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["  "]
[" Pression atmosph."," Prégonflage (bars)","Volume du ballon (litres)","Seuil mini du pressostat (bars)","Seuil maxi du pressostat (bars)"]
[1.013,1.2,150,1.4,4.5]
{"$rows_empty":27}
[null,"Volume à P mini","Volume à P maxi",null,"La courbe coupe mini et Maxi"]
[null,13,90,null," mini OK",null," eau disponible avant redémarrge si pression maxi au départ du puisage."]
[null,"litres d'eau","litres d'eau",null,"Maxi OK",null,null,77," litres d'eau   (90 - 13)"]
[]
[]
["Nota : ","Pour des capacités importantes, prendre un sous multiple du volume du ballon et multiplier les VOLUMES du rapport correspondant."]
[null,"Exemple : ","Pour un ballon de 1000 litres (prendre Volume ballon = 100 l - prégonflage 1,2b - P mini = 1,4b -  P Maxi = 3,5b)"]
[null,null," Volume d'eau mini = 90 l      Volume d'eau maxi = 510 l       et eau disponible = 420 l."]
[]
[]
[]
[{"$nulls":6},"Procédure pour le gonflage du ballon.    Prégonflage à vide"]
[]
[{"$nulls":6},"Partir de la pression du seuil mini du pressostat, par exemple 1,4 bar"]
[{"$nulls":6},"La pression de gonflage devrait donc être de 1,4 - 0,2 = 1,2 bar  (0,2 ou 0,3 est une valeur généralement admise)"]
[]
[{"$nulls":6},"1) couper l 'alimentation électrique de la pompe."]
[{"$nulls":6},"2) ouvrir le robinet d'utilisation d'eau pour que la pression interne soit nulle, ce qui va vider toute la réserve d'eau du ballon."]
[{"$nulls":6},"3) gonfler le ballon à 1,2 bar. Ce qui va chasser toute l'eau résiduelle de la vessie puisque la sortie est ouverte."]
[{"$nulls":6},"Nota 1 : Ne fermer le robinet d'utilisation que lorsqu'il n'y a plus d'eau qui sort."]
[{"$nulls":6},"5) remettre l'alimentation électrique. La pression va remonter jusqu'au seuil maxi puis, la pompe doit s'arrêter normalement."]
[{"$nulls":6}," N'importe quel gonfleur convient. (le ballon doit posséder une valve quand même)"]
[]
[{"$nulls":6},"Nota 2 : On suppose que le robinet d'utilisation se trouve au même niveau que le ballon."]
[{"$nulls":6},"    Si le robinet d'utilisation se trouve au 3 ème étage (+ 10 m), il faudrait en  tenir compte. (décalage de 1 bar environ)"]
[{"$nulls":6},"    Déconnecter la sortie du ballon dans ce cas."]
[]
[]
[{"$nulls":6},"Cas du ballon sans  vessie"]
["     Complément pour une cuve supposée cylindrique (sans vessie) posée horizontalement.",{"$nulls":5},"Voici comment je vois l'affaire. L'objectif étant d'adopter le même principe."]
[null,"(d'abord compléter les valeurs de base pour obtenir le graphe ci-dessus)",{"$nulls":4},"1) couper l 'alimentation électrique de la pompe."]
[null,"Si la cuve est équipée d'un indicateur de niveau (tube de verre)  vous pourrez vérifier",{"$nulls":4},"2) ouvrir le robinet d'utilisation d'eau pour que la pression interne soit nulle."]
[null,"et ajuster la pression de gonflage en utilisant la hauteur d'eau dans la cuve.",{"$nulls":4},"3) Envoyer de l'air pour chasser l'eau par les robinets de sortie."]
[{"$nulls":6},"4) lorsqu'il n'y a plus d'eau qui sort, fermer les robinets."]
[null,"Diamètre de la cuve",{"$nulls":4},"5) continuer à gonfler."]
[null,75,{"$nulls":4},"6)  lorsque la pression atteint 1,2 bars (l'exemple), mettre en marche la pompe et arrêter le gonflage."]
[null,"en cm",{"$nulls":4},"Le seul problème est que l'eau est en contact avec l'air qui va se dissoudre dans l'eau."]
[]
["Avec vessie, les volumes sont les mêmes mais pas les hauteurs d'eau.",{"$nulls":5},"Autre méthode si le ballon possède une jauge de niveau d'eau visible (tube de verre)"]
[{"$nulls":6},"Partant des valeurs fournies par le graphe (volumes), il est possible de calculer les hauteurs d'eau dans le ballon."]
[null,"Niveau eau Max. (à l'arrêt de la pompe pression Max.)",null,null,{"v":43.4151072675006,"d":"43.42"}," cm","- Pour la pression mini, pour la pression Maxi, et même la hauteur d'air."]
