{"id":1010,"date":"2021-12-09T21:19:53","date_gmt":"2021-12-09T21:19:53","guid":{"rendered":"https:\/\/www.apti.cz\/?p=1010"},"modified":"2021-12-09T21:19:53","modified_gmt":"2021-12-09T21:19:53","slug":"vodni-raz-v-potrubi","status":"publish","type":"post","link":"https:\/\/www.apti.cz\/index.php\/2021\/12\/09\/vodni-raz-v-potrubi\/","title":{"rendered":"Vodn\u00ed r\u00e1z v potrub\u00ed"},"content":{"rendered":"\n<p><strong>Ka\u017ed\u00e1 zm\u011bna pr\u016ftoku potrub\u00edm napln\u011bn\u00fdm kapalinou vyvol\u00e1 i zm\u011bnu tlaku v potrub\u00ed. Tak\u00e9 ka\u017ed\u00e1 zm\u011bna tlaku v potrub\u00ed vyvol\u00e1 i zm\u011bnu pr\u016ftok\u016f. Zm\u011bny tlaku a pr\u016ftoku jsou na sebe v\u00e1z\u00e1ny a \u0161\u00ed\u0159\u00ed se potrub\u00edm ve form\u011b vln. Tento jev se naz\u00fdv\u00e1 vodn\u00ed r\u00e1z.<\/strong><\/p>\n\n\n\n<p><strong>Ing. Josef Z\u00e1ruba, CSc.<\/strong><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; V mnoha p\u0159\u00edpadech jsou zm\u011bny tlaku vyvolan\u00e9 vodn\u00edm r\u00e1zem tak mal\u00e9, \u017ee neovlivn\u00ed dimenzov\u00e1n\u00ed potrub\u00ed. V n\u011bkter\u00fdch p\u0159\u00edpadech jsou v\u0161ak pro jeho dimenzov\u00e1n\u00ed rozhoduj\u00edc\u00ed. Nedocen\u011bn\u00ed vlivu vodn\u00edho r\u00e1zu vedlo ji\u017e mnohokr\u00e1t k hav\u00e1rii potrub\u00ed. N\u011bkdy je obt\u00ed\u017en\u00e9 spolehliv\u011b odhadnout, zda je t\u0159eba se v dan\u00e9m p\u0159\u00edpad\u011b vodn\u00edm r\u00e1zem zab\u00fdvat nebo zda je jeho vliv mo\u017eno zanedbat.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; V\u00fdpo\u010det vodn\u00edho r\u00e1zu, zvl\u00e1\u0161t\u011b ve slo\u017eit\u011bj\u0161\u00edch potrubn\u00edch syst\u00e9mech, je n\u00e1ro\u010dn\u00fd a neobejde se bez zjednodu\u0161uj\u00edc\u00edch p\u0159edpoklad\u016f. V\u00fdpo\u010det se prov\u00e1d\u00ed obvykle za p\u0159edpokladu platnosti n\u00e1sleduj\u00edc\u00ed soustavy dvou parci\u00e1ln\u00edch diferenci\u00e1ln\u00edch rovnic:<\/p>\n\n\n\n<p>&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<em>&nbsp;&nbsp;&nbsp;&nbsp; \u2202v&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u03bb\u03f1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u2202p<\/em><br><em>&nbsp;\u03f1 \u2015&nbsp; +&nbsp; \u2015 \u2321v\u2321v&nbsp;&nbsp; +&nbsp;&nbsp; \u2015&nbsp;<\/em>&nbsp;&nbsp;=&nbsp; 0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ( 1 ),<br><em>&nbsp;\u2202t&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2D&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u2202x<\/em><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>&nbsp;&nbsp;\u2202v&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u2202p<\/em><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a<sup>2<\/sup>\u03f1&nbsp;<\/em>&nbsp;\u2015&nbsp;&nbsp; +&nbsp;&nbsp; \u2015&nbsp;&nbsp; =&nbsp; 