm Schedule 40 pipe has an outside diameter of 114.30 mm, a wall thickness of 6.02 mm, giving a bore of 102.26 mm. A 100 mm Schedule 80 pipe has an outside diameter of 114.30 mm, a wall thickness of 8.56 mm, giving a bore of 97.18 mm.Only Schedules 40 and 80 cover the full range from 15 mm up to 600 mm nominal sizes and are the most commonly used schedule for steam pipe installations. This Tutorial considers Schedule 40 pipework as covered in BS 1600. Tables of schedule numbers can be obtained from BS 1600 which are used as a reference for the nominal pipe size and wall thickness in millimetres. Table 10.2.1 compares the actual bore sizes of different sized pipes, for different schedule numbers. In mainland Europe, pipe is manufactured to DIN standards, and DIN 2448 pipe is included in Table 10.2.1.Table 10.2.1 Comparison of pipe standards and actual bore diameters.In the United Kingdom, piping to EN 10255, (steel tubes and tubulars suitable for screwing to BS 21 threads) is also used in applications where the pipe is screwed rather than flanged. They are commonly referred to as 'Blue Band' and 'Red Band'; this being due to their banded identification marks. The different colours refer to particular grades of pipe:• •Red Band, being heavy grade, is commonly used for steam pipe applications. Blue Band, being medium grade, is commonly used for air distribution systems, although it is sometimes used for low-pressure steam systems.The coloured bands are 50 mm wide, and their positions on the pipe denote its length. Pipes less than 4 metres in length only have a coloured band at one end, while pipes of 4 to 7 metres in length have a coloured band at either end.Fig. 10.2.1 Red band, branded pipe, - heavy gradeFig. 10.2.2 Blue band, branded pipe, - medium grade, between 4-7 metres in lengthTop Pipe material Pipes for steam systems are commonly manufactured from carbon steel to ASME (ANSI) B 16.9 A106. The same material may be used for condensate lines, although copper tubing is preferred in some industries. For high temperature superheated steam mains, additional alloying elements, such as chromium and molybdenum, are included to improve tensile strength and creep resistance at high temperatures. Typically, pipes are supplied in 6 metre lengths. Top Pipeline sizing The objective of the steam distribution system is to supply steam at the correct pressure to the point of use. It follows, therefore, that pressure drop through the distribution system is an important feature. Liquids Bernoulli's Theorem (Daniel Bernoulli 1700 - 1782) is discussed in Block 4 - Flowmetering. D'Arcy (D'Arcy Thompson 1860 - 1948) added that for fluid flow to occur, there must be more energy at Point 1 than Point 2 (see Figure 10.2.3). The difference in energy is used to overcome frictional resistance between the pipe and the flowing fluid.Fig. 10.2.3 Friction in pipesBernoulli relates changes in the total energy of a flowing fluid to energy dissipation expressed either in terms of a head loss hf (m) or specific energy loss g hf (J/kg). This, in itself, is not very useful without being able to predict the pressure losses that will occur in particular circumstances. Here, one of the most important mechanisms of energy dissipation within a flowing fluid is introduced, that is, the loss in total mechanical energy due to friction at the wall of a uniform pipe carrying a steady flow of fluid. The loss in the total energy of fluid flowing through a circular pipe must depend on: L = The length of the pipe (m) D = The pipe diameter (m) u = The mean velocity of the fluid flow (m/s) μ = The dynamic viscosity of the fluid (kg/m s=Pa s) ρ = The fluid density (kg/m) ks = The roughness of the pipe wall* (m) *Since the energy dissipation is associated with shear stress at the pipe wall, the nature of the wall surface will be influential, as a smooth surface will interact with the fluid in a different way than a rough surface. All these variables are brought together in the D'Arcy-Weisbach equation (often referred to as the D'Arcy equation), and shown as Equation 10.2.1. This equation also introduces a dimensionless term referred to as the friction factor, which relates the absolute pipe roughness to the density, velocity and viscosity of the fluid and the pipe diameter. The term that relates fluid density, velocity and viscosity and the pipe diameter is called the Reynolds number, named after Osborne Reynolds (1842-1912, of Owens College, Manchester, United Kingdom), who pioneered this technical approach to energy losses in flowing fluids circa 1883. The D'Arcy equation (Equation 10.2.1):Equation 10.2.1Where for equation 10.2.1 using SI based units: hf = Head loss to friction (m) f = Friction factor (dimensionless)L = Length (m) u = Flow velocity (m/s) g = Gravitational constant (9.81 m/s2) D = Pipe diameter (m) Where for equation 10.2.1 using Imperial based units: hf = Head loss to friction (ft) f = Friction factor (dimensionless) L = Length (ft) u = Flow velocity (ft/s) g = Gravitational constant (32.17 ft/s2) D = Pipe diameter (ft) Interesting point Readers in some parts of the world may recognise the D'Arcy equation in a slightly different form, as shown in Equation 10.2.2. Equation 10.2.2 is similar to Equation 10.2.1 but does not contain the constant 4.Equation 10.2.2The reason for the difference is the type of friction factor used. It is essential that the right version of the D'Arcy equation be used with the selected friction factor. Matching the wrong equation to the wrong friction factor will result in a 400% error and it is therefore important that the correct combination of equation and friction factor is utilised. Many textbooks simply do not indicate which friction factors are defined, and a judgement must sometimes be based on the magnitudes quoted. Equation 10.2.2 tends to be used by those who traditionally work in Imperial units, and still tends to be used by practitioners in the United States and Pacific rim regions even when metric pipe sizes are quoted. Equation 10.2.1 tends to be used by those who traditionally work in SI units and tends more to be used by European practitioners. For the same Reynolds number and relative roughness, the 'Imperial based friction factor' will be exactly four times larger than the 'SI based friction factor'. Friction factors can be determined either from a Moody chart or, for turbulent flows, can be calculated from Equation 10.2.3, a development of the Colebrook - White formula.Equation 10.2.3Where: f = Friction factor (Relates to the SI Moody chart) ks = Absolute pipe roughness (m) D = Pipe bore (m) Re = Reynolds number (dimensionless) However, Equation 10.2.3 is difficult to use because the friction factor appears on both sides of the equation, and it is for this reason that manual calculations are likely to be carried out by using the Moody chart. On an SI style Moody chart, the friction factor scale might typically range from 0.002 to 0.02, whereas on anImperial style Moody chart, this scale might range from 0.008 to 0.08. As a general rule, for turbulent flow with Reynolds numbers between 4000 and 100000, 'SI based' friction factors will be of the order suggested by Equation 10.2.4, whilst 'Imperial based' friction factors will be of the order suggested by Equation 10.2.5.Equation 10.2.4 - 'SI based' friction factorsEquation 10.2.5 - 'Imperial based' friction factorsThe friction factor used will determine whether the D'Arcy Equation 10.2.1 or 10.2.2 is used. For 'SI based' friction factors, use Equation 10.2.1; for 'Imperial based' friction factors, use Equation 10.2.2. Example 10.2.1 - Water pipe Determine the velocity, friction factor and the difference in pressure between two points 1 km apart in a 150 mm constant bore horizontal pipework system if the water flowrate is 45 m³/h at 15°C.In essence, the friction factor depends on the Reynolds number (Re) of the flowing liquid and the relative roughness (kS/d) of the inside of the pipe; the former calculated from Equation 10.2.6, and the latter from Equation 10.2.7. Reynolds number (Re)Equation 10.2.6Where: Re = Reynolds number ρ = Density of water u = Velocity of water D = Pipe diameter From Equation 10.2.6: = 1000 kg/m = 0.71 m/s = 0.15 mμ = Dynamic viscosity of water (at 15°C) = 1.138 x 10-3 kg/m s (from steam tables)The pipe roughness or 'ks' value (often quoted as 'e' in some texts) is taken from standard tables, and for 'commercial steel pipe' would generally be taken as 0.000045 metres. From this the relative roughness is determined (as this is what the Moody chart requires).Equation 10.2.7From Equation 10.2.7:The friction factor can now be determined from the Moody chart and the friction head loss calculated from the relevant D'Arcy Equation. From the European Moody chart (Figure 10.2.4), Where: ks/D = 0.0003 Re = 93585: Friction factor (f) = 0.005Fig. 10.2.4 'SI based' Moody chart (abridged)From the European D'Arcy equation (Equation 10.2.1) :From the USA / AUS Moody chart (Figure 10.2.5), Where: ks/D = 0.0003 Re = 93 585 Friction factor (f) = 0.02Fig. 10.2.5 ‘Imperial based’ Moody chart (abridged)From the USA / AUS D'Arcy equation (Equation 10.2.2):The same friction head loss is obtained by using the different friction factors and relevant D'Arcy equations. In practice whether for water pipes or steam pipes, a balance is drawn between pipe size and pressure loss. Top Steam Oversized pipework means: • Pipes, valves, fittings, etc. will be more expensive than necessary.•Higher installation costs will be incurred, including support work, insulation, etc.•For steam pipes a greater volume of condensate will be formed due to the greater heat loss. This, in turn, means that either: - More steam trapping is required, or - Wet steam is delivered to the point of use.In a particular example:• •The cost of installing 80 mm steam pipework was found to be 44% higher than the cost of 50 mm pipework, which would have had adequate capacity. The heat lost by the insulated pipework was some 21% higher from the 80 mm pipeline than it would have been from the 50 mm pipework. Any non-insulated parts of the 80 mm pipe would lose 50% more heat than the 50 mm pipe, due to the extra heat transfer surface area.Undersized pipework means: • A lower pressure may only be available at the point of use. This may hinder equipment performance due to only lower pressure steam being available.