[null,"Niveau eau min. ( à la remise en marche pression mini.) ",null,null,{"v":10.633082921258815,"d":"10.63"}," cm","Que le ballon soit couché ou vertical.  (considérer que le ballon est cylindrique pour faciliter les calculs)"]
[]
[]
[null,null,"Profil de la cuve"]
{"$rows_empty":87}
[{"$nulls":3},"affichage traits rouges"]
["Ma_table en vert","Pression   (bars)","Vol. d'eau contenue","P mini","P maxi"]
[null,{"v":1.2000000000000002,"d":"1.20"},0,1.4,4.5]
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[null,{"v":1.3083286713286713,"d":"1.31"},7,1.4,4.5]
[null,{"v":1.3246760563380282,"d":"1.32"},8,1.4,4.5]
[null,{"v":1.341255319148936,"d":"1.34"},9,1.4,4.5]
[null,{"v":1.3580714285714284,"d":"1.36"},10,1.4,4.5]
[null,{"v":1.3751294964028777,"d":"1.38"},11,1.4,4.5]
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{"sheet":"Feuil1","index":1,"n_rows":119,"n_cols":17,"rows_kept":119,"hidden":true,"flags":["formulas_cached_only"]}
[{"$nulls":12},"Zone utilisée pour la feuille \"Feuil2_Géryko\"  Ne rien modifier ici."]
["        Hauteur d'eau dans un tuyau (ou cuve supposée parfaitement cylindrique) en fonction du taux de remplissage."]
[{"$nulls":13},"Construction d'une table (Rappel exemple)"]
[null,"Les aires du segment de disque et aire du cercle étant connues, on peut déterminer le rapport.",{"$nulls":11},"La zone du cadre ci-dessous doit être vide,"]
[null,"L'aire d'un segment du disque se calcule à l'aide de la fomule suivante :",{"$nulls":11},"1) Placer les formules ligne (vert pâle) (= ….),  "]
[null,"A = R² arc cos (h/R) - h  racine² (R²-h²) c'est à dire l'aire du secteur arc de cercle moins l'aire du triangle.",{"$nulls":11},"2) Entrer les valeurs en ordonnée (le pas) de la variable, en colonne (jaune)."]
[null,"ou ","A = R² / 2 (α - sin α)",null,"(α en radians)",{"$nulls":8},"   Option recommandée : Nommer la zone jaune + blanche (Insertion/nom/…) sans la rangée verte."]
[null,"donc"," (α - sin α) = A * 2 / R²",{"$nulls":10},"3) Sélectionner le cadre complet depuis cellule (rouge) à dernière cellule  (en bas à droite)."]
[{"$nulls":13},"4) Cliquer \"Données\"  , \"Table…\""]
[null,null,"diamètre de la cuve = ",75,"valeur de \"Feuil2_Géryko\"",{"$nulls":9},"ne rien mettre dans \"cellule d'entrée en LIGNE\""]
[null,null,"R = ",37.5,"valeur de \"Feuil2_Géryko\"",{"$nulls":4},"valeurs de \"Feuil2_Géryko\"",{"$nulls":3},"5) Entrer dans \"cellule d'entrée en COLONNE\" les coordonnées de la cellule (%) qui fournit le résultat en jaune. (Ici D12)"]
[null,null,"remplissage = ",{"v":0.85,"d":"85.00%"}," Attention, cellule D12 utilisée pour construire la Table1",{"$nulls":4},"capacité citerne",150]
[null,null,"aire totale = ",{"v":4417.864669110647,"d":"4417.86"},null,null," (mais % modifiable pour le tableau Exemple.)",null,null,"à pression  max",90]
[null,null,"aire segment = ",{"v":662.6797003665971,"d":"662.68"},"(partie haute sans eau)",{"$nulls":4},"à pression min",13]
[{"$nulls":9}," % de remplissage",{"v":0.6,"d":"60%"},"max",{"$nulls":3},"Zone ne sert pas. Mise pour exemple."]