0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ( 2 ),<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>&nbsp;&nbsp;\u2202x&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u2202t<\/em><\/p>\n\n\n\n<p>kde&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;<em>x<\/em>&nbsp;je d\u00e9lkov\u00e1 sou\u0159adnice potrub\u00ed,<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>t&nbsp;<\/em>je \u010das,<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>v (x,t)<\/em>&nbsp;je pr\u016fm\u011brn\u00e1 rychlost v profilu&nbsp;<em>x<\/em>&nbsp;v \u010dase&nbsp;<em>t<\/em>,<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>p (x,t)&nbsp;<\/em>je tlak profilu&nbsp;<em>x<\/em>&nbsp;v \u010dase<em>&nbsp;t<\/em>,<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>\u03f1&nbsp;<\/em>&nbsp;je hustota kapaliny,<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>\u03bb<\/em>&nbsp;je ztr\u00e1tov\u00fd koeficient,<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>D&nbsp;<\/em>je vnit\u0159n\u00ed pr\u016fm\u011br potrub\u00ed,<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>a<\/em>&nbsp;je rychlost \u0161\u00ed\u0159en\u00ed tlakov\u00e9 vlny potrub\u00edm.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Z \u0159e\u0161en\u00ed soustavy rovnic (1), (2) vypl\u00fdv\u00e1, \u017ee n\u00e1hl\u00e1 zm\u011bna pr\u016fm\u011brn\u00e9 rychlosti&nbsp;<em>\u2206v<\/em>&nbsp;vyvol\u00e1 n\u00e1hlou zm\u011bnu tlaku&nbsp;<em>\u2206p<\/em>&nbsp;ur\u010denou vztahem<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>\u2206p&nbsp; =&nbsp; \u2013 a \u03f1 \u2206v<\/em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ( 3 ).<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Vztah (3) m\u016f\u017ee slou\u017eit k prvn\u00edmu odhadu nejv\u011bt\u0161\u00edho mo\u017en\u00e9ho zv\u00fd\u0161en\u00ed tlaku vyvolan\u00e9ho vodn\u00edm r\u00e1zem. Nejvy\u0161\u0161\u00ed mo\u017en\u00e1 hodnota rychlosti \u0161\u00ed\u0159en\u00ed tlakov\u00e9 vlny&nbsp;<em>a<\/em>&nbsp;je rychlost \u0161\u00ed\u0159en\u00ed zvuku a ta je pro vodu zhruba 1400 m\/s. Hustota vody je zhruba 1000 kg\/m<sup>3<\/sup>. Znam\u00e9nko \u2013 vyjad\u0159uje, \u017ee pokles rychlosti vyvol\u00e1 zv\u00fd\u0161en\u00ed tlaku. Ze vztahu (3) vypl\u00fdv\u00e1, \u017ee sn\u00ed\u017een\u00ed rychlosti proud\u011bn\u00ed vody o 1 m\/s m\u016f\u017ee vyvolat zv\u00fd\u0161en\u00ed tlaku a\u017e o 1,4\u00d710<sup>6&nbsp;<\/sup>Pa to je zhruba 140 m vodn\u00edho sloupce. Ve skute\u010dn\u00fdch p\u0159\u00edpadech b\u00fdv\u00e1 zv\u00fd\u0161en\u00ed tlaku zp\u016fsoben\u00e9 vodn\u00edm r\u00e1zem podstatn\u011b ni\u017e\u0161\u00ed, ale jsou i p\u0159\u00edpady, kdy se zv\u00fd\u0161en\u00ed tlaku t\u011bmto hodnot\u00e1m bl\u00ed\u017e\u00ed nebo je i p\u0159evy\u0161uj\u00ed.