• •There is a risk of steam starvation. There is a greater risk of erosion, waterhammer and noise due to the inherent increase in steam velocity.As previously mentioned, the friction factor (f) can be difficult to determine, and the calculation itself is time consuming especially for turbulent steam flow. As a result, there are numerous graphs, tables and slide rules available for relating steam pipe sizes to flowrates and pressure drops. One pressure drop sizing method, which has stood the test of time, is the 'pressure factor' method. A table of pressure factor values is used in Equation 10.2.2 to determine the pressure drop factor for a particular installation.Equation 10.2.8Where: F = Pressure factor P1 = Factor at inlet pressure P2 = Factor at a distance of L metres L = Equivalent length of pipe (m) Example 10.2.2 Consider the system shown in Figure 10.2.6, and determine the pipe size required from the boiler to the unit heater branch line. Unit heater steam load = 270 kg/h.Fig. 10.2.6 System used to illustrate Example 10.2.2Although the unit heater only requires 270 kg/h, the boiler has to supply more than this due to heat losses from the pipe. The allowance for pipe fittings The length of travel from the boiler to the unit heater is known, but an allowance must be included for the additional frictional resistance of the fittings. This is generally expressed in terms of 'equivalent pipe length'. If the size of the pipe is known, the resistance of the fittings can be calculated. As the pipe size is not yet known in this example, an addition to the equivalent length can be used based on experience.• • •If the pipe is less than 50 metres long, add an allowance for fittings of 5%. If the pipe is over 100 metres long and is a fairly straight run with few fittings, an allowance for fittings of 10% would be made. A similar pipe length, but with more fittings, would increase the allowance towards 20%.In this instance, revised length = 150 m + 10% = 165 m The allowance for the heat losses from the pipe The unit heater requires 270 kg/h of steam; therefore the pipe must carry this quantity plus the quantity of steam condensed by heat losses from the main. As the size of the main is yet to be determined, the true calculations cannot be made, but, assuming that the main is insulated, it may be reasonable to add 3.5% of the steam load per 100 m of the revised length as heat losses. In this instance, the additional allowance =Revised boiler load = 270 kg/h + 5.8% = 286 kg/h From Table 10.2.2 (an extract from the complete pressure factor table, Table 10.2.5, which can be found in the Appendix at the end of this Tutorial) 'P' can be determined by finding the pressure factors P1 and P2, and substituting them into Equation 10.2.8.Table 10.2.2 Extract from pressure factor table (Table 10.2.5)From the pressure factor table (see Table 10.2.2): P1 (7.0 bar g) = 56.38 P2 (6.6 bar g) = 51.05 Substituting these pressure factors (P1 and P2) into Equation 10.2.8 will determine the value for 'F': Equation 10.2.8.Following down the left-hand column of the pipeline capacity and pressure drop factors table (Table 10.2.6 Extract shown in Table 10.2.3); the nearest two readings around the requirement of 0.032 are 0.030 and 0.040. The next lower factor is always selected; in this case, 0.030.Table 10.2.3 Extract from pipeline capacity and pressure factor table (Table 10.2.6)Although values can be interpolated, the table does not conform exactly to a straight-line graph, so interpolation cannot be absolutely correct. Also, it is bad practice to size any pipe up to the limit of its capacity, and it is important to have some leeway to allow for the inevitable future changes in design. From factor 0.030, by following the row of figures to the right it will be seen that:• •A 40 mm pipe will carry 229.9 kg/h. A 50 mm pipe will carry 501.1 kg/h.Since the application requires 286 kg/h, the 50 mm pipe would be selected. Having sized the pipe using the pressure drop method, the velocity can be checked if required.Where:Viewed in isolation, this velocity may seem low in comparison with maximum permitted velocities. However, this steam main has been sized to limit pressure drop, and the next smaller pipe size would have given a velocity of over 47 m/s, and a final pressure less than the requirement of 6.6 bar g, which is unacceptable. As can be seen, this procedure is fairly complex and can be simplified by using the nomogram shown in Figure 10.2.9 (in the Appendix of this Tutorial). The method of use is explained in Example 10.2.3. Example 10.2.3 Using the data from Example 10.2.2, determine the pipe size using the nomogram shown in Figure 10.2.7. Inlet pressure = 7 bar g Steam flowrate = 286 kg/hMinimum allowable P2 = 6.6 bar gMethod • Select the point on the saturated steam line at 7 bar g, and mark Point A.• • • •From point A, draw a horizontal line to the steam flowrate of 286 kg/h, and mark Point B. From point B, draw a vertical line towards the top of the nomogram (Point C). Draw a horizontal line from 0.24 bar/100 m on the pressure loss scale (Line DE). The point at which lines DE and BC cross will indicate the pipe size required. In this case, a 40 mm pipe is too small, and a 50 mm pipe would be used.Fig. 10.2.7 Steam pipeline sizing chart - Pressure dropSizing pipes on velocity From the knowledge gained at the beginning of this Tutorial, and particularly the notes regarding the D'Arcy equation (Equation 10.2.1), it is acknowledged that velocity is an important factor in sizing pipes. It follows then, that if a reasonable velocity could be used for a particular fluid flowing through pipes, then velocity could be used as a practical sizing factor. As a general rule, a velocity of 25 to 40 m/s is used when saturated steam is the medium. 40 m/s should be considered an extreme limit, as above this, noise and erosion will take place particularly if thesteam is wet. Even these velocities can be high in terms of their effect on pressure drop. In longer supply lines, it is often necessary to restrict velocities to 15 m/s to avoid high pressure drops. It is recommended that pipelines over 50 m long are always checked for pressure drop, no matter what the velocity. By using Table 10.2.4 as a guide, it is possible to select pipe sizes from known data; steam pressure, velocity and flowrate.Table 10.2.4 Saturated steam pipeline capacities in kg/h for different velocities (Schedule 40 pipe)Alternatively the pipe size can be calculated arithmetically. The following information is required, and the procedure used for the calculation is outlined below. Information required to calculate the required pipe size: From this information, the cross sectional area (A) of the pipe can be calculated:Rearranging the formula to give the diameter of the pipe (D) in metres:Example 10.2.4 A process requires 5 000 kg/h of dry saturated steam at 7 bar g. For the flow velocity not to exceed 25 m/s, determine the pipe size. WhereTherefore, using:Since the steam velocity must not exceed 25 m/s, the pipe size must be at least 130 mm; the nearest commercially available size, 150 mm, would be selected. Again, a nomogram has been created to simplify this process, see Figure 10.2.6. Example 10.2.5 Using the information from Example 10.2.4, use Figure 10.2.6 to determine the minimum acceptable pipe size u vg = Flow velocity (m/s) = Specific volume (m³/kg)s= Mass flowrate (kg/s) = Volumetric flowrate (m³/s) = ms x vgInlet pressure Steam flowrate=7 bar g = 5000 kg/h 25 m/sMaximum velocity =Method: • Draw a horizontal line from the saturation temperature line at 7 bar g (Point A) on the pressure scale to the steam mass flowrate of 5 000 kg/h (Point B).• •From point B, draw a vertical line to the steam velocity of 25 m/s (Point C). From point C, draw a horizontal line across the pipe diameter scale (Point D). A pipe with a bore of 130 mm is required; the nearest commercially available size, 150 mm, would be selected.Fig. 10.2.8 Steam pipeline sizing chart - VelocitySizing pipes for superheated steam duty Superheated steam can be considered as a dry gas and therefore carries no moisture. Consequently there is no chance of pipe erosion due to suspended water droplets, and steam velocities can be as high as 50 to 70 m/s ifthe pressure drop permits this. The nomograms in Figures 10.2.5 and 10.2.6 can also be used for superheated steam applications. Example 10.2.6 Utilising the waste heat from a process, a boiler/superheater generates 30 t/h of superheated steam at 50 bar g and 450°C for export to a neighbouring power station. If the velocity is not to exceed 50 m/s, determine: 1. The pipe size based on velocity (use Figure 10.2.8). 2. The pressure drop if the pipe length, including allowances, is 200 m (use Figure 10.2.9). Part 1• • • •Using Figure 10.2.8, draw a vertical line from 450°C on the temperature axis until it intersects the 50 bar line (Point A). From point A, project a horizontal line to the left until it intersects the steam 'mass flowrate' scale of 30 000 kg/h (30 t/h) (Point B). From point B, project a line vertically upwards until it intersects 50 m/s on the 'steam velocity' scale (Point C). From Point C, project a horizontal line to the right until it intersects the 'inside pipe diameter' scale.The 'inside pipe diameter' scale recommends a pipe with an inside diameter of about 120 mm. From Table 10.2.1 and assuming that the pipe will be Schedule 80 pipe, the nearest size would be 150 mm, which has a bore of 146.4 mm. Part 2• • • •Using Figure 10.2.7, draw a vertical line from 450°C on the temperature axis until it intersects the 50 bar line (Point A). From point A, project a horizontal line to the right until it intersects the 'steam mass flowrate' scale of 30 000 kg/h (30 t/h) (Point B). From point B, project a line vertically upwards until it intersects the 'inside pipe diameter' scale of (approximately) 146 mm (Point C). From Point C, project a horizontal line to the left until it intersects the 'pressure loss bar/100 m' scale (Point D).The 'pressure loss bar/100 m' scale reads about 0.9 bar/100 m. The pipe length in the example is 200 m, so the pressure drop is:This pressure drop must be acceptable at the process plant. Using formulae to establish steam flowrate on pressure drop Empirical formulae exist for those who prefer to use them. Equations 10.2.9 and 10.2.10 are shown below. These have been tried and tested over many years, and which appear to give results close to the pressure factor method. The advantage of using these formulae is that they can be programmed into a scientific calculator, or a spreadsheet, and consequently used without the need to look up tables and charts. Equation 10.2.10 requires the specific volume of steam to be known, which means it is necessary to look up this value from a steam table. Also, Equation 10.2.10 should be restricted to a maximum pipe length of 200 metres. Pressure drop formula 1Equation 10.2.9.Where:P1 = Upsteam pressure (bar a) P2 = Downstream pressure (bar a) L = Length of pipe (m) s = Mass flowrate (kg/h) D = Pipe diameter (mm) Pressure drop formula 2 (Maximum pipe length: 200 metres)Equation 10.2.10.ΔP = Pressure drop (bar) L = Length of pipe = Mass flowrate(kg/h) D = Pipe diameter (mm) Where: Top Summary• •vg = Specific volume of steam (m3/kg)The selection of piping material and the wall thickness required for a particular installation is stipulated in standards such as EN 45510 and ASME 31.1. Selecting the appropriate pipe size (nominal bore) for a particular application is based on accurately identifying pressure and flowrate. The pipe size may be selected on the basis of: - Velocity (usually pipes less than 50 m in length). - Pressure drop (as a general rule, the pressure drop should not normally exceed 0.1 bar/50 m.AppendixTable 10.2.5 Pressure drop factor (F) tableTable 10.2.6 Pipeline capacity from pressure drop factorFig 10.2.9 Steam pipeline sizing chart - Pressure dropFig 10.2.10 Steam pipeline sizing chart - Velocity。