[null,null,"posons k = (α - sin α) =  ",0.9424777960769382,"  pour simplifier l'écriture sous Excel (α radians)",{"$nulls":4}," % de remplissage",{"v":0.08666666666666667,"d":"9%"},"min"]
[{"$nulls":4},"Espace de k ( k compris entre 0 et 2 PI, 0 à 6,28)",{"$nulls":8},"table","hauteur","h","k"]
[{"$nulls":13},"Table1",{"v":59.442653358029816,"d":"59.44"},{"v":21.942653358029812,"d":"21.94"},0.9424777960769385]
[null,"En modifiant la valeur de D12 on peut \"jouer\" avec ce tableau. (Ne rien modifier d'autre)",{"$nulls":11},{"v":0,"d":"0%"},{"v":0.8140314962038673,"d":"0.81"}]
[null,"Exemple","α","sin α","k ","ecart ","ecart / 2",{"$nulls":6},{"v":0.01,"d":"1%"},{"v":2.4976026657640844,"d":"2.50"}]
[null,"si α = 2",2,0.9092974268256817,1.0907025731743183,-0.14822477709738013,-0.07411238854869007,{"$nulls":6},{"v":0.02,"d":"2%"},{"v":3.927952332505299,"d":"3.93"}]
[null,"α + ecart/2",1.92588761145131,0.9376147552456784,0.9882728562056315,-0.04579506012869339,-0.022897530064346694,null,null,"Table2",{"v":59.442653358029816,"d":"59.44"},null,null,{"v":0.03,"d":"3%"},{"v":5.160862235959776,"d":"5.16"}]
[null,null,1.9029900813869634,0.9453291967755192,0.9576608846114442,-0.015183088534506006,-0.007591544267253003,null,null,{"v":0.6,"d":"60.00%"},{"v":43.4151072675006,"d":"43.42"},null,null,{"v":0.04,"d":"4%"},{"v":6.271074338011719,"d":"6.27"}]
[null,null,1.8953985371197104,0.9477776691731504,0.94762086794656,{"v":-0.005143071869621818,"d":"-0.0051430719"},{"v":-0.002571535934810909,"d":"-0.0025715359"},null,null,{"v":0.08666666666666667,"d":"8.67%"},{"v":10.633082921258815,"d":"10.63"},null,null,{"v":0.05,"d":"5%"},{"v":7.298119210770192,"d":"7.30"}]
[null,null,1.8928270011848995,0.9485946791116893,0.9442323220732103,{"v":-0.0017545259962721271,"d":"-0.0017545260"},{"v":-0.0008772629981360636,"d":"-0.0008772630"},{"$nulls":6},{"v":0.06,"d":"6%"},{"v":8.264169855836819,"d":"8.26"}]
[null,null,1.8919497381867636,0.9488719620970539,0.9430777760897097,{"v":-0.000599980012771506,"d":"-0.0005999800"},{"v":-0.000299990006385753,"d":"-0.0002999900"},{"$nulls":6},{"v":0.07,"d":"7%"},{"v":9.18296727419743,"d":"9.18"}]
[null,null,1.8916497481803778,0.9489666146076665,0.9426831335727113,{"v":-0.00020533749577311688,"d":"-0.0002053375"},{"v":-0.00010266874788655844,"d":"-0.0001026687"},{"$nulls":6},{"v":0.08,"d":"8%"},{"v":10.063727788375875,"d":"10.06"}]
[null,null,1.8915470794324913,0.9489989889210035,0.9425480905114878,{"v":-7.029443454964479e-05,"d":"-0.0000702944"},{"v":-3.5147217274822395e-05,"d":"-0.0000351472"},{"$nulls":6},{"v":0.09,"d":"9%"},{"v":10.913005179150069,"d":"10.91"}]
[null,null,1.8915119322152165,0.9490100695183223,0.9425018626968942,{"v":-2.406661995602022e-05,"d":"-0.0000240666"},{"v":-1.203330997801011e-05,"d":"-0.0000120333"},{"$nulls":6},{"v":0.1,"d":"10%"},{"v":11.73566902030922,"d":"11.74"}]
[null,null,1.8914998989052385,0.9490138628995393,0.9424860360056992,{"v":-8.239928761089033e-06,"d":"-0.0000082399"},{"v":-4.119964380544516e-06,"d":"-0.0000041200"},{"$nulls":6},{"v":0.11,"d":"11%"},{"v":12.535462512603718,"d":"12.54"}]
[null,null,1.891495778940858,0.9490151616457301,0.9424806172951279,{"v":-2.8212181897302457e-06,"d":"-0.0000028212"},{"v":-1.4106090948651229e-06,"d":"-0.0000014106"},{"$nulls":6},{"v":0.12,"d":"12%"},{"v":13.31534194708928,"d":"13.32"}]
[null,null,1.891494368331763,0.9490156063116951,0.942478762020068,{"v":-9.65943129815905e-07,"d":"-0.0000009659"},{"v":-4.829715649079525e-07,"d":"-0.0000004830"},{"$nulls":6},{"v":0.13,"d":"13%"},{"v":14.077694280400525,"d":"14.08"}]