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Ve skute\u010dn\u00fdch p\u0159\u00edpadech neb\u00fdv\u00e1 zm\u011bna rychlosti n\u00e1hl\u00e1. Doba, za kterou se rychlost proud\u011bn\u00ed zm\u011bn\u00ed, m\u016f\u017ee v\u00fdrazn\u011b zmen\u0161it zm\u011bny tlaku vyvolan\u00e9 vodn\u00edm r\u00e1zem.&nbsp; Je t\u0159eba porovnat dobu&nbsp;<em>\u2206t,<\/em>&nbsp;za kterou dojde ke zm\u011bn\u011b rychlosti<strong>,<\/strong>&nbsp; s dobou periody r\u00e1zov\u00e9 vlny&nbsp;<em>T<\/em>. V nejjednodu\u0161\u0161\u00edm p\u0159\u00edpad\u011b, pro potrub\u00ed d\u00e9lky&nbsp;<em>l&nbsp;<\/em>konstantn\u00edho pr\u016f\u0159ezu, kter\u00e9 m\u00e1 uz\u00e1v\u011br na konci, je doba periody ur\u010dena vztahem<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>4 l<\/em><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<em>T&nbsp;<\/em>&nbsp;=&nbsp;&nbsp; \u2015&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (4).<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>a<\/em><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Za dobu periody dob\u011bhne r\u00e1zov\u00e1 vlna dvakr\u00e1t od uz\u00e1v\u011bru k za\u010d\u00e1tku potrub\u00ed a zp\u011bt. Pokud uz\u00e1v\u011br uzav\u0159e potrub\u00ed b\u011bhem doby krat\u0161\u00ed ne\u017e&nbsp;<em>T<\/em>\/2, pak se jedn\u00e1 o tak zvan\u00fd tot\u00e1ln\u00ed r\u00e1z a maxim\u00e1ln\u00ed zv\u00fd\u0161en\u00ed tlaku je ur\u010deno vztahem (3). Prodlu\u017eov\u00e1n\u00edm doby uzav\u00edr\u00e1n\u00ed potrub\u00ed se m\u016f\u017ee zm\u011bna tlaku vyvolan\u00e1 vodn\u00edm r\u00e1zem v\u00fdrazn\u011b zmen\u0161it. Z\u00e1le\u017e\u00ed v\u0161ak i na pr\u016fb\u011bhu zav\u00edr\u00e1n\u00ed potrub\u00ed. Mnoho uz\u00e1v\u011br\u016f je konstruov\u00e1no tak, \u017ee v po\u010d\u00e1te\u010dn\u00ed dob\u011b uzav\u00edr\u00e1n\u00ed se rychlost proud\u011bn\u00ed m\u011bn\u00ed m\u00e1lo a k hlavn\u00ed zm\u011bn\u011b doch\u00e1z\u00ed a\u017e na konci uzav\u00edr\u00e1n\u00ed potrub\u00ed. Z hlediska vodn\u00edho r\u00e1zu je podstatn\u00e9, o kolik se sn\u00ed\u017e\u00ed rychlost proud\u011bn\u00ed&nbsp;<em>v<\/em>&nbsp;b\u011bhem poloviny periody&nbsp;<em>T<\/em>.