基于知识工程的岸边集装箱起重机臂架俯仰机构参数化研究

基于知识工程的岸边集装箱起重机臂架俯仰机构参数化研究

0 引言岸边集装箱起重机(以下简称岸桥)作为安装在港口、码头前沿,又是船舶集装箱装卸的主要设备,对其提出了越来越高的要求,特别是大型集装箱船舶的发展。

促使岸桥向着重型化、大型化、高效化、智能化、标准化、节能环保的方向发展。

岸桥是一种专业装卸集装的港口机械设备,其结构巨大,构成复杂,设计困难,其主要包括起升机构,臂架俯仰机构,小车运行机构,大车运行机构、托架小车系统、金属结构、机器房、辅助部件、电气系统等。

其结构形式多种多样,设计计算复杂,传统的手工设计方法无法满足计算要求,设计周期过长,工作量繁重,且较难保证设计质量。

臂架俯仰机构是岸桥的一个主要机构,当船舶停靠或起航时通过该机构实现岸桥前大梁的升起和放下,方便船舶进出海港。

因此,当船舶进出港口码头时臂架俯仰机构才需要工作,使用率低,但安全性要求很高。

虽然其结构布置形式较为固定,相似性很高,但因其不同吨位,外伸距不同,计算选型配套件也会不同。

每次设计均需重新计算、选型、画图改图,重复性劳动较多,工作量很大。

该文通过对岸桥臂架俯仰机构多种布置形式的研究和对应布置形式符合国内外设计标准的设计计算研究,提出了基于知识工程的参数化设计方法,可有效解决设计过程中计算的复杂性,结构的多样性,简化过程,避免重复设计。

该参数化设计方法一旦实现,可以确保设计计算的统一性,完整性,只需输入设计参数,即可实现岸桥臂架俯仰机构的快速设计,大大缩短设计周期,提高设计质量。

通过对岸桥臂架俯仰机构参数化的研究,逐步扩展到对岸桥金属机构,起升机构,运行基于知识工程的岸边集装箱起重机臂架俯仰机构参数化研究黄进前 郭珍吉 周振江河南卫华重型机械股份有限公司 长垣 453400摘 要:提出了一种岸边集装箱起重机臂架俯仰机构的参数化设计方法,该方法以知识工程为理论依据,以Pro/E 为参数化平台,以知识工程库和机构模型库为支撑,采用VB系统开发软件,SQL Server 2012数据库存储,针对目前CAD技术在起重机设计过程中的应用现状,设计开发了基于知识工程的岸边集装箱起重机臂架俯仰机构参数化设计系统,给出了系统结构设计、实现功能和实现方法。

GB_50235—2010工业金属管道工程施工规范

GB_50235—2010工业金属管道工程施工规范
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3.1.5 压力管道施工前,施工单位应向管道 安装工程所在地的质量技术监督部门办理书 面告知文件,并应接受监督检验单位的监督 检验。 3.1.6 管道施工应符合国家现行的环境保护、 安全技术和劳动保护等有关规定。
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3.2 管道分级
3.2.1 工业金属管道应按设计压力、设计温度、 介质的毒性危害程度和火灾危险性划分为 GC1、GC2、GC3三个级别。管道分级应符 合表3.2.1的规定。
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2.1.9 管道支承件 pipe-supporting elements 将管道的自重、输送流体的重量、由于操作压力和 温差所造成的荷载以及振动、风力、地震、雪载、 冲击和位移应变引起的荷载等传递到管架结构上去 的管道元件。包括管道安装件和附着件。 2.1.10 安装件 fixtures 将负荷从管子或管道附着件上传递到支承结构或设 备上的管道元件。它包括吊杆、弹簧支吊架、斜拉 杆、平衡锤、松紧螺栓、支撑杆、链条、导轨、锚 固件、鞍座、垫板、滚柱、托座和滑动支架等。
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表3.2.1 管道分级
管道级别
GC1
适用范围
1 毒性程度为极度危害介质的管道。 2 毒性程度为高度危害气体介质的管道 3 工作温度高于标准沸点的高度危害液体介质的管道。 4 设计压力≥4MPa,火灾危险性为甲、乙类可燃气体介质的管道 5 设计压力≥4MPa,火灾危险性为甲类可燃液体和液化烃介质的管道。 6 设计压力≥10MPa的管道。 7 设计压力≥4MPa,且设计温度≥400℃的管道。 1 设计压力<10MPa,且设计温度<400℃,工作温度不高于标准沸点的 高度危害液体介质的管道 2 毒性程度为中度、轻度危害流体介质的下列管道: 1) 设计压力<10MPa、≥4MPa,且设计温度<400℃; 2) 设计压力<4MPa。 3 设计压力<10MPa、≥4MPa,且设计温度<400℃的乙、丙类可燃液体 介质的管道。 4 设计压力<4MPa的可燃流体介质的管道 5 下列情况的无毒、非可燃流体介质的管道: 1) 设计压力<10MPa、≥4MPa,且设计温度<400℃; 2) 设计压力<4MPa、>1MPa; 3) 设计压力≤1MPa,且设计温度≤-20℃或>185℃。 设计压力≤1MPa,设计温度>-20℃但≤185℃的无毒、非可燃流体介质的 管道