[null,null,1.8914938853601981,0.9490157585582712,0.9424781268019269,{"v":-3.3072498872854794e-07,"d":"-0.0000003307"},{"v":-1.6536249436427397e-07,"d":"-0.0000001654"},{"$nulls":6},{"v":0.14,"d":"14%"},{"v":14.824482573369846,"d":"14.82"}]
[null,null,1.8914937199977038,0.949015810685251,0.9424779093124528,{"v":-1.1323551463160442e-07,"d":"-0.0000001132"},{"v":-5.661775731580221e-08,"d":"-0.0000000566"},{"$nulls":6},{"v":0.15,"d":"15%"},{"v":15.557346641970206,"d":"15.56"}]
[null,null,1.8914936633799464,0.9490158285327788,0.9424778348471676,{"v":-3.87702294712966e-08,"d":"-0.0000000388"},{"v":-1.93851147356483e-08,"d":"-0.0000000194"},{"$nulls":6},{"v":0.16,"d":"16%"},{"v":16.277674771830117,"d":"16.28"}]
[null,null,1.8914936439948318,0.9490158346435177,0.9424778093513141,{"v":-1.3274375931793259e-08,"d":"-0.0000000133"},{"v":-6.637187965896629e-09,"d":"-0.0000000066"},{"$nulls":6},{"v":0.17,"d":"17%"},{"v":16.986656099374876,"d":"16.99"}]
[null,null,1.8914936373576439,0.9490158367357477,0.9424778006218961,{"v":-4.5449579655354455e-09,"d":"-0.0000000045"},{"v":-2.2724789827677228e-09,"d":"-0.0000000023"},{"$nulls":6},{"v":0.18,"d":"18%"},{"v":17.68531969970776,"d":"17.69"}]
[null,null,1.891493635085165,0.9490158374520976,0.9424777976330674,{"v":-1.5561292254773207e-09,"d":"-0.0000000016"},{"v":-7.780646127386603e-10,"d":"-0.0000000008"},{"$nulls":6},{"v":0.19,"d":"19%"},{"v":18.37456430461627,"d":"18.37"}]
[null,null,1.8914936343071003,0.9490158376973657,0.9424777966097345,{"v":-5.3279636258452e-10,"d":"-0.0000000005"},{"v":-2.6639818129226e-10,"d":"-0.0000000003"},{"$nulls":6},{"v":0.2,"d":"20%"},{"v":19.055181271360933,"d":"19.06"}]
[null,null,1.891493634040702,0.949015837781342,0.94247779625936,{"v":-1.824218553991841e-10,"d":"-0.0000000002"},{"v":-9.121092769959205e-11,"d":"-0.0000000001"},{"$nulls":6},{"v":0.21,"d":"21%"},{"v":19.72787259613262,"d":"19.73"}]
[null,null,1.8914936339494912,0.9490158378100942,0.942477796139397,{"v":-6.24588158970596e-11,"d":"-0.0000000001"},{"v":-3.12294079485298e-11,"d":"-0.0000000000"},{"$nulls":6},{"v":0.22,"d":"22%"},{"v":20.39326522699945,"d":"20.39"}]
[null,null,1.8914936339182618,0.9490158378199387,0.942477796098323,{"v":-2.138489385572484e-11,"d":"-0.0000000000"},{"v":-1.069244692786242e-11,"d":"-0.0000000000"},{"$nulls":6},{"v":0.23,"d":"23%"},{"v":21.051922571178576,"d":"21.05"}]
[null,null,1.8914936339075692,0.9490158378233092,0.94247779608426,{"v":-7.321809825100445e-12,"d":"-0.0000000000"},{"v":-3.6609049125502224e-12,"d":"-0.0000000000"},{"$nulls":6},{"v":0.24,"d":"24%"},{"v":21.704353845889273,"d":"21.70"}]
[null,null,1.8914936339039083,0.9490158378244633,0.942477796079445,{"v":-2.5068835896036035e-12,"d":"-0.0000000000"},{"v":-1.2534417948018017e-12,"d":"-0.0000000000"},{"$nulls":6},{"v":0.25,"d":"25%"},{"v":22.351021751268114,"d":"22.35"}]
[null,null,1.891493633902655,0.9490158378248584,0.9424777960777965,{"v":-8.583134203377085e-13,"d":"-0.0000000000"},{"v":-4.2915671016885426e-13,"d":"-0.0000000000"},{"$nulls":6},{"v":0.26,"d":"26%"},{"v":22.992348822998515,"d":"22.99"}]
[null,null,1.8914936339022257,0.9490158378249937,0.942477796077232,{"v":-2.9387603461827894e-13,"d":"-0.0000000000"},{"v":-1.4693801730913947e-13,"d":"-0.0000000000"},{"$nulls":6},{"v":0.27,"d":"27%"},{"v":23.628722735461913,"d":"23.63"}]
[null,null,1.8914936339020787,0.9490158378250401,0.9424777960770386,{"v":-1.0047518372857667e-13,"d":"-0.0000000000"},{"v":-5.0237591864288333e-14,"d":"-0.0000000000"},{"$nulls":6},{"v":0.28,"d":"28%"},{"v":24.26050076290258,"d":"24.26"}]