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; V pr\u016fb\u011bhu vodn\u00edho r\u00e1zu se tlak v potrub\u00ed nejen zvy\u0161uje, ale i sni\u017euje. M\u016f\u017ee dos\u00e1hnout i tlaku ni\u017e\u0161\u00edho ne\u017e je tlak atmosferick\u00fd. To je pro n\u011bkter\u00e1 potrub\u00ed nebezpe\u010dn\u00e9. St\u00e1v\u00e1 se i to, \u017ee tlak v potrub\u00ed poklesne na absolutn\u00ed nulu. Proto\u017ee dal\u0161\u00ed pokles tlaku nen\u00ed mo\u017en\u00fd, vodn\u00ed sloupec se p\u0159etrhne a v potrub\u00ed se vytvo\u0159\u00ed prostor vypln\u011bn\u00fd jen vodn\u00edmi parami. Ten se postupn\u011b zv\u011bt\u0161uje a pak op\u011bt zmen\u0161uje a\u017e zanikne. Z\u00e1nik m\u016f\u017ee zp\u016fsobit rychl\u00e9 zv\u00fd\u0161en\u00ed tlaku i p\u0159i pomal\u00e9m uzav\u00edr\u00e1n\u00ed potrub\u00ed.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Pro v\u00fdpo\u010det pr\u016fb\u011bhu tlaku a pr\u016ftoku v potrub\u00ed b\u011bhem vodn\u00edho r\u00e1zu bylo vypracov\u00e1no v\u00edce postup\u016f. Ru\u010dn\u00ed v\u00fdpo\u010dty, a\u0165 ji\u017e grafick\u00e9 nebo numerick\u00e9, jsou prakticky pou\u017eiteln\u00e9 jen pro nejjednodu\u0161\u0161\u00ed p\u0159\u00edpady. V sou\u010dasn\u00e9 dob\u011b se pr\u016fb\u011bh vodn\u00edho r\u00e1zu po\u010d\u00edt\u00e1 zpravidla numericky, na po\u010d\u00edta\u010d\u00edch, \u0159e\u0161en\u00edm soustavy rovnic (1), (2). Proud\u011bn\u00ed v potrub\u00ed v\u00fdrazn\u011b ovliv\u0148uj\u00ed i r\u016fzn\u00e1 za\u0159\u00edzen\u00ed, kter\u00e1 jsou k n\u011bmu p\u0159ipojena.&nbsp; Pro v\u00fdpo\u010det mus\u00ed b\u00fdt potrub\u00ed schematizov\u00e1no. \u010casto nejsou dostate\u010dn\u011b p\u0159esn\u011b zn\u00e1m\u00e9 charakteristiky p\u0159ipojen\u00fdch za\u0159\u00edzen\u00ed ani hodnoty konstant, kter\u00e9 se v rovnic\u00edch vyskytuj\u00ed. To sni\u017euje p\u0159esnost v\u00fdpo\u010dt\u016f. I nevhodn\u00fd zp\u016fsob schematizace m\u016f\u017ee zp\u016fsobit velk\u00e9 nep\u0159esnosti v\u00fdsledk\u016f v\u00fdpo\u010dt\u016f.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; P\u0159i \u0159e\u0161en\u00ed slo\u017eit\u011bj\u0161\u00edch syst\u00e9m\u016f potrub\u00ed je t\u0159eba zadat velk\u00e9 mno\u017estv\u00ed vstupn\u00edch dat. V zad\u00e1n\u00ed se snadno ud\u011blaj\u00ed chyby a n\u011bkdy je obt\u00ed\u017en\u00e9 je odhalit.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; V\u00fdrazn\u00e9 sn\u00ed\u017een\u00ed rychlosti \u0161\u00ed\u0159en\u00ed tlakov\u00e9 vlny potrub\u00edm, a tedy i sn\u00ed\u017een\u00ed zm\u011bn tlaku zp\u016fsoben\u00e9 vodn\u00e9m r\u00e1zem, m\u016f\u017ee zp\u016fsobit pru\u017enost potrub\u00ed nebo t\u0159eba p\u0159\u00edtomnost bublinek plynu v kapalin\u011b. Inkrustace a usazeniny pevn\u00fdch l\u00e1tek v potrub\u00ed mohou zm\u011bny tlaku naopak zv\u00fd\u0161it. Tlakov\u00e9 ztr\u00e1ty, vyj\u00e1d\u0159en\u00e9 koeficientem&nbsp;<em>\u03bb<\/em>, v\u00fdrazn\u011b sni\u017euj\u00ed extr\u00e9mn\u00ed hodnoty tlaku hlavn\u011b u dlouh\u00fdch potrub\u00ed.