Piping Practice Guide Line

Piping Practice Guide Line

NEW BUILDING PIPE GUIDE LINEGeneral Comments:- Present Guide Line shows the most frequently piping practices found on board for hull parts.- It is a complement of Rules.- Usually shipyard's have an own standards approved by GL but, some times doesn't include the piping Practices, only in such cases present Guide Line can be used.-Copy of Standards Approved for each shipyard must be available in each GL site office for surveyor's consultant.-Size of pipes: There are many different standards exist for pipe sizes, and their prevalence varies depending on industry and geographical area. The pipe sizedesignation generally includes two numbers; one that indicates the outside (OD) ornominal diameter, and the other that indicates the wall thickness. In the earlytwentieth century, American pipe was sized by inside diameter. This practice wasabandoned to improve compatibility with pipe fittings that must usually fit the OD of the pipe, but it has had a lasting impact on modern standards around the world.In North America and the UK, pressure piping is usually specified by N ominal P ipeS ize (NPS) and schedule (SCH). Pipe sizes are documented by a number of standards, including API 5L, ANSI/ASME B36.10M in the US, and BS 1600 and BS 1387 inthe United Kingdom. Typically the pipe wall thickness is the controlled variable, and the I nside D iameter (I.D.) is allowed to vary.In Europe, pressure piping uses the same pipe IDs and wall thicknesses as N ominalP ipe S ize, but labels them with a metric Diameter Nominal (DN) instead of theimperial NPS. For NPS larger than 14, the DN is equal to the NPS multiplied by 25.(Not 25.4) This is documented by European Standard (EN) 10255 (formerly DIN2448 and BS 1387) and ISO 65, and it is often called DIN or ISO pipe.Japan has its own set of standard pipe sizes, often called Japanese IndustrialStandard.(JIS) pipe. Please see below a equivalence table that can be useful for ourdaily work.Division East Asia - Germnischer LloydSee Table-1 showing the main standard pipes used by all shipyards, also it isincluded the weight of pipe itself and with water inside very useful for the pipesupports dimension. Table-2 overview recognized by GL: Comparison of GL pipeGrades and standard pipe grades.TABLE 1WEIGHTS AND WALL THICKNESS PIPES SCHEDULE 40 / 80NOMINAL BORE(N.D.)OUTSIDEDIAMETER(O.D)SCHEDULE 40 SCHEDULE 80mm Inch mm WT WEIGHT(Kg/m)Water inpipe Kg/mTotalweightkg/mWTWEIGHT(Kg/m)Water inpipe Kg/mTotalweightkg/m3 1/8 10.3 1.730.365 0.037 0.402 2.41 0.469 0.024 0.493 6 1/4 13.7 2.240.633 0.067 0.7 3.02 0.497 0.046 0.543 10 3/8 17.2 2.310.845 0.122 0.967 3.2 1.1 0.09 1.19 15 1/2 21.3 2.771.27 0.195 1.465 3.75 1.62 0.15 1.77 20 3/4 26.72.871.68 0.3452.0253.91 2.2 0.28 2.48 25 1 33.4 3.382.5 0.5573.0574.55 3.24 0.464 3.704 32 11/4 42.2 3.56 3.38 0.967 4.347 4.85 4.46 0.83 5.29 40 11/2 48.3 3.68 4.05 1.316 5.366 5.08 5.41 1.142 6.552 50 2 60.3 3.915.44 2.163 7.603 5.54 7.48 1.903 9.383 65 21/2 73 5.16 8.63 3.086 11.716 7.01 11.4 2.732 14.132 80 3 88.9 5.4911.3 5.351 16.651 7.62 15.3 4.261 19.561 90 31/2 101.6 5.74 13.6 7.124 20.724 8.08 18.6 6.207 24.807 100 4 114.3 6.0216.1 9.151 25.251 8.56 22.3 7.417 29.717 125 5 141.3 6.5521.8 13.97 35.77 9.53 31 11.74 42.74 150 6 168.3 7.1129.1 19.79 48.89 11 42.7 16.82 59.52 200 8 219.1 8.1842.8 34.48 77.28 12.7 64.6 29.47 94.07 250 10 273 8.74 62.3 54.51 116.81 15.1 96 46.31 142.31 300 12 323.8 9.52 72.8 77.18 149.98 17.45 132 65.52 197.52 350 14 355.6 11.1394.49 93.45 187.94 19.05 158.08 79.17 237.25 400 16 406.4 12.7 124 122.72 246.72 21.41 204.4 103.9 308.3 450 18 457.2 14.27156.73 155.18 311.91 23.8 255.77 131.73 387.5 500 20 508 15.06184.08 192.68 376.76 26.19 312.9 163.4 476.3 600 24 609.6 17.45256.22 279.83 536.05 30.34 435.8 235.58 671.38TABLE - 2Comparison of GL pipe grades and standard pipe gradesStandard Recognized By GL : Correspond to the GL requirements of pipes grades, following standardized pipes grades can be used:General PurposepipesPIPES GRADES ACCORDING TOStreght category or pipe grade EN10216-1or EN10217-1EN1021-3 orEN10217-3EN10305-1 EN10305-2 ISO9329-1 ISO9329-2 JIS G3454GL-R360 P235TR2 E235+N E235+N TS360 TW360 STPG370 GL-410 P265TR2 P275NL1 E275+N TS410 TW410 STPG410 GL-490 P355N E355+N E355+N TS500 TW500High Temp. Steelpipes PIPES GRADES ACCORDING TOStreght category or pipegradeEN10216-2 EN10217-2 ISO9329-2 ISO9330-2 JIS G3462 JIS G3456GL-R360W P235GH P235GH PH23 PH26 STPT370GL-R410W P265GH P265GH PH26 PH26 STPT410GL-R460W PH29 STPT480GL-R510W 20MnNb6 PH335 PH35GL-R0, 3Mo 16Mo3 16Mo3 16Mo3 16Mo3GL-R1Cr0,5Mo 13CrMo4-5 13CrMo4-5 13CrMo4-5 STBA22GL-R2,25Cr1Mo 10CrMo9-10 10CrMo9-10 10CrMo9-10 STBA24Tought at sub-zeroTemp pipes PIPES GRADES ACCORDING TOStreght category or pipe grade EN10216-4or EN10217-4EN10216-3orEN10217-3DINI17458 orDIN17457ISO 9329-3 orISO 9330-6ISO9329-4or ISO9330-6ASTMA312MJIS G3460 JIS G3459GL-R360T P215NLP255QL PH26 PL25 STPT370 STPL380GL-3690T P265NL P275NL1P275NL2 PH26 STPT410GL-490T P355NL1P355NL2 13MnNi6-3 STPT480GL-R0,5Ni 13MnNi6-3 16Mo3 12Ni14GL-R3,5Ni 12Ni14 13CrMo4-5 X10Ni9 STPL450 GL-R9Ni X10Ni9 10CrMo9-10 TP 304 L STPL6901.4306 X6CrNiMoTi17-12X2CrNi1810 TP 316 L SUS304LTP1.4404 X6CrNiNb18-10X2CrNiMo17-12TP 321 SUS316LTP1.4541 X6CrNiTi18-10 X6CrNiTi18-10 TP 347 SUS321LTP1.4550 X2CrNiMo17-13-2X6CrNiNb18-10SUS347TP1.4571 X2CrNi19-11 X6CrNiMoTi17-12SUS316TiTPNote : Up to now Chinese standard are not includedA.- PIPE PIECE WELDING-ScopeThis standard covers the procedure for pipe piece weldinga)Carbon steel and carbon manganese steel using metal arc welding processb)Al-Brass and Cu-Ni using TIG or MIG welding processc)Stainless steel using TIG or Arc welding process.-CuttingPipes to be cut by flame or machine-Consumables:Shall be approved by Class and used according to manufacturer’s instruction.-Re-welding Defects:All defects shall be removed by grinding, chipping or gauging. Welding repairs welds must be made in the same way as original welds.-CleaningSurfaces for welding shall be clear and free from paint, oil or scale on the materialwhich is detrimental to welding. Also slag, rust, or flux remaining on any weld beads shall removed before the next successive bead is laid down.-Re-welding DefectsAll defects shall be removed by grinding, chipping or gouging. Welding repairs welds must be made in the same way as for original welds.- Others- Inert Gas Purging: In order to avoid surface oxidation, stainless steel pipes must be sufficiently purged with inert gas to remove all oxygen inside the pipe in thewelding area.- In aluminum- Brass and stainless steel pipe welding, preheating and heat treatmentis not to be performed.Different Thickness Between Pipesb)StainlessSteel, Non Ferrous PipeApplication:Thick. of Pipe Joint Position of WeldingPipe to PipePipe to B.W FittingALLPipe to Comp..FLG.All Positions- Edge Preparation2.- FILLET WELDThick. of Pipe Joint Position of WeldingPipe to FlangePipe to socket 2.8 ≤ tPipe to sleeve All Positionswashing Water CleaningC.- PIPE SUPPORT1. - General Comments:- The pipe support fillet welding leg is to be 0,7T but, not exceed 8mm. (T = thickness of pipe support angle).- Face direction of pipe support angles is to be fitted in practice, as shown on thefollowing drawings, in principleKeep away (min. 2 mm)Upper5.- Dimension of Support Leg1.- NO UPPER NUT to be used for nominal pipe ia, 80A & Below pipe except heating coil and longitudinal direction main pipe (15A -80A).2) Clearance : 0.1 – 3.0 mm; where movement is consideredGeneral dimension of pipe band to be recommended do it as follow:Pipe N.D. Pipe Out Dia.Nut of U-boltSupport AngleSupport Pipe15 21.7 M10 50X50X6 34.0 X 3.4T20 27.2 M10 50X50X6 “ 25 34 M10 50X50X6 “ 32 42.7 M10 50X50X6 “ 40 48.6 M10 50X50X6 “ 50 60.5 M10 50X50X6 48.6 X4.05T(40A)65 76.3 M12 50X50X6 “ 80 89.1 M12 65X65X6 “ 100 114.3 M16 65X65X6 60.5 X5.2T(65A)125 139.8 M16 65X65X6 “ 150 165.2 M16 75X75X6 “ 200 216.3 M20 75X75X6 76.3 X5.2T(65A)250 267.4 M20 75X75X6 “ 300 318.5 M24 100X100X10 114.3 X6.0T(100A) 350 355.6 M24 100X100X10 “ 400 406.4 M24 100X100X10 “ 450 457.2 M30 100X100X13 “ 500 508 M30 100X100X13 “ 550 558.8 M30 100X100X13 “ 600 609.6 M30 130X130X12 139.8 X6.6T(125A) 650 660.4 M36 130X130X12 “ 700 711.2 M36 130X130X12 “ 750762 M36 130X130X15 165.2 X7.1T(150A)Clearance Upper6. - Support Fitting Details:a) Mild Steel (A-Grade)7.- Method of Installation Support Pipea) Application area : In tanks, Cargo Holds and enclosed spaces ( Pump Room,Bosun Store, etc.)Keep Away Min. 2 mmMin. 10Maximum Limitation the Support (legs) Welded on Structure without Pad Plate Deck Under Deck UnderStandard Support Shape and scantlingD. - PENETRATIONS1.- Types and uses of common penetrations installed on board:a) Water Tight Bulkhead and Deck Pipe PenetrationType : CF dType : SFPIPE SIZE L H 660.4 and Above 350 Min. 250 Type : CF View”A”Type : STb) Non - Tight Bulkhead and Deck Pipe Penetration- t ≥ t1- H = 75 as a coaming on deck - L = d/2To be applied where reinforcement For reinforcement of opening of an opening is requiredH is to be adequately considered.Type : D Type: TType : A Type : NCJGQ IQST- Division EA - Germanischer Lloyd 26PENETRATION TABLESLEEVE LENGTH / WEIGHT PIPE SIZE SLEEVE PIPE CONN. PENETRATION N.D O.D DdtTL WT/kg L D1 WT/kgSLEEVE MATERIAL10 17.3 27.2 19.4 3.9 1.05 50 0.11 100 30 0.22 STPG 38 #80 20A 15 21.7 34.0 25.0 4.5 1.65 50 0.16 100 36 0.33 STPG 38 #80 25A 20 27.2 42.7 29.9 6.4 1.35 50 0.29 100 47 0.57STPG 38 #160 32A(SRM)25 34.0 46.0 35.8 5.1 0.90 50 0.26 100 50 0.51 (STPG 38 #80 40A) 32 42.7 55.0 44.0 5.5 0.65 50 0.34 100 58 0.67 (STPG 38 #80 50A)40 48.6 63.5 51.5 6.0 1.45 50 0.37 100 64 0.7550 60.5 76.3 62.3 7.0 0.90 50 0.60 100 80 1.20 STPG 30 #80 65A 65 76.3 96.0 78.8 8.6 1.25 50 0.93 100 100 1.85 (STPG 38 #80 100A) 80 89.1 108.2 91.0 8.6 0.95 75 1.58 150 112 3.17 (STPG 38 #80 100A) 100 114.3 135.4 116.4 9.5 1.05 75 2.21 150 140 4.42 (STPG 38 #80 125A) 125 139.8 165.2 143.2 11.0 1.70 75 3.14 150 170 6.27 STPG 38 #80 150A 150 165.2 193.4 168.0 12.7 1.40 75 4.24 150 197 8.49 (STPG 38 #80 200A) 200 216.3 244.5 219.1 12.7 1.40 75 5.45 150 250 10.89 SS400(244.5×12.7) 250 267.4 296.0 270.6 12.7 1.60 75 6.65 150 300 13.31 SS400(269.0×12.7) 300 318.5 347.0 321.6 12.7 1.55 75 7.85 150 351 15.71 SS400(347.0×12.7) 350 355.6 384.0 358.6 12.7 1.50 75 8.72 150 388 17.44 SS400(384.0×12.7) 400 406.4 435.0 409.6 12.7 1.60 75 9.92 150 440 19.84 SS400(435.0×12.7) 450 457.2 486.0 460.6 12.7 1.70 75 11.12 150 490 22.24 SS400(486.0×12.7) 500 508.0 537.0 511.6 12.7 1.80 75 12.32 150 541 24.63 SS400(537.0×12.7) 550 558.8 587.8 561.6 12.7 1.80 75 13.49 150 592 26.98 SS400(587.8×12.7) 600 609.6 638.6 612.2 12.7 1.80 75 14.69 150 643 29.38 SS400(638.6×12.7) 650 660.4 689.4 663.6 12.7 1.80 75 15.89 150 694 31.78 SS400(689.4×12.7) 700 711.2 740.2 714.6 12.7 1.80 75 17.08 150 744 34.16 SS400(740.2×12.7) 750762.0791.0 765.6 12.7 1.80 75 18.28 150 795 36.59 SS400(791.0×12.7)Tolerances (O.D.) N.D. 150 and Below : ± 0.8 mm N.D. 200 and Above : ±1.5 mmL ± 1Bulkhead or DeckØD1tSLEEVEDeck or BHD- Run Pipe ; ND 15 and Above - Boss : 1 ¼” and Below, M36 and belowDetail “D”3. - Branch ConnectionApplicationThink. of Pipe Joint Material Position of Welding 2.8 ≤ tPipeto Pipe Steel and Stainless SteelAll PositionsEdge Preparationt o = The smaller of Sharp edge to be6 mm. or 0.7 t ground smoothlyt c = The smaller of 6 mm Sharp Edge to be or 0.7t ground smoothly w = 1 – 3 mmDetail “ A “ “B - B”Detail “C”F. - PIPE JOINT1. - Bolt & Nut for Flange JointTypeFigureMaterial Pressure RemarkSS4005K,10K,16K = M20 & belowS45CWhere surrounded by liquid, it is to bespecially considered in chemical tankersHEX Bolt / NutSUS 31620K, 30K, 40K, 63K, 210K, 280K, 350K = All size5K,10K,16K = &To be appliedaccording to building specificationSTUD Bolt / NutTe Same As Hex. Bolt / NutStud bolt/nut to be applied to set-on flange and butterfly valve, * 2) flap check valve, etcTOOT WasherSUS 304For the flange of cargo, i.e. line, e.c.p main line and tank cleaning lines except no outside painting lines, tooth washers are to be fitted at two(2) bolts/nuts in order to improve the earth connections.N ote : 1) At flap check valve, it is to be applied as follows:- Wafer Type 950A-150A) ; all Stud Bolts / nuts- Flange Type (200A and above) ; ½ Stud Bolt/ Nuts and ½ Hex. Bolt/Nuts.2) The screw thread of pitch 3mm should be applied to the flange and valvewitch pressure to be applied 16 kg/cm2 and above and designation of bolt screw to be applied M30.2. - Socket Weld Joints for Ferrous Pipe- ND40 and below - For Pipes Class III in airsounding and glycol water pipes, steam feed water and condensate system, etc.3. – Silver Brazed coupling for Non-Ferrous PipeUsed for high pressure hydraulicpipe (pipe tick; SC160)Picture show a weld joint with a double weld, it is recommended in order to protect the pipe galvanized.Each cargo pipe is fixedby 7 – 8 clamps ofabove design principleLongitudinal ViewPROPOSED REINFORCEMENT。