[null,null,1.8914936339020285,0.9490158378250558,0.9424777960769727,{"v":-3.452793606584237e-14,"d":"-0.0000000000"},{"v":-1.7263968032921184e-14,"d":"-0.0000000000"},{"$nulls":6},{"v":0.29,"d":"29%"},{"v":24.88801355932272,"d":"24.89"}]
[null,null,1.8914936339020112,0.9490158378250613,0.9424777960769499,{"v":-1.176836406102666e-14,"d":"-0.0000000000"},{"v":-5.88418203051333e-15,"d":"-0.0000000000"},{"$nulls":6},{"v":0.3,"d":"30%"},{"v":25.511568382856126,"d":"25.51"}]
[null,null,1.8914936339020052,0.9490158378250632,0.942477796076942,{"v":-3.885780586188048e-15,"d":"-0.0000000000"},{"v":-1.942890293094024e-15,"d":"-0.0000000000"},{"$nulls":6},{"v":0.31,"d":"31%"},{"v":26.131451863930376,"d":"26.13"}]
[null,null,1.8914936339020032,0.9490158378250638,0.9424777960769394,{"v":-1.2212453270876722e-15,"d":"-0.0000000000"},{"v":-6.106226635438361e-16,"d":"-0.0000000000"},{"$nulls":6},{"v":0.32,"d":"32%"},{"v":26.74793239633872,"d":"26.75"}]
[null,null,1.8914936339020025,0.949015837825064,0.9424777960769385,{"v":0,"d":"0.0000000000"},{"v":0,"d":"0.0000000000"},{"$nulls":6},{"v":0.33,"d":"33%"},{"v":27.36126221477425,"d":"27.36"}]
[null,null,1.8914936339020025,0.949015837825064,0.9424777960769385,{"v":0,"d":"0.0000000000"},{"v":0,"d":"0.0000000000"},{"$nulls":6},{"v":0.34,"d":"34%"},{"v":27.971679210270835,"d":"27.97"}]
[{"$nulls":13},{"v":0.35,"d":"35%"},{"v":28.579408525504434,"d":"28.58"}]
[null,null,"et donc α = ",{"v":108.374602198448,"d":"108.37"},"degès (pour information)",{"$nulls":8},{"v":0.36,"d":"36%"},{"v":29.184663964405274,"d":"29.18"}]
[null,"Reste à trouver la distance h entre le centre du cercle et la corde.",{"$nulls":11},{"v":0.37,"d":"37%"},{"v":29.787649244570638,"d":"29.79"}]
[{"$nulls":6},"vérifications 2 valeurs complémentaires",{"$nulls":6},{"v":0.38,"d":"38%"},{"v":30.388559116189565,"d":"30.39"}]
[{"$nulls":6},"90 / 10 %","98 / 2 %",{"$nulls":5},{"v":0.39,"d":"39%"},{"v":30.987580367351573,"d":"30.99"}]
[{"$nulls":6},67.48,75.81,{"$nulls":5},{"v":0.4,"d":"40%"},{"v":31.584892732499405,"d":"31.58"}]
[{"$nulls":6},12.52,4.12,{"$nulls":5},{"v":0.41,"d":"41%"},{"v":32.18066971826308,"d":"32.18"}]
[null,null,"h = ",{"v":21.942653358029812,"d":"21.94"},null,"total = 2R = ",80,79.93,{"$nulls":5},{"v":0.42,"d":"42%"},{"v":32.775079358851,"d":"32.78"}]
[{"$nulls":13},{"v":0.43,"d":"43%"},{"v":33.36828491149342,"d":"33.37"}]
[null,null,"hauteur d'eau = ",{"v":59.442653358029816,"d":"59.44"},{"$nulls":9},{"v":0.44,"d":"44%"},{"v":33.9604455010561,"d":"33.96"}]
[{"$nulls":13},{"v":0.45,"d":"45%"},{"v":34.55171672181645,"d":"34.55"}]
[null,"rappel des bases : ","http://villemin.gerard.free.fr/GeomLAV/Cercle/aaaAIRE/Segment.htm",{"$nulls":10},{"v":0.46,"d":"46%"},{"v":35.142251203477535,"d":"35.14"}]
[{"$nulls":13},{"v":0.47,"d":"47%"},{"v":35.7321991477509,"d":"35.73"}]
[{"$nulls":13},{"v":0.48,"d":"48%"},{"v":36.32170884124317,"d":"36.32"}]
[{"$nulls":13},{"v":0.49,"d":"49%"},{"v":36.91092714991239,"d":"36.91"}]
[{"$nulls":13},{"v":0.5,"d":"50%"},{"v":37.5,"d":"37.50"}]
[{"$nulls":13},{"v":0.51,"d":"51%"},{"v":38.089072850087625,"d":"38.09"}]
[{"$nulls":13},{"v":0.52,"d":"52%"},{"v":38.678291158756835,"d":"38.68"}]
[{"$nulls":13},{"v":0.53,"d":"53%"},{"v":39.267800852249124,"d":"39.27"}]
[{"$nulls":13},{"v":0.54,"d":"54%"},{"v":39.85774879652248,"d":"39.86"}]
[{"$nulls":13},{"v":0.55,"d":"55%"},{"v":40.44828327818355,"d":"40.45"}]
[{"$nulls":13},{"v":0.56,"d":"56%"},{"v":41.039554498943914,"d":"41.04"}]