&nbsp;<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Jak postupovat p\u0159i n\u00e1vrhu potrub\u00ed, aby nebylo p\u0159i provozu ohro\u017eeno vodn\u00edm r\u00e1zem ? V mnoha p\u0159\u00edpadech se jedn\u00e1 o cel\u00fd syst\u00e9m potrub\u00ed, na kter\u00fd jsou p\u0159ipojena r\u016fzn\u00e1 za\u0159\u00edzen\u00ed, kter\u00e1 mohou vodn\u00ed r\u00e1z zp\u016fsobit nebo ovlivnit. N\u011bkdy nejsou zn\u00e1m\u00e9 ani v\u0161echny mo\u017en\u00e9 manipulace s t\u011bmito za\u0159\u00edzen\u00edmi. V syst\u00e9mu m\u016f\u017ee proudit i jin\u00e1 kapalina ne\u017e voda. Jako prvn\u00ed orienta\u010dn\u00ed krok je mo\u017eno doporu\u010dit v\u00fdpo\u010det hodnoty&nbsp;<em>\u2206p<\/em>&nbsp;podle vztahu (3). Pokud se syst\u00e9m skl\u00e1d\u00e1 z \u00fasek\u016f potrub\u00ed r\u016fzn\u00e9ho&nbsp; pr\u016fm\u011bru nebo r\u016fzn\u00e9 konstrukce, pak m\u016f\u017ee vyj\u00edt pro ka\u017ed\u00fd \u00fasek jin\u00e1 hodnota&nbsp;<em>\u2206p<\/em>.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Pokud hodnota&nbsp;&nbsp;<em>\u2206p<\/em>&nbsp;vych\u00e1z\u00ed p\u0159\u00edli\u0161 vysok\u00e1, je vhodn\u00e9 zjistit, &nbsp;k jak\u00e9 nejv\u011bt\u0161\u00ed zm\u011bn\u011b rychlosti&nbsp;<em>\u2206v&nbsp;<\/em>dojde v \u010dasov\u00e9 intervalu&nbsp;<em>T<\/em>\/2. Takovou zm\u011bnu rychlosti je pak mo\u017eno dosadit do vztahu (3) pro odhad maxim\u00e1ln\u00edch zm\u011bn tlaku. Ten pak m\u016f\u017ee b\u00fdt podstatn\u011b ni\u017e\u0161\u00ed.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Kdy\u017e p\u0159edch\u00e1zej\u00edc\u00ed \u00favahy vedou k nep\u0159ijateln\u00fdm hodnot\u00e1m zm\u011bn tlaku vyvolan\u00fdch vodn\u00edm r\u00e1zem, je pro dal\u0161\u00ed up\u0159esn\u011bn\u00ed nutn\u00fd v\u00fdpo\u010det vodn\u00edho r\u00e1zu. Probl\u00e9m je v tom, \u017ee&nbsp; v\u00fdpo\u010det vy\u017eaduje hlub\u0161\u00ed znalosti vodn\u00edho r\u00e1zu a vhodn\u00fd po\u010d\u00edta\u010dov\u00fd program. Proto se \u010dasto v\u00fdpo\u010det neprov\u00e1d\u00ed a vych\u00e1z\u00ed se ze zku\u0161enost\u00ed s podobn\u00fdmi, ji\u017e realizovan\u00fdmi syst\u00e9my, kter\u00e9 dob\u0159e funguj\u00ed. Protir\u00e1zov\u00e1 opat\u0159en\u00ed se d\u011blaj\u00ed obdobn\u00e1. N\u011bkdy se navrhuj\u00ed protir\u00e1zov\u00e1 opat\u0159en\u00ed ani\u017e by bylo jist\u00e9, \u017ee jsou skute\u010dn\u011b nutn\u00e1. Je to n\u011bkdy v\u00fdhodn\u011bj\u0161\u00ed ne\u017e prov\u00e1d\u011bt v\u00fdpo\u010det. Ve slo\u017eit\u011bj\u0161\u00edch p\u0159\u00edpadech nedok\u00e1\u017ee toti\u017e ani v\u00fdpo\u010det v\u017edy postihnout v\u0161echny mo\u017en\u00e9 p\u0159\u00ed\u010diny vodn\u00edho r\u00e1zu s dostate\u010dnou p\u0159esnost\u00ed. V n\u00e1ro\u010dn\u011bj\u0161\u00edch p\u0159\u00edpadech je proto vhodn\u00e9 postupovat p\u0159i zah\u00e1jen\u00ed provozu syst\u00e9mu opatrn\u011b a zm\u011bny tlaku m\u011b\u0159it. Manipulace je t\u0159eba prov\u00e1d\u011bt tak, aby zm\u011bny tlaku byly z po\u010d\u00e1tku co nejmen\u0161\u00ed a postupn\u011b se zv\u011bt\u0161ovaly.