机械英语考试试题及答案

机械英语考试试题及答案

机械英语考试试题及答案一、选择题(每题2分,共20分)1. The term "mechanical engineering" refers to:A. The study of machinesB. The design and manufacture of mechanical systemsC. The operation of machineryD. The maintenance of mechanical equipment答案:B2. What is the function of a bearing in a mechanical system?A. To reduce frictionB. To increase efficiencyC. To provide powerD. To transmit motion答案:A3. The process of converting thermal energy into mechanical energy is known as:A. ElectrificationB. CombustionC. ThermodynamicsD. Hydrodynamics答案:C4. In mechanical design, the principle of "KISS" stands for:A. Keep It Simple, StupidB. Keep It Short and SimpleC. Keep It Simple and SafeD. Keep It Simple, Smart答案:A5. A gear train is used to:A. Change the direction of motionB. Increase the speed of rotationC. Decrease the speed of rotationD. All of the above答案:D6. What does CAD stand for in mechanical engineering?A. Computer-Aided DesignB. Computer-Aided DraftingC. Computer-Aided DevelopmentD. Computer-Aided Diagnostics答案:A7. The SI unit for force is:A. NewtonB. JouleC. PascalD. Watt答案:A8. What is the purpose of a flywheel in a mechanical system?A. To store energyB. To increase speedC. To reduce noiseD. To dissipate heat答案:A9. The term "hydraulics" is associated with the study of:A. Fluid dynamicsB. Solid mechanicsC. Structural analysisD. Thermal engineering答案:A10. The process of cutting a material to a specific shape is known as:A. MachiningB. CastingC. ForgingD. Extrusion答案:A二、填空题(每空1分,共10分)11. The formula for calculating the moment of a force is \( F \times d \), where \( F \) is the force and \( d \) is the_______.答案:distance from the pivot12. A _______ is a device that converts linear motion into rotational motion.答案:crank13. In a four-stroke internal combustion engine, the four strokes are intake, compression, _______, and exhaust.答案:power14. The _______ of a material is its ability to resist deformation under load.答案:stiffness15. The term "overhaul" in mechanical maintenance refers to a thorough inspection and _______ of a machine or its parts.答案:repair16. The _______ of a machine is the study of how forces act on and within a body.答案: statics17. A _______ is a type of machine that uses a screw to convert rotational motion into linear motion.答案:screw jack18. The _______ of a system is the point around which the system rotates.答案:pivot19. The _______ of a lever is the ratio of the effort arm to the load arm.答案:mechanical advantage20. The _______ is a type of bearing that allows for rotation with minimal friction.答案:ball bearing三、简答题(每题5分,共30分)21. Explain the difference between static and dynamic equilibrium in mechanical systems.答案:Static equilibrium refers to a state where the net force and net moment acting on a body are zero, resulting in no acceleration. Dynamic equilibrium occurs when the net force is zero, but the body is in motion with constant velocity.22. What is the purpose of a clutch in a vehicle?答案:A clutch is used to engage and disengage the power transmission from the engine to the transmission system, allowing the vehicle to start, stop, and change gears smoothly.23. Describe the function of a governor in an engine.答案:A governor is a device that automatically controls the speed of an engine by regulating the fuel supply or the valve settings, ensuring the engine operates within safespeed limits.24. What are the three primary types of joints in structural engineering?答案:The three primary types of joints are pinned joints, fixed joints, and sliding joints, each serving different purposes in connecting and supporting structural elements.25. Explain the。