[{"$nulls":13},{"v":0.57,"d":"57%"},{"v":41.63171508850658,"d":"41.63"}]
[{"$nulls":13},{"v":0.58,"d":"58%"},{"v":42.22492064114901,"d":"42.22"}]
[{"$nulls":13},{"v":0.59,"d":"59%"},{"v":42.819330281736924,"d":"42.82"}]
[{"$nulls":13},{"v":0.6,"d":"60%"},{"v":43.4151072675006,"d":"43.42"}]
[{"$nulls":13},{"v":0.61,"d":"61%"},{"v":44.012419632648445,"d":"44.01"}]
[{"$nulls":13},{"v":0.62,"d":"62%"},{"v":44.611440883810445,"d":"44.61"}]
[{"$nulls":13},{"v":0.63,"d":"63%"},{"v":45.212350755429384,"d":"45.21"}]
[{"$nulls":13},{"v":0.64,"d":"64%"},{"v":45.81533603559474,"d":"45.82"}]
[{"$nulls":13},{"v":0.65,"d":"65%"},{"v":46.420591474495595,"d":"46.42"}]
[{"$nulls":13},{"v":0.66,"d":"66%"},{"v":47.02832078972918,"d":"47.03"}]
[{"$nulls":13},{"v":0.67,"d":"67%"},{"v":47.6387377852258,"d":"47.64"}]
[{"$nulls":13},{"v":0.68,"d":"68%"},{"v":48.25206760366131,"d":"48.25"}]
[{"$nulls":13},{"v":0.69,"d":"69%"},{"v":48.868548136069684,"d":"48.87"}]
[{"$nulls":13},{"v":0.7,"d":"70%"},{"v":49.488431617143895,"d":"49.49"}]
[{"$nulls":13},{"v":0.71,"d":"71%"},{"v":50.11198644067729,"d":"50.11"}]
[{"$nulls":13},{"v":0.72,"d":"72%"},{"v":50.739499237097476,"d":"50.74"}]
[{"$nulls":13},{"v":0.73,"d":"73%"},{"v":51.37127726453813,"d":"51.37"}]
[{"$nulls":13},{"v":0.74,"d":"74%"},{"v":52.00765117700152,"d":"52.01"}]
[{"$nulls":13},{"v":0.75,"d":"75%"},{"v":52.6489782487319,"d":"52.65"}]
[{"$nulls":13},{"v":0.76,"d":"76%"},{"v":53.295646154110784,"d":"53.30"}]
[{"$nulls":13},{"v":0.77,"d":"77%"},{"v":53.94807742882147,"d":"53.95"}]
[{"$nulls":13},{"v":0.78,"d":"78%"},{"v":54.606734773000596,"d":"54.61"}]
[{"$nulls":13},{"v":0.79,"d":"79%"},{"v":55.272127403867444,"d":"55.27"}]
[{"$nulls":13},{"v":0.8,"d":"80%"},{"v":55.944818728639135,"d":"55.94"}]
[{"$nulls":13},{"v":0.81,"d":"81%"},{"v":56.625435695383764,"d":"56.63"}]
[{"$nulls":13},{"v":0.82,"d":"82%"},{"v":57.314680300292295,"d":"57.31"}]
[{"$nulls":13},{"v":0.83,"d":"83%"},{"v":58.01334390062517,"d":"58.01"}]
[{"$nulls":13},{"v":0.84,"d":"84%"},{"v":58.72232522816991,"d":"58.72"}]
[{"$nulls":13},{"v":0.85,"d":"85%"},{"v":59.442653358029816,"d":"59.44"}]
[{"$nulls":13},{"v":0.86,"d":"86%"},{"v":60.17551742663022,"d":"60.18"}]
[{"$nulls":13},{"v":0.87,"d":"87%"},{"v":60.922305719599976,"d":"60.92"}]
[{"$nulls":13},{"v":0.88,"d":"88%"},{"v":61.684658052914095,"d":"61.68"}]
[{"$nulls":13},{"v":0.89,"d":"89%"},{"v":62.464537487418866,"d":"62.46"}]
[{"$nulls":13},{"v":0.9,"d":"90%"},{"v":63.26433097983859,"d":"63.26"}]
[{"$nulls":13},{"v":0.91,"d":"91%"},{"v":64.08699482180104,"d":"64.09"}]
[{"$nulls":13},{"v":0.92,"d":"92%"},{"v":64.9362722176685,"d":"64.94"}]
[{"$nulls":13},{"v":0.93,"d":"93%"},{"v":65.81703276393145,"d":"65.82"}]
[{"$nulls":13},{"v":0.94,"d":"94%"},{"v":66.73583038425592,"d":"66.74"}]
[{"$nulls":13},{"v":0.95,"d":"95%"},{"v":67.70188230805023,"d":"67.70"}]
[{"$nulls":13},{"v":0.96,"d":"96%"},{"v":68.72893538408255,"d":"68.73"}]
[{"$nulls":13},{"v":0.97,"d":"97%"},{"v":69.83920118896094,"d":"69.84"}]
[{"$nulls":13},{"v":0.98,"d":"98%"},{"v":71.07247030103149,"d":"71.07"}]
[{"$nulls":13},{"v":0.99,"d":"99%"},{"v":72.50518275603808,"d":"72.51"}]
[{"$nulls":13},{"v":1,"d":"100%"},{"v":74.19948690830694,"d":"74.20"}]

{"sheet":"Feuil2","index":2,"n_rows":71,"n_cols":10,"rows_kept":71,"hidden":true,"merged":[[50,5,50,6],[50,8,50,9]],"flags":["formulas_cached_only"]}
["        Hauteur d'eau dans un tuyau (ou cuve supposée parfaitement cylindrique) en fonction du taux de remplissage."]
