DI 007 - Inenaional Sympoium on Digial induial adiology and Compued Tomogaphy, June 5-7, 007, Lyon, Fance eviied he Mahemaical Deivaion all Thickne Meauemen o Pipe o adiogaphy Ab.. Hamzah and Sii M. M. Ami Non Deucive Teing(NDT) Goup, Induial Technology Diviion, Malayian Nuclea Agency, Bangi, 43000 Kajang, Selango, Malayia; Phone:+603 895050, Fa:+6038950907; e-mail: azak_hamzah@nucleamalayia.gov.my, e-mail: madiha_ami@nucleamalayia.gov.my Abac all hickne meauemen o pipe i vey impoan o he ucual inegiy o he induial plan. Hoeve, he adiogaphy mehod ha an advanage becaue he abiliy o peneaing he inulaed pipe. Thi ill have economic benei o induy. Moeove, he ea o digial adiogaphy ha moe advanage becaue he peed o adiogaphic ok, le epoue ime and no chemical ued o ilm developmen. Eihe he convenional adiogaphy o digial adiology, he all hickne meauemen i uing he angenial adiogaphy echnique (TT). In cae, o a lage diamee, pipe (moe han inche) he deeminaion maimum peneaion all hickne mu be aken ino he conideaion. Thi pape i eviied he mahemaical deivaion o he deeminaion o all hickne meauemen baed on angenial adiogaphy echnique (TT). The mahemaical appoach ued in hi deivaion i he Pyhagoa heoem and geomeical pinciple. In ode o deive he maimum peneaion all hickne a imila appoach i ued. Keyod : all hickne meauemen, angenial adiogaphy, maimum peneaion all hickne. Inoducion The mo pominen advanage in adiogaphy a Non-Deucive Teing (NDT) echnique egadle he convenional o digial adiogaphy i he abiliy o peneae he inulaed pipe. A e kno induial adiogaphy i moe popula o deec deec in he elding and caing. Hoeve, a e yea back, all hickne meauemen ha becoming moe popula and i i vey cucial in he aemen o ucual inegiy o induial plan. Thee ae o mehod in aeing all hickne; he double all mehod and Tangenial adiogaphy Technique (TT). The double all mehod i an eablihed mehod ued by he adiogaphe. Fo angenial adiogaphy, a ceain geomeical eup o pipe inpecion i needed. In he pape, e ae eviied he mahemaical deivaion he all hickne meauemen o pipe uing adiogaphy mehod.. Tangenial adiogaphy Tangenial adiogaphy i a mehod employed o pipe inpecion o monio cooion and evaluae all hickne ihou emoving he inulao. In hi mehod, a ceain geomeical e-up o pipe inpecion i needed. In hi mehod, only pa o he adiogaph, hich lie belo he angenial locaion, ae inepeed. The middle pa o he image i ignoed []. In obaining he good image a he angenial locaion ha i he chod, he elecion o opimum enegy i vey impoan. Thi i due o he chod egmen, hich ha dieence in hickne ha vaie om he hinne o he maimum peneaed all hickne. The elecion o opimum enegy i cucial o peven bun-o eec a he
hinne poion o he ample and caeing o oo bigh image a he hicke egmen. Theeoe, he elecion o he iadiaion ouce ued mu be accoding o he maimum o he peneaed hickne.. all Thickne Deivaion eviied [] The main pupoe o he Tangenial adiogaphy echnique i o evaluae he all hickne. In deiving he all hickne equaion, he mahemaical appoach on Pyhagoa heoem and geomeical pinciple ae ued. The deeminaion o he all hickne uing angenial mehod i epeened in Figue. Y(0,y) Z(0,z) B (,h) (-) D(,) h I-9 (-) O(0,0) C H A(,0) T (-) Figue. The chemaic diagam o deeminaion o all hickne Fom Fig., AY i he angen o he cicle o adiu a poin B (,h). h i he lengh o he pependicula dopped om B o H on OA. Uing Pyhagoa heoem, alo h AB AC CB ( ) ( ) ( ) AB AH..() Aea o ABC h AC ( ) ( )h bu alo aea o ABC BC AB and olving o h,. Hence, h o h ( ) ( )
h [ ] ( ) ( ). () Theeoe () and () imply ( ) ( ) ( ) (3) Ne, ince he gadien o AB i he ame a ha o BY, y h 0 h h y. Thi implie 0 ( ) ( ) ( ) ( )..... (4) ( ) Fom Fig., AZ i he angen o he cicle o adiu - a poin D(,). i he lengh o he pependicula dopped om D o T on OA. By Pyhagoa heoem, AD AC CD ( ) ( ) and by Pyhagoa heoem, AD AT...... (5) bu alo aea o ACD CD AD The aea o ACD AC ( ) ( ) ( ) ( ) ( ). Thi implie ( ) ( ) ( ) and olving o, e obain o ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( )... (6)
Theeoe (5) and (6) implie [ ] o.... (7) The gadien o AD i he ame a ha o DZ, 0 z 0. Thi implie, z ) (. (8) No z y o ha and quaing boh ide o he equaion,. Le θ. No θ implie θ θ + and ubiuing o θ, +.(9)
. Maimum Peneaion all Thickne [3] Tangenial adiogaphy i a mehod ued o aeing he eidual all hickne o pipeline hee cooion o eoion i likely o occu. Hoeve, hee ei limi in adoping hi mehod epecially in deemining he ouce ued. In obaining he coec value o he eidual all hickne he calculaion on maimum peneaion all hickne, L ma mu ake ino conideaion, a hi i o enue he appopiae adiaion enegy being ued. A (D a /)- B D a / Figue. The chemaic diagam o deemine L ma. Le AB be he maimum peneaed all hickne L ma., i he ue all hickne and D a i he oue diamee. Uing Pyhagoa heoem, Da + D a Da 4 Da 4 + D a 0.(3) Solve (3) and yield D a..(4) Squae oo (4) on boh ide o he equaion. Thi yield, Since ABL ma and AB, hence, Da...(5) L ma.(6)
Subiue (6) in (5) o obain 3. Concluion L ma Da (7) I i impoan o induial adiogaphe o undeand he deivaion o he all hickne meauemen a lea hey kno he baic paamee and he limiaion o he echnique hen peoming he epeimen. Acknoledgemen The auho ould like o hank he IAEA o coodinaing and he inancial uppoing on hi eeach pojec. eeence. Validaion o Poocol o Cooion and Depoi Evaluaion in Lage Diamee Pipe by adiogaphy, epo o he nd CM o he CP, Ianbul Tukey, pp 3, Mach 004, IAEA.. S.M.M.Ami, A..Hamzah, H.A.Kaim and M.B. Zubi, Analyical Sudie O Tangenial adiogaphy Mehod eviied, peened a he Coneence on Advance in Theoeical Science (CATS 003) /Advanced Technology Conge (ATC 003) 003. 3. S.M.M.Ami, A..Hamzah, S.Sayui, A.Ama and S.ejab, Tangenial adiogaphy Technique(TT) Fo Pipe all Thickne Meauemen Uing adiaion Mahemaical Appoach, poceeding MINT &D Semina eeach and Developmen, Semina B, pp70-76, MINT, July 004.