Hilfer_分数阶脉冲随机发展方程的平均原理

Hilfer_分数阶脉冲随机发展方程的平均原理

第 63 卷第 1 期2024 年 1 月Vol.63 No.1Jan.2024中山大学学报(自然科学版)(中英文)ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS SUNYATSENIHilfer分数阶脉冲随机发展方程的平均原理*吕婷1,杨敏1,王其如21. 太原理工大学数学学院,山西太原 0300242. 中山大学数学学院,广东广州 510275摘要:利用分数阶微积分理论、半群性质、不等式技巧和随机分析理论,建立了分数布朗运动驱动的Hilfer 分数阶脉冲随机发展方程的平均原理,证明了原方程的适度解均方收敛于无脉冲平均方程的适度解,并通过实例说明了所得理论结果的适用性.关键词:平均原理;Hilfer分数阶导数;脉冲随机发展方程;分数布朗运动中图分类号:O211.63 文献标志码:A 文章编号:2097 - 0137(2024)01 - 0145 - 09Averaging principle for Hilfer fractional impulsivestochastic evolution equationsLÜ Ting1, YANG Min1, WANG Qiru21. School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China2. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, ChinaAbstract:By using fractional calculus,semigroup theories,inequality techniques and stochastic analysis theories, an averaging principle for Hilfer fractional impulsive stochastic evolution equations driven by fractional Brownian motion is established. The mild solution of the original equations converges to the mild solution of the reduced averaged equations without impulses in the mean square sense is proved. And an example is presented to illustrate the applicability of our obtained theoretical results.Key words:averaging principle; Hilfer fractional derivative; impulsive stochastic evolution equations;fractional Brownian motion在实际生活中,系统常受外力影响或内部产生的“噪声”干扰,所以,随机微分方程可以更加准确的刻画系统的变化特征,因而研究随机微分方程是很有必要的且存在实际的应用价值. 另外,现实生活中的许多现象都有长期后效作用,Mandelbrot et al.(1968)研究表明分数布朗运动可以较好的描述长期后效现象,这推动了更多学者们对分数布朗运动驱动的随机微分方程的广泛关注. 分数布朗运动(fBm)最早是由Kolmogorov(1940)提出的一个依赖于Hurst参数H∈(0,1)的高斯随机过程,当H=1/2时,分数布朗运动简化为标准布朗运动;当H≠1/2时,分数布朗运动既不是半鞅也不是Markov过程;当H >1/2 时,分数布朗运动具有自相似性、长时记忆性等特征,这些性质使分数布朗运动可以引入到数理金融(Bollerslev et al.,1996)、网络通信(Leland et al.,1994)、生物医学工程(de la Fuente et al.,2006;Boudrahem et al.,2009)等随机模型中作为随机噪声项,得以更好的描述系统特征和保证模型性能. 除此之外,具有脉冲干扰的微分方程能准确的呈现出系统的瞬时变化规律,因此,脉冲随机微分方程吸引了很多学者的关注,详见文DOI:10.13471/ki.acta.snus.2023A006*收稿日期:2023 − 01 − 16 录用日期:2023 − 03 − 22 网络首发日期:2023 − 11 − 15基金项目:国家自然科学基金(12001393,12071491);山西省自然科学基金(201901D211103)作者简介:吕婷(1999年生),女;研究方向:分数阶随机微分方程;E-mail:********************通信作者:杨敏(1986年生),男;研究方向:泛函微分方程理论及其应用;E-mail:******************第 63 卷中山大学学报(自然科学版)(中英文)献(Sakthivel et al.,2013;Ren et al.,2014;Liu et al.,2020).另一方面,平均原理作为一种高效、准确的近似分析方法,在非线性动力系统的研究中发挥着重要作用. 它的主要思想是对原始动力系统进行简化得到一个平均系统,并且这个简化后的平均系统可以反映原系统的动力学行为. 目前为止,随机微分系统的平均原理理论已经获得了极大的发展. 例如,Cerrai et al.(2009)研究了一类随机反应扩散模型的平均原理;Ma et al.(2019)研究了Lévy 噪声驱动的脉冲随机微分方程的周期平均原理;Cui et al.(2020)在非Lipschitz 系数条件下,考虑了脉冲中立型随机微分方程的平均原理;Ahmed et al.(2021)探索出含泊松跳和时滞的Hilfer 分数阶随机微分方程的平均原理;Liu et al.(2022a )在非Lipschitz 系数条件和无周期条件下,考虑了由分数布朗运动驱动的脉冲随机微分方程的平均原理.但现有研究存在两方面不足:一是大多数平均原理建立在有限维空间上,很少考虑空间是无穷维的情形(Xu et al.,2020;Liu et al.,2022b ),二是Caputo 分数阶脉冲随机微分方程已有相应的平均原理研究(Wang et al.,2020;Xu et al.,2011;刘健康等,2023),但Hilfer 分数阶脉冲随机发展方程的平均原理尚未见到研究结果. 基于上述讨论,本文在Hilbert 空间上考虑如下Hilfer 分数阶脉冲随机发展方程的平均原理ìíîïïïïïïD γ,β0+x (t )=Ax (t )+f (t ,x t )+h (t ,x t )d B H Q (t )d t , t ≠t k , t ∈J =(0,b ],Δx (t k )=I k (x (t k ))=x (t +k )-x (t -k ), t =t k ,k =1,2,⋯,m ,x (t )=φ(t ), -λ≤t <0,I (1-β)(1-γ)0+x (0)=φ0,(1)其中D γ,β是Hilfer 分数阶导数,γ∈[]0,1,β∈()12,1,x (⋅)取值于实可分Hilbert 空间X . 闭线性算子A :D (A )⊂X →X 是强连续算子半群{S (t )}t ≥0的无穷小生成元. B H Q (t )是定义在实可分Hilbert 空间Y 上的分数布朗运动,其中Hurst 参数H ∈()12,1. P C ()[]-λ,0;X 指从[]-λ,0到X 上所有具有càdlàg 路径的连续函数φ构成的空间,其范数 φP C =sup-λ≤t ≤0φ(t )<+∞,x t =x (t +τ)(τ∈[-λ,0])是P C -值的随机过程. x (t -k )和x (t +k )分别表示x (t )在t =t k 时的左极限和右极限,I k 表示x (t )在t =t k 时刻的脉冲扰动,脉冲时间序列{t k }满足0<t 1<⋯<t m <t m +1=b . 系数函数 f :J ×P C →X ,h :J ×P C →L 02(Y ,X ). 1 预备知识假设(Ω,F ,{F t }t ≥0,P )是一个带流的完备概率空间,其中{F t }t ≥0满足通常条件,即{F t }t ≥0是右连续的且F 0包含所有零测集. {B H (t )}t ∈R 是带有Hurst 参数H ∈()12,1的一维分数布朗运动,即B H (t )是一个中心高斯过程且具有以下协方差函数R H (t ,s )=E (B H (t )B H (s ))=12()t 2H +s 2H -|t -s |2H, t ,s ∈R =(-∞,+∞).记X 和Y 是两个实可分Hilbert 空间,L (Y ,X )是从Y 映射到X 上所有有界线性算子构成的空间. Q ∈L (Y )是一个非负自伴算子,满足Qe n =λn e n ,有限迹tr Q =∑n =1∞λn <+∞,其中{λn }≥0,(n =1,2,⋯)是一个非负有界实数序列,{e n }(n =1,2,⋯)是空间Y 上一组标准正交基. {B H n (t )}n ∈N +是独立于完备概率空间(Ω,F ,P )的一维标准分数布朗运动序列,现在我们在空间Y 上定义无穷维分数布朗运动如下:B HQ(t )=∑n =1∞B H n(t )Q 12e n =∑n =1∞B H n (t )λn e n , t ≥0,则B H Q (t )∈L 2(Ω,Y )且在空间Y 中收敛,其中L 2(Ω,Y )表示所有强可测,平方可积的Y -值随机过程组成的146第 1 期吕婷,等:Hilfer 分数阶脉冲随机发展方程的平均原理空间.若ψ∈L (Y ,X )并且使得ψQ 12是Hilbert-Schmidt 算子,满足范数 ψ2L 02=∑n =1∞λn ψe n 2<+∞,则ψ被称为从Y 映射到X 的Q -Hilbert-Schmidt 算子. 记L 02≔L 02(Y ,X )是所有Q -Hilbert-Schmidt 算子ψ∈L (Y ,X )构成的空间,定义空间L 02的内积为ψ1,ψ2L 02=∑n =1∞ψ1e n ,ψ2e n ,则L 02(Y ,X )是一个可分Hilbert 空间. 引理1(Abouagwa et al.,2021) 对任意ϕ:J →L 02(Y ,X ),∫0bϕ(s )2L 02d s <+∞成立, 当t ∈J ,∑n =1∞ϕ(t )Q 12e n 一致收敛,则对任意t 1,t 2∈J 且t 2>t 1,有E∫t 1t 2ϕ(s )d B H Q(s )2≤2H (t 2-t 1)2H -1∫t 1t 2ϕ(s )2L 02d s .定义1(Yang et al.,2017a ) 函数f :[a ,+∞)→R 是一个Lebesgue 可积函数,对任意β∈(0,1),函数f 的β阶Riemann-Liouville 积分定义为I βa +f (t )=1Γ(β)∫a t (t -s )β-1f (s )d s , t >a ,β>0,其中Γ(⋅)是Gamma 函数.定义2(Yang et al.,2017a ) 函数f :[a ,+∞)→R 的β阶Riemann-Liouville 分数阶导数定义为LD βa +f (t )=1Γ(n -β)d nd t n∫at (t -s )n -1-βf (s )d s , t >a , n -1<β<n ,其中n ∈N +. 定义3(Yang et al.,2017a ) 函数f :[a ,+∞)→R 且f ∈C n [a ,+∞),f 的β阶Caputo 分数阶导数定义为CD βa +f (t )=1Γ(n -β)∫at (t -s )n -1-βf (n )(s )d s , t >a , n -1<β<n ,其中C n [a ,+∞)表示在区间[a ,+∞)上n 次连续可微的函数构成的空间,n ∈N +.定义4(Sheng et al.,2022) 函数f :[a ,+∞)→R 的Hilfer 分数阶导数定义为D γ,βa+f (t )=I γ(1-β)a +d d t I (1-γ)(1-β)a+f (t ), 0≤γ≤1,0<β<1.注1(Sheng et al.,2022) 当γ=0,0<β<1,a =0,则Hilfer 分数阶导数对应经典的Riemann-Liou ‐ville 分数阶导数D 0,β+f (t )=d d tI 1-β0+f (t )=L D β0+f (t ).当γ=1,0<β<1,a =0,则Hilfer 分数阶导数对应经典的Caputo 分数阶导数D 1,β0+f (t )=I 1-β0+dd tf (t )=C D β0+f (t ).引理2 方程(1)等价于如下的积分方程x (t ) = φ0t (γ-1)(1-β)Γ(γ(1-β)+β)+1Γ(β)∫0t (t -s )β-1(Ax (s )+f (s ,x s ))d s+1Γ(β)∫0t (t -s )β-1h (s ,x s )d B H Q(s )+t (γ-1)(1-β)Γ(γ(1-β)+β)∑0<t k <tIk(x t k). (2)证明 可参考文献(Yang et al.,2017a ;Ahmed et al.,2018). 为了给出方程(1)的适度解,引入以下Wright-type 函数M β(θ)=∑n =1∞(-θ)n -1(n -1)Γ(1-βn ), 0<β<1,θ∈C .147第 63 卷中山大学学报(自然科学版)(中英文)引理3(Yang et al.,2017a ) 若积分等式(2)成立,其等价于如下的等式:x (t )=S γ,β(t )φ0+∫0t Tβ(t -s )f (s ,x s )d s +∫0t Tβ(t -s )h (s ,x s )d B H Q (s )+∑0<t k <tSγ,β(t -t k )I k (x t k)=S γ,β(t )φ0+∫0t (t -s )β-1P β(t -s )f (s ,x s )d s +∫0t (t -s )β-1P β(t -s )h (s ,x s )d B H Q (s )+∑0<t k <tSγ,β(t -t k )I k (x t k),(3)其中P β(t )=∫∞βθM β(θ)S (t βθ)d θ,T β(t )=t β-1P β(t ),S γ,β(t )=I γ(1-β)0+T β(t ).定义5 若一个P C -值的随机过程x :[-λ,b ]→X 满足以下条件,则称x (t )是方程(1)的适度解.(i ) x (t )是F t -适应的且∫0bE x (s )2d s <+∞几乎必然成立;(ii ) x (t )=φ(t ),-λ≤t ≤0;(iii ) 当t ∈J 时,x (t )具有càdlàg 路径且对任意t ∈J 有x (t )=S γ,β(t )φ0+∫0t (t -s )β-1P β(t -s )f (s ,x s )d s+ ∫t(t -s )β-1P β(t -s )h (s ,x s )d B H Q (s )+∑0<t k <tSγ,β(t -t k )I k (x t k). (4)本文中,我们假设如下条件成立:(H0)当t ≥0时,S (t )是一致算子拓扑连续的,且S (t )是一致有界的,即存在M >1,使得supt ∈[0,+∞)S (t )<M .引理4(Yang et al.,2017b ) 在条件(H0)下,对任意t >0,{P β(t )}t >0和{S γ,β(t )}t >0是线性算子,且对任意x ∈X 有P β(t )x ≤M Γ(β) x , S γ,β(t )x ≤Mt (γ-1)(1-β)Γ(γ(1-β)+β) x .