[]
[null,"En utilisant la méthode de newton."]
[null,"L'aire d'un segment du disque se calcule à l'aide de la fomule suivante :"]
[null,"A = R² arc cos (h/R) - h  racine² (R²-h²) c'est à dire l'aire du secteur arc de cercle moins l'aire du triangle."]
[null,"formule se simplifie en prenant x = h/R,  (et h = Rx).    Elle devient  :"]
[null,"A = R² arc cos (x) - Rx racine² (R²-(Rx)²)  ---à  A = R² arc cos (x) - Rx . R racine² (1-x²)  et donc :"]
[]
[{"$nulls":5},"On connaît A donc A/R² et on cherche x."]
[]
[null,"- Pour simplifier on cherchera x compris entre 0 et 1, entre une citerne vide et demi pleine."]
[null," ( soit A/R² <= pi/2 ) et on cherche x ( 0 <= x <= 1)"]
[null,"- Dans l'autre cas, on peut faire le calcul inverse qui consiste à prendre x pour la partie encore vide de la"]
[null,"  citerne mais l'idée est de présenter le principe du calcul :"]
[{"$nulls":5},"          cette fonction est décroissante avec une dérivée "]
[]
[]
[]
[null,"Le principe général est de partir d'un point de la courbe et de se projeter sur un point plus près de X"]
[null," tel que f(X) = 0,  la projection se faisant en utilisant la tangente à la courbe à chaque fois."]
[null,"Si x0 est un point de départ , la tangente en (x0,f(x0)) a pour équation :"]
[null,"   T(x0) = f(x0) + (x - x0) f ' (x0)"]
[null,"la nouvelle abscisse que l'on cherche est donc"]
[null,"  x1 = x0 - f(x0) / f ' (x0) et ainsi de suite."]
[null,"  x(n + 1) = xn - f(xn) / f ' (xn)"]
[null,"Dans l'exemple qui suit, prenons au hasard A/R² = 0,5 et x0 = 0,2 . On obtient dans ce cas"]
[null,"x0 = 0,2"]
[null,"x1 = 0,54368"]
[null,"x2 = 0,567315"]
[null,"x3 = 0,56753978"]
[null,"etc …"]
[]
[null,"remplissage = ",{"v":0.52,"d":"52.00%"},"(exemple modifiable)"]
[null,"R = ",40,"(exemple modifiable)"]
[null,"A maxi. = ",{"v":5026.548245743669,"d":"5026.55"}]
[null,"liquide = A = ",{"v":2613.805087786708,"d":"2613.81"}]
[null,"A/R² = ",{"v":1.6336281798666925,"d":"1.63"}]
[]
[null,null,"x (0<=x<=1)"," x rac² (1-x²)","arc cos(x)","f (x)","f ' (x)"]
[null,"x0 = ",0.2]
[null,"x1 = ",{"v":-0.03481877942155981,"d":"-0.03481878"},{"v":0.19595917942265426,"d":"0.19595918"},{"v":1.3694384060045657,"d":"1.36943841"},{"v":-0.4601489532847811,"d":"-0.46015"},{"v":-1.9595917942265424,"d":"-1.95959"}]
[null,"x2 = ",{"v":-0.0314209028972758,"d":"-0.03142090"},{"v":-0.034797666792300355,"d":"-0.03479767"},{"v":1.6056221454668935,"d":"1.60562215"},{"v":0.006791632392501468,"d":"0.00679"},{"v":-1.9987872849301327,"d":"-1.99879"}]
[null,"x3 = ",{"v":-0.031421097566848126,"d":"-0.03142110"},{"v":-0.03140538856039328,"d":"-0.03140539"},{"v":1.602222402159394,"d":"1.60222240"},{"v":-3.891469051442442e-07,"d":"-0.00000"},{"v":-1.999012483063695,"d":"-1.99901"}]
[null,"x4 = ",{"v":-0.031421097566848126,"d":"-0.03142110"},{"v":-0.03140558294155708,"d":"-0.03140558"},{"v":1.6022225969251342,"d":"1.60222260"},{"v":0,"d":"0.00000"},{"v":-1.9990124708242263,"d":"-1.99901"}]
[null,"x5 = ",{"v":-0.031421097566848126,"d":"-0.03142110"},{"v":-0.03140558294155708,"d":"-0.03140558"},{"v":1.6022225969251342,"d":"1.60222260"},{"v":0,"d":"0.00000"},{"v":-1.9990124708242263,"d":"-1.99901"}]