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Protir\u00e1zov\u00fdch opat\u0159en\u00ed bylo navr\u017eeno mnoho druh\u016f. Ka\u017ed\u00e9 z nich m\u00e1 sv\u00e9 p\u0159ednosti a nedostatky. Jako \u010dasto pou\u017e\u00edvan\u00e9 je mo\u017eno jmenovat nap\u0159\u00edklad \u00fapravu pr\u016fb\u011bhu manipulace, kter\u00e1 vyvol\u00e1v\u00e1 vodn\u00ed r\u00e1z, poji\u0161\u0165ovac\u00ed ventil, zavzdu\u0161\u0148ovac\u00ed ventil,&nbsp; vzdu\u0161n\u00edk, vyrovn\u00e1vac\u00ed komoru nebo p\u0159epad. Ka\u017ed\u00e9 z nich se hod\u00ed pro jin\u00e9 p\u0159\u00edpady. Detailn\u00ed v\u00fdpo\u010det vodn\u00edho r\u00e1zu se zpravidla prov\u00e1d\u00ed jen pro velk\u00e1 vodn\u00ed d\u00edla, kde by jeho n\u00e1sledky mohly zp\u016fsobit v\u00e1\u017en\u00e9 \u0161kody. U men\u0161\u00edch potrubn\u00edch syst\u00e9m\u016f je b\u011b\u017en\u00e9 protir\u00e1zov\u00e1 opat\u0159en\u00ed navrhnout podle odhadu a v p\u0159\u00edpad\u011b nutnosti je doplnit nebo upravit a\u017e dodate\u010dn\u011b, podle v\u00fdsledk\u016f m\u011b\u0159en\u00ed na hotov\u00e9m d\u00edle.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Program\u016f pro v\u00fdpo\u010det vodn\u00edho r\u00e1z\u016f existuje mnoho. Jejich vyu\u017eit\u00ed v\u0161ak nar\u00e1\u017e\u00ed na obt\u00ed\u017ee.&nbsp; Asi nejjednodu\u0161\u0161\u00ed je si v\u00fdpo\u010det vodn\u00edho r\u00e1zu zajistit u n\u011bkoho, kdo se takov\u00fdmi v\u00fdpo\u010dty zab\u00fdv\u00e1. Je to pak ot\u00e1zka n\u00e1klad\u016f, odborn\u00fdch znalosti toho, kdo v\u00fdpo\u010det prov\u00e1d\u00ed, a vstupn\u00edch dat. Bez spr\u00e1vn\u00fdch vstupn\u00edch dat nen\u00ed mo\u017eno prov\u00e9st spr\u00e1vn\u00fd v\u00fdpo\u010det. Pot\u00ed\u017ee b\u00fdvaj\u00ed t\u0159eba s charakteristikami za\u0159\u00edzen\u00ed, kter\u00e1 jsou sou\u010d\u00e1st\u00ed syst\u00e9mu. N\u011bkdy je nem\u00edv\u00e1 v pot\u0159ebn\u00e9m rozsahu ani v\u00fdrobce za\u0159\u00edzen\u00ed. Za\u0159\u00edzen\u00ed se v pr\u016fb\u011bhu r\u00e1zu n\u011bkdy dost\u00e1vaj\u00ed do stav\u016f, kter\u00e9 se jinak b\u011b\u017en\u011b nevyskytuj\u00ed. Proto se charakteristiky pro tyto stavy \u010dasto ani neprom\u011b\u0159uj\u00ed. Charakteristiky je pak nutno bu\u010f dodate\u010dn\u011b dom\u011b\u0159it nebo odhadnout.