定义6(Liu ,2007) 设X n (n ≥1),X 是同一概率空间(Ω,F ,P )上的随机变量,若E (|X n |2)<+∞,且lim n →∞E (|X n -X |2)=0成立,则称X n 均方收敛于X .2 平均原理接下来,我们建立Hilfer 分数阶脉冲随机发展方程的平均原理.首先,定义方程(1)的扰动形式为ìíîïïïïïïD γ,β0+x ε(t )=Ax ε(t )+εf (t ,x ε,t )+εHh (t ,x ε,t )d B H Q (t )d t , t ≠t k ,t ∈J =(0,b ],Δx ε(t k)=x ε(t +k )-x ε(t -k )=εI k (x ε(t k )), t =t k ,k =1,2,⋯,m ,x ε(t )=φ(t ), -λ≤t <0,I (1-β)(1-γ)0+x ε(0)=φ0.(5)然后根据方程(1)适度解的定义,可以得到方程(5)的适度解为:x ε(t )=S γ,β(t )φ0+ε∫0t (t -s )β-1P β(t -s )f (s ,x ε,s )d s+ εH∫0t (t -s )β-1P β(t -s )h (s ,x ε,s )d B HQ (s )+ε∑0<t k <tSγ,β(t -t k )I k (x ε,t k), (6)其中ε∈(0,ε0]是一个很小的正参数,ε0是一个固定的常数.为了得出本文的主要结果,假设系数函数f ,h 具有周期T ,则存在正整数m ∈N +,使得0<t 1<…<t m <T ,那么对整数k >m ,有t k =t k -m +T ,I k =I k -m . 现引入可测的系数函数f ˉ:P C →X ,h ˉ:148第 1 期吕婷,等:Hilfer 分数阶脉冲随机发展方程的平均原理P C →L 02(Y ,X ),-I k :P C →X ,其中f ˉ(x )=1T∫T f (s ,x )d s ,hˉ(x )=1T∫Th (s ,x )d s ,-I (x )=1T ∑k =1m I k (x ). 另外,我们做如下假设:(H1) 对任意x ,y ∈P C ,t ∈J ,存在正常数M 1使得f (t ,x )-f (t ,y )2∨ h (t ,x )-h (t ,y )2L 02≤M 21 x -y 2.(H2) 对任意的x ,y ∈P C ,存在正常数c k 和d k ,使脉冲函数I k 满足I k (x )2≤c k , I k (x )-I k (y )2≤d k x -y 2.(H3) 对所有T ∈J ,x ∈P C ,存在有界函数ρi (T )>0(i =1,2)使得1T ∫0T f (s ,x )-f ˉ(x )2d s ≤ρ1(T )()1+ x 2,1T∫0T h (s ,x )-h ˉ(x )2d s ≤ρ2(T )()1+ x 2,其中lim T →∞ρi (T )=0(i =1,2).则方程(5)对应如下无脉冲项平均系统:ìíîïïïïD γ,β0+z ε(t )=Az ε(t )+εf ˉ(z ε,t )+ε-I (z ε,t )+εH h ˉ(z ε,t)d B H Q (t )d t , t ∈J =(0,b ],I (1-β)(1-γ)0+z ε(0)=φ0,z ε(t )=φ(t ),-λ≤t <0.(7)参考文献(Gu et al.,2015)中引理2.12的证明,可以得到方程(7)的适度解z ε(t )为z ε(t )=S γ,β(t )φ0+ε∫0t (t -s )β-1P β(t -s )f ˉ(z ε,s )d s+ εH∫t (t -s )β-1P β(t -s )h ˉ(z ε,s )d B H Q (s )+ε∫t (t -s )β-1P β(t -s )-I (z ε,s )d s . (8)定理1 假设条件(H0)~(H3)成立,则当ε趋于零时,方程(5)的适度解x ε(t )均方收敛于平均方程(7)的适度解z ε(t ). 即任意给定一个很小的数δ>0,存在M 0>0,α∈(0,1)以及ε1∈(0,ε0],使得当ε∈(0,ε1]时有E()sup t ∈[-λ,M 0ε-α]x ε(t )-z ε(t )2≤δ.证明 由式(6)和式(8),有x ε(t )-z ε(t )=ε∫0t(t -s )β-1P β(t -s )[f (s ,x ε,s)-f ˉ(z ε,s)]d s + εH∫0t(t -s )β-1P β(t -s )[]h (s ,x ε,s )-hˉ(z ε,s)d B HQ(s )+ ε()∑0<t k <tSγ,β(t -t k )I k (x ε,t k)-∫0t (t -s )β-1P β(t -s )-I (z ε,s )d s ,(9)从而对任意ν∈(0,b ],利用基本不等式得到E ()sup 0<t ≤νx ε(t )-z ε(t )2≤3ε2E ()sup 0<t ≤ν∫0t (t -s )β-1P β(t -s )[]f (s ,x ε,s )-f ˉ(z ε,s )d s 2+ 3ε2HE ()sup 0<t ≤ν∫0t (t -s )β-1P β(t -s )[h (s ,x ε,s )-h ˉ(z ε,s )]d B H Q(s )2+ 3ε2E ()sup 0<t ≤ν ∑0<t k<tS γ,β(t -t k )I k (x ε,t k)-∫0t(t -s )β-1P β(t -s )-I (z ε,s )d s 2≤N 1+N 2+N 3. (10)对于第1项,由引理4可得149第 63 卷中山大学学报(自然科学版)(中英文)N 1≤6M 2Γ2(β)ε2E ()sup 0<t ≤ν∫0t(t -s )β-1[]f (s ,x ε,s )-f (s ,z ε,s )d s 2 +6M 2Γ2(β)ε2E ()sup 0<t ≤ν∫0t(t -s )β-1[]f (s ,z ε,s )-f ˉ(z ε,s )d s 2≔N 11+N 12 . ()11利用假设条件(H1)和Cauchy-Schwarz 不等式得到N 11≤6M 2M 21ε2ν2β-1(2β-1)Γ2(β)∫νE()sup 0<s 1≤sx ε,s 1-z ε,s12d s =Λ11ε2ν2β-1∫νE()sup0<s 1≤sx ε,s 1-z ε,s12d s ,(12)其中Λ11=6M 2M 21(2β-1)Γ2(β).由假设条件(H3)得到N 12≤6M 2ε2ν2β-1(2β-1)Γ2(β)E ()sup 0<t ≤νt ⋅1t ∫0t f (s ,z ε,s )-f ˉ(z ε,s )2d s ≤Λ12ε2ν2β,(13)其中Λ12=6M 2(2β-1)Γ2(β)sup 0<t ≤νρ1(t )()1+E ()sup 0<t ≤νz ε,t2. 对于第2项,由引理4可以推出N 2≤6M 2Γ2(β)ε2HE ()sup 0<t ≤ν∫0t (t -s )β-1[]h (s ,x ε,s )-h (s ,z ε,s )d B HQ (s )2+ 6M 2Γ2(β)ε2HE ()sup 0<t ≤ν∫0t (t -s )β-1[]h (s ,z ε,s )-h ˉ(z ε,s )d B H Q(s )2≔N 21+N 22 . (14)由引理1、假设条件(H1)和Cauchy-Schwarz 不等式得到N 21≤12M 2H Γ2(β)ε2H ν2H -1E ()sup0<t ≤ν∫t (t -s )2(β-1) h (s ,x ε,s )-h (s ,z ε,s )2d s≤Λ21ε2H ν2(H +β-1)∫0νE()sup0<s 1≤sxε,s 1-z ε,s12d s ,(15)其中Λ21=12M 2M 21H(2β-1)Γ2(β).由引理1、假设条件(H1)和假设条件(H3)得到N 22≤12M 2H (2β-1)Γ2(β)ε2H ν2(H +β-1)E ()sup 0<t ≤νt ⋅1t ∫0th (s ,z ε,s)-h ˉ(z ε,s )2d s ≤Λ22ε2H ν2H +2β-1,(16)其中Λ22=12M 2H(2β-1)Γ2(β)sup 0<t ≤νρ2(t )()1+E ()sup 0<t ≤νz ε,t 2. 对于第3项,由基本不等式得到N 3≤6ε2E ()sup 0<t ≤ν∑0<t k<t S γ,β(t -t k )I k (x ε,t k)2+ 6ε2E ()sup 0<t ≤ν∫0t (t -s )β-1P β(t -s )-I (z ε,s )d s 2≔N 31+N 32, (17)由引理4、假设条件(H2)和Cauchy-Schwarz 不等式得到N 31≤6ε2M 2ν2(γ-1)(1-β)Γ2(γ(1-β)+β)E ()sup 0<t ≤ν∑0<t k<t I k (x ε,tk)2≤6ε2M 2mν2(γ-1)(1-β)Γ2(γ(1-β)+β)E ()sup 0<t ≤ν∑k =1m I k (x ε,t k)2≤6ε2M 2m 2c k ν2(γ-1)(1-β)Γ2(γ(1-β)+β)=Λ31ε2ν2(γ-1)(1-β), (18)其中Λ31=6m 2M 2c kΓ2(γ(1-β)+β).150第 1 期吕婷,等:Hilfer 分数阶脉冲随机发展方程的平均原理N 32≤6M 2ε2Γ2(β)E ()sup 0<t ≤ν∫0t(t -s )β-1I ˉ(z ε,s )d s 2≤6M 2ε2ν2β-1(2β-1)Γ2(β)E ()sup 0<t ≤ν∫0tI ˉ(z ε,s)2d s≤6M 2mε2ν2β-1(2β-1)T 2Γ2(β)E ()sup 0<t ≤ν∑k =1m∫0tI k(zε,s)2d s ≤6M 2m 2c k ε2ν2β-2(2β-1)Γ2(β)=Λ32ε2ν2(β-1), (19)其中Λ32=6M 2m 2c k(2β-1)Γ2(β).将估计式(11)~(19)代入式(10),则对任意ν∈(0,b ],得到不等式E ()sup 0<t ≤νx ε(t )-z ε(t )2≤Λ12ε2ν2β+Λ22ε2H ν2H +2β-1+Λ31ε2ν2(γ-1)(1-β)+Λ32ε2ν2(β-1)+ (Λ11ε2ν2β-1+Λ21ε2Hν2(H +β-1))∫0νE()sup0<s 1≤sxε,s 1-z ε,s12d s . (20)令Ξ(ν)=E ()sup 0<t ≤νx ε(t )-z ε(t )2,由于E()sup -λ≤t <0x ε(t )-z ε(t )2=0,则Ξ(s +τ)=E()sup0<s 1≤sx ε,s 1-z ε,s12=E()sup 0<s 1≤sx ε(s 1+τ)-z ε(s 1+τ)2, τ∈[-λ,0),因此,Ξ(ν)≤Λ12ε2ν2β+Λ22ε2H ν2H +2β-1+Λ31ε2ν2(γ-1)(1-β)+Λ32ε2ν2(β-1) + (Λ11ε2ν2β-1+Λ21ε2Hν2(H +β-1))∫0νΞ(s +τ)d s . (21)对任意ν∈(0,b ],令Θ(ν)=sup -λ≤t ≤νΞ(t ),则Ξ(t )≤Θ(t ),Ξ(t +τ)≤Θ(t ),τ∈[-λ,0). 从而得到Θ(ν)=sup -λ≤t ≤νΞ(t )≤max{}sup -λ≤t ≤0Ξ(t )+sup 0<t ≤νΞ(t )≤Λ12ε2ν2β+Λ22ε2H ν2H +2β-1+ Λ31ε2ν2(γ-1)(1-β)+Λ32ε2ν2(β-1)+()Λ11ε2ν2β-1+Λ21ε2Hν2(H +β-1)∫0νΘ(s )d s . (22)由Gronwall 不等式,可推出Θ(ν)≤()Λ12ε2ν2β+Λ22ε2H ν2H +2β-1+Λ31ε2ν2(γ-1)(1-β)+Λ32ε2ν2(β-1)exp ()Λ11ε2ν2β+Λ21ε2H ν2H +2β-1, (23)即有E()sup -λ<t ≤νx ε(t )-z ε(t )2≤()Λ12ε2ν2β+Λ22ε2H ν2H +2β-1+Λ31ε2ν2(γ-1)(1-β)+Λ32ε2ν2(β-1)× exp ()Λ11ε2ν2β+Λ21ε2H ν2H +2β-1. (24)即存在M 0>0和α∈(0,1),使得对所有t ∈(0,M 0ε-α]⊂(0,b ]满足E()sup 0<t ≤M 0ε-αx ε(t )-z ε(t )2≤με1-α,其中常数μ=(Λ12M 2β0ε1+α-2αβ+Λ22M 2H +2β-10ε2α(1-H -β)+2H -1+Λ31M 2(γ-1)(1-β)0ε2α(1-γ)(1-β)+α+1)+Λ32M 2(β-1)0ε3α-2αβ+1exp ()Λ11M 2β0ε2-2αβ+Λ21M 2H +2β-10ε2H -α(2H +2β-1) . (25)所以对任意给定的数δ>0,存在ε1∈(0,ε0],使得对任意ε∈(0,ε1]和t ∈[-λ,M 0ε-α]⊂ [-λ,b ],有E()supt ∈[-λ,M 0ε-α]x ε(t )-z ε(t )2≤δ.定理1证毕.注2 现有文献考虑的是有限维空间上含泊松跳以及Wiener 过程的无脉冲扰动的Hilfer 分数阶随机微分方程的平均原理(Ahmed et al.,2021;Luo et al.,2021),与之相比,本文考虑了分数布朗运动驱动的含脉冲项的Hilfer 分数阶随机微分方程. 更为重要的是,我们在Hilbert 空间上建立了具有算子的Hilfer 分数阶151第 63 卷中山大学学报(自然科学版)(中英文)脉冲随机发展方程的平均原理,一定程度上丰富了Hilfer 分数阶随机微分方程的平均原理的相关理论.3 实例为了说明所得结果的适用性,我们考虑以下含脉冲的Hilfer 分数阶随机发展方程ìíîïïïïïïïïïïD γ,23x ε(t ,z )=∂2∂z2x ε(t ,z )+εsin 2(t )x ε,t (z )+2εH cos 2(t )x ε,t(z )d B H Q (t )d t , I 13(1-γ)x ε(0,z )=φ0,Δx ε(t k ,z )=εx ε(t k ,z )(4+k )(5+k ), z ∈[0,π],k ∈1,2,⋯,m ,x ε(θ,z )=φ(θ,z ), θ∈[-λ,0],z ∈[0,π],x ε(t ,0)=x ε(t ,π)=0, t ∈(0,m π].(26)令空间X =Y =L 2[0,π],系数函数f ()t ,x ε,t =sin 2(t )x ε,t (z ),h ()t ,x ε,t =2cos 2(t )x ε,t (z ),脉冲函数I k =x ε(t k ,z )(4+k )(5+k ).定义算子A :D (A )→X ,Ax ε(t ,z )=∂2∂z2x ε(t ,z ),其中定义域D (A )={}x ∈X , x ,x '全连续,x ″∈X , x (0)=x (π)=0,则A 是强连续算子半群{S (t )}t ≥0的无穷小生成元,且对任意t ≥0,S (t )是紧的、解析且自伴的,由一致有界定理可知存在一个常数M >0,使得 S (t )≤M ,且A 有离散谱,其特征值是-n 2,n ∈N +,对应的标准正交特征向量为ωn (z )=(nz ),n =1,2,⋯,则当x ∈D (A )时,Ax =-∑n =1∞n 2x ,ωn ωn . 为了定义算子Q :Y →Y ,选择一组非负有界实数序列{λn }n ≥1,并在Y 中选取标准正交基{e n }n ≥1,使得Qe n =λn e n 成立,并且假设tr (Q )=∑n =1∞λn <+∞,从而可以定义随机过程B H Q(t )=∑n =1∞λn B H n (t )e n ,其中H ∈()1/2,1,{B Hn(t )}n ∈N +,是一个独立于完备概率空间(Ω,F ,P )的一维标准分数布朗运动序列.