[null,"x6 = ",{"v":-0.031421097566848126,"d":"-0.03142110"},{"v":-0.03140558294155708,"d":"-0.03140558"},{"v":1.6022225969251342,"d":"1.60222260"},{"v":0,"d":"0.00000"},{"v":-1.9990124708242263,"d":"-1.99901"}]
[null,"x7 = ",{"v":-0.031421097566848126,"d":"-0.03142110"},{"v":-0.03140558294155708,"d":"-0.03140558"},{"v":1.6022225969251342,"d":"1.60222260"},{"v":0,"d":"0.00000"},{"v":-1.9990124708242263,"d":"-1.99901"}]
[null,"x8 = ",{"v":-0.031421097566848126,"d":"-0.03142110"},{"v":-0.03140558294155708,"d":"-0.03140558"},{"v":1.6022225969251342,"d":"1.60222260"},{"v":0,"d":"0.00000"},{"v":-1.9990124708242263,"d":"-1.99901"}]
[null,"x9 = ",{"v":-0.031421097566848126,"d":"-0.03142110"},{"v":-0.03140558294155708,"d":"-0.03140558"},{"v":1.6022225969251342,"d":"1.60222260"},{"v":0,"d":"0.00000"},{"v":-1.9990124708242263,"d":"-1.99901"}]
[null,"X9 nécessaire pour 100% et 0%"]
[{"$nulls":5},"Newton",null,null,"1ère méthode"]
[null,"degrés = ",{"v":183.60118528860136,"d":"183.60"}," (pour information)",null,"table","hauteur liquide",null,"table","hauteur liquide"]
[null," radians = ",{"v":3.204445193850269,"d":"3.20"},{"$nulls":3},{"v":41.256843902673936,"d":"41.26"},null,null,{"v":0,"d":"0.00"}]
[null,"hauteur liqude = ",{"v":41.256843902673936,"d":"41.26"},null,null,{"v":0,"d":"0%"},{"v":0.003448868431362939,"d":"0.00"},null,{"v":0,"d":"0%"},{"v":0.8683002626174812,"d":"0.87"}]
[{"$nulls":5},{"v":0.05,"d":"5%"},{"v":7.784654539195216,"d":"7.78"},null,{"v":0.05,"d":"5%"},{"v":7.784660491488225,"d":"7.78"}]
[{"$nulls":5},{"v":0.1,"d":"10%"},{"v":12.518046954698384,"d":"12.52"},null,{"v":0.1,"d":"10%"},{"v":12.518046954996503,"d":"12.52"}]
[{"$nulls":5},{"v":0.15,"d":"15%"},{"v":16.594503084768192,"d":"16.59"},null,{"v":0.15,"d":"15%"},{"v":16.594503084768238,"d":"16.59"}]
[{"$nulls":5},{"v":0.2,"d":"20%"},{"v":20.325526689451618,"d":"20.33"},null,{"v":0.2,"d":"20%"},{"v":20.325526689451664,"d":"20.33"}]
[{"$nulls":5},{"v":0.4,"d":"40%"},{"v":33.69055224799939,"d":"33.69"},null,{"v":0.4,"d":"40%"},{"v":33.690552247999385,"d":"33.69"}]
[{"$nulls":5},{"v":0.45,"d":"45%"},{"v":36.8551645032709,"d":"36.86"},null,{"v":0.45,"d":"45%"},{"v":36.85516450327089,"d":"36.86"}]
[{"$nulls":5},{"v":0.5,"d":"50%"},{"v":40,"d":"40.00"},null,{"v":0.5,"d":"50%"},{"v":40,"d":"40.00"}]
[{"$nulls":5},{"v":0.55,"d":"55%"},{"v":43.144835496729115,"d":"43.14"},null,{"v":0.55,"d":"55%"},{"v":43.14483549672912,"d":"43.14"}]
[{"$nulls":5},{"v":0.6,"d":"60%"},{"v":46.30944775200064,"d":"46.31"},null,{"v":0.6,"d":"60%"},{"v":46.30944775200064,"d":"46.31"}]
[{"$nulls":5},{"v":0.8,"d":"80%"},{"v":59.67447331054842,"d":"59.67"},null,{"v":0.8,"d":"80%"},{"v":59.674473310548414,"d":"59.67"}]
[{"$nulls":5},{"v":0.85,"d":"85%"},{"v":63.40549691523181,"d":"63.41"},null,{"v":0.85,"d":"85%"},{"v":63.405496915231794,"d":"63.41"}]
[{"$nulls":5},{"v":0.9,"d":"90%"},{"v":67.48195304530164,"d":"67.48"},null,{"v":0.9,"d":"90%"},{"v":67.48195304516116,"d":"67.48"}]
[{"$nulls":5},{"v":0.95,"d":"95%"},{"v":72.21534546080477,"d":"72.22"},null,{"v":0.95,"d":"95%"},{"v":72.21534112858691,"d":"72.22"}]
[{"$nulls":5},{"v":1,"d":"100%"},{"v":79.99663922444788,"d":"80.00"},null,{"v":1,"d":"100%"},{"v":79.14611936886072,"d":"79.15"}]
[{"$nulls":8},"Nb d'itérations est donc un peu trop limité"]
[]
[null,"Ce graphique ne représente que la première étape."]