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Dal\u0161\u00ed mo\u017enost\u00ed je v\u00fdpo\u010det vodn\u00edho r\u00e1zu prov\u00e9st vlastn\u00edmi silami. V dne\u0161n\u00ed dob\u011b asi nep\u0159ich\u00e1z\u00ed v \u00favahu jin\u00e9 ne\u017e numerick\u00e9 \u0159e\u0161en\u00ed na po\u010d\u00edta\u010di. Program je mo\u017eno si vyrobit nebo sehnat ji\u017e hotov\u00fd. Sestavovat vlastn\u00ed program pro jednor\u00e1zov\u00e9 vyu\u017eit\u00ed pro slo\u017eit\u011bj\u0161\u00ed syst\u00e9m potrub\u00ed by bylo asi p\u0159\u00edli\u0161 n\u00e1ro\u010dn\u00e9. Je mo\u017en\u00e9 pou\u017e\u00edt a p\u0159\u00edpadn\u011b upravit n\u011bjak\u00fd hotov\u00fd jednoduch\u00fd program. To by se asi neobe\u0161lo bez spolupr\u00e1ce s jeho autorem. Nakonec by bylo asi v\u00fdhodn\u011bj\u0161\u00ed u autora programu v\u00fdpo\u010det p\u0159\u00edmo objednat.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Je tak\u00e9 mo\u017en\u00e9 si zajistit slo\u017eit\u011bj\u0161\u00ed, obecn\u011bj\u0161\u00ed program, sezn\u00e1mit se podrobn\u011bji s teorii vodn\u00edho r\u00e1zu a v\u00fdpo\u010dty prov\u00e1d\u011bt vlastn\u00edmi silami. To m\u016f\u017ee b\u00fdt vhodn\u00e9 v p\u0159\u00edpad\u011b, \u017ee se p\u0159edpokl\u00e1d\u00e1 v\u011bt\u0161\u00ed po\u010det v\u00fdpo\u010dt\u016f vodn\u00edho r\u00e1zu pro r\u016fzn\u00e9 potrubn\u00ed syst\u00e9my. Ceny takov\u00fdch program\u016f b\u00fdvaj\u00ed vysok\u00e9 a ne v\u017edy k nim existuj\u00ed podrobn\u00e9 n\u00e1vody. Nen\u00ed ani z\u00e1ruka, \u017ee v programu nejsou chyby. Neb\u00fdv\u00e1 k dispozici zdrojov\u00fd k\u00f3d, kter\u00fd by umo\u017enil chyby opravit. Jednou z mo\u017enost\u00ed&nbsp; je vyu\u017e\u00edt program WTHM.EXE. Jedn\u00e1 se o dosti obecn\u00fd program pro \u0159e\u0161en\u00ed vodn\u00edho r\u00e1zu v syst\u00e9mech potrub\u00ed. Jeho podrobn\u00fd popis a n\u00e1vod k pou\u017eit\u00ed je v publikaci&nbsp; Josef Z\u00e1ruba: Water Hammer in Pipe-line Systems, Academia, Prague 1993. Program, v\u010detn\u011b zdrojov\u00fdch k\u00f3d\u016f, je zdarma. Program i publikace jsou k dispozici v n\u011bkter\u00fdch knihovn\u00e1ch \u010cesk\u00e9 republiky.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Vodn\u00ed r\u00e1z je mo\u017eno vyu\u017e\u00edt pro m\u011b\u0159en\u00ed pr\u016ftok\u016f a charakteristik r\u016fzn\u00fdch za\u0159\u00edzen\u00ed na hotov\u00fdch d\u00edlech. Princip spo\u010d\u00edv\u00e1 v tom, \u017ee se m\u011b\u0159\u00ed pr\u016fb\u011bh tlaku v potrub\u00ed p\u0159i jeho uzav\u00edr\u00e1n\u00ed a z nam\u011b\u0159en\u00fdch hodnot se po\u010d\u00edtaj\u00ed pr\u016ftoky. M\u011b\u0159en\u00ed tlak\u016f v potrub\u00ed je mnohem jednodu\u0161\u00ed ne\u017e m\u011b\u0159en\u00ed pr\u016ftok\u016f, zvl\u00e1\u0161t\u011b u potrub\u00ed v\u011bt\u0161\u00edch pr\u016fm\u011br\u016f. Pokud se sou\u010dasn\u011b m\u011b\u0159\u00ed i parametry ur\u010duj\u00edc\u00ed stav p\u0159ipojen\u00fdch za\u0159\u00edzen\u00ed, daj\u00ed se ur\u010dit i jejich charakteristiky. K v\u00fdpo\u010dt\u016fm je mo\u017eno pou\u017e\u00edt v\u00fd\u0161e uveden\u00fd program a publikaci, ve kter\u00e9 jsou pops\u00e1ny postupy v\u00fdpo\u010dt\u016f.