取T =π,则f ˉ(x )=1π∫πf (s ,x )d s =12x , h ˉ(x )=1π∫0πh (s ,x )d s =x ,I ˉ(x )=1π∑k =1m x (4+k )(5+k )=mx 5(5+m )π,于是方程(26)的平均系统为ìíîïïïïïïïïïïïïD γ,23y ε(t ,z )=Ay ε(t ,z )+ε()m 5(5+m )π+12y ε,t (z )+y ε,t εH (z )d B H Q (t )d t ,I 13(1-γ)y ε(0,z )=φ0,y ε(θ,z )=φ(θ,z ), θ∈[-λ,0],z ∈[0,π],y ε(t ,0)=y ε(t ,π)=0.(27)显然,平均系统(27)比原系统(26)简单. 假设条件(H0)~(H3)满足,根据定理1,当ε趋于零时,系统 (26)的适度解均方收敛于平均系统(27)的适度解.参考文献:刘健康,王进斌,徐伟,2023. 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hen deciding the tube diameters required for plumbing systems a number of factors have to be taken intoaccount if an adequate flow rate is to be achieved without using oversized tube.The volume flow rate required and the pressure available are very important,other factors to consider include the length of the tube and the number of fittings used.In this first half of a two part article we shall look at the basic principles and procedures to determine copper tube diameters which will satisfy the demand required and give an economical installation.Assessment of likely demandA s the number of discharge points fitted to an installation increases the proportion that will be in use at any one time reduces.Research has provided a system to estimate probable demand based on Loading Units.These take into account the flow rate,frequency and length of use of common sanitary appliances.See T able 1 for values,it also gives BS 6700 recommended design flow rates.T o use it the number of each type of appliance fed by a pipe is multiplied by the loading unit.These can then be totalled for a group of appliances and then converted into a flow rate in litres per second using Figure 1.If necessary,any other water fittings requiring high or continuous flow rates can then be added to give a total flow rate.An example:consider a mains water service with a minimum pressure of 3 bar serving a dwelling with a kitchen,bathroom,en-suite shower and cloaks WC.This might comprise the following discharge points:Loading unitsBathroom3/4" bath taps 2 @ 10 = 201/2" basin taps 2 @ 1.5 = 3WC cistern 1 @ 2 = 2En-suite Shower 2 @ 3 = 6Kitchen1/2" sink taps2 @3 = 615mm w/machine taps 2 @ 3 = 6CloaksBasin spray tap 1 @ 0 = 0WC cistern 1 @ 2 = 2T otal loading units45Figure 1 gives us a probable flow rate of 0.72 l/s.Available headOn mains pressure systems the minimum pressure at peak demand periods can be obtained from the water supplier or measured on site.On cistern fed systems the head available should be measured vertically from the cistern outlet to the discharge point.Where the supply is sufficient half the cistern height or 0.5m can be added.One bar pressure is approximately equal to ten metres head.So,multiply by 10 to convert bars to metres head,in this case 3 bar is 30m.Head loss through tube,fittings and valvesCopper tube has a smooth bore and this means that relatively little head is lost as the water flows.The relationship between tube diameter,length,flow rate and head loss are illustrated in Figure 2.The head loss and water velocity can be found by aligning a ruler with the particular tube diameter and flow rate ing the previously determined flow rate,a 22mm service passing 0.72 l/s would use about 0.33 metres head for each metre run of tube.The water velocity would be about 2.5m/s,this is below the BS 6700recommended maximum of 3m/s for cold water and so not likely to create flow noises.PIPE SIZING FOR HOT AND COLD WATERPART ONE - BASIC PRINCIPLES21WT able 1Loading units and flow rates,hot or cold water suppliesSanitary Loading Flow fitting unit value rate (l/s)WC Cistern20.11/2” Washbasin tap1.50.15Spray mixer tap-0.043/4” Bath tap100.3Shower mixer 30.11/2” Sink or Washing30.2machine tapFittingsThe loss of head due to bends, elbows and tees can best be given as an equivalent length of tube.A bend has about half the resistance of an elbow,so, where pressure is low it is better to use bends where possible.Losses for tees are added on a change of direction only. Where the numbers of fittings to be used can be estimated they can be multiplied to give an equivalent length. This can then be added to the actual length of the tube.An alternative,where the numbers of fittings cannot be forecast,is to add a percentage to the length of tube.This can vary between about 10% and 40% depending on the complexity of the layout.T aps and valvesHead loss through stop valves isrelatively large,see T able 2 for equivalentlengths.These equivalent lengths can alsobe added to the length of tube.Lossesthrough gate valves and quarter turn ballvalves can be ignored.If the actual length of the 22mmservice mentioned previously was 10metres and 4 bends and a stop valvewere fitted the total equivalent lengthwould be:actual length of tube 10.0mequivalent length of bends 4 at 0.4 = 1.6mequivalent length of valve 1 at 7.0 = 7.0mgiving a total equivalent length of 18.6mAlternatively,the actual head loss forvalves can be established using Figure 3and then subtracted from the headavailable.For example the 22mm stop valveflowing at 0.72 l/s has a resistance ofabout 1.75 metres head.Figure 4 gives the head requiredfor a given float valve orifice andflow rate.For example a float operatedvalve with a 4mm orifice passing0.1 l/s requires a head pressure ofabout 6m.Water metersWhere a water meter is to befitted the loss of head at therequired flow rate should besubtracted from the head available.The manufacturers data sheet canbe consulted to find the head loss.Permissible head lossOnce the head pressureavailable and the effective length oftube has been found thepermissible loss of head per metrerun can be determined.This isdone by dividing the head available bythe total effective length of tube.In the case of our service pipeexample with a head of water of 30mand an effective length of 18.6m,thiswould be:30 / 18.6 = 1.6m/m.Residual headReferring back to Figure 2 our 22mmservice pipe with a flow of 0.72 l/s onlyuses about 0.33m/m of head.So,in total18.6 x 0.33 = 6.1m,say 6m,head wouldbe used up leaving 30 - 6 = 24m residualhead remaining for the internalinstallation.Final tube diameterIf insufficient residual head remainsselect a larger tube diameter to reducethe head used.If only a small percentageof the head available has been usedconsider a smaller tube diameter.In anycase,however,check that the flowvelocity is not greater than the BS 6700recommendation of 3m/s for cold and2.5m/s for hot water.A lso,to preventsluggish flow and the settlement ofdetritus in long runs of horizontal tube,keep the velocity above 0.5m/s byavoiding use of oversized tube.The above procedures can be usedto determine tube diameters fora complete installation.Keep thisarticle handy and next month we willput them into practice with astraightforward systematic methodbased on a tabulation chart.22。

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