<\/p>\n\n\n\n<p><a href=\"https:\/\/www.elsevier.com\/books\/water-hammer-in-pipe-line-systems\/zaruba\/978-0-444-98722-8\">Water Hammer in Pipe-line Systems, Academia<\/a><\/p>\n\n\n\n<p>Ilustra\u010dn\u00ed foto:&nbsp;<a href=\"https:\/\/unsplash.com\/@dvnil?utm_source=unsplash&amp;utm_medium=referral&amp;utm_content=creditCopyText\">Danil Sorokin<\/a>,&nbsp;<a href=\"https:\/\/unsplash.com\/s\/photos\/pipeline?utm_source=unsplash&amp;utm_medium=referral&amp;utm_content=creditCopyText\">Unsplash<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ka\u017ed\u00e1 zm\u011bna pr\u016ftoku potrub\u00edm napln\u011bn\u00fdm kapalinou vyvol\u00e1 i zm\u011bnu tlaku v potrub\u00ed. Tak\u00e9 ka\u017ed\u00e1 zm\u011bna tlaku v potrub\u00ed vyvol\u00e1 i zm\u011bnu pr\u016ftok\u016f. Zm\u011bny tlaku a pr\u016ftoku jsou na sebe v\u00e1z\u00e1ny&#8230;<\/p>\n","protected":false},"author":1,"featured_media":1011,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[6,4,9,8,11],"tags":[],"class_list":["post-1010","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-potrubi","category-rizeni-rizik","category-strojni-zarizeni","category-tlakova-zarizeni","category-vzdelavani"],"jetpack_featured_media_url":"https:\/\/www.apti.cz\/wp-content\/uploads\/2021\/12\/Header_IND_598_prumyslove_potrubi.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.apti.cz\/index.php\/wp-json\/wp\/v2\/posts\/1010","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.apti.cz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.apti.cz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.apti.cz\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.apti.cz\/index.php\/wp-json\/wp\/v2\/comments?post=1010"}],"version-history":[{"count":1,"href":"https:\/\/www.apti.cz\/index.php\/wp-json\/wp\/v2\/posts\/1010\/revisions"}],"predecessor-version":[{"id":1012,"href":"https:\/\/www.apti.cz\/index.php\/wp-json\/wp\/v2\/posts\/1010\/revisions\/1012"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.apti.cz\/index.php\/wp-json\/wp\/v2\/media\/1011"}],"wp:attachment":[{"href":"https:\/\/www.apti.cz\/index.php\/wp-json\/wp\/v2\/media?parent=1010"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.apti.cz\/index.php\/wp-json\/wp\/v2\/categories?post=1010"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.apti.cz\/index.php\/wp-json\/wp\/v2\/tags?post=1010"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}