{"id":8264,"date":"2020-06-19T10:35:01","date_gmt":"2020-06-19T09:35:01","guid":{"rendered":"https:\/\/www.vtei.cz\/?p=8264"},"modified":"2024-07-17T10:41:20","modified_gmt":"2024-07-17T09:41:20","slug":"research-of-flow-through-bridge-structure-with-free-water-surface-and-submerged-inlet","status":"publish","type":"post","link":"https:\/\/www.vtei.cz\/en\/2020\/06\/research-of-flow-through-bridge-structure-with-free-water-surface-and-submerged-inlet\/","title":{"rendered":"Research of flow through bridge structure with free water surface and submerged inlet"},"content":{"rendered":"

<\/i> This article is available in Czech only. For translation or more information on this topic, please contact author.<\/h4>\n

 <\/p>\n

Souhrn<\/h2>\n

P\u0159\u00edsp\u011bvek prezentuje v\u00fdsledky hydraulick\u00e9ho v\u00fdzkumu proud\u011bn\u00ed mostn\u00edm objektem s\u00a0volnou hladinou a\u00a0zatopen\u00fdm vtokem na fyzik\u00e1ln\u00edm modelu. Srovn\u00e1v\u00e1 dosavadn\u00ed poznatky s\u00a0nam\u011b\u0159en\u00fdmi daty a\u00a0diskutuje rozd\u00edly. P\u0159\u00edsp\u011bvek obsahuje anal\u00fdzu tvorby z\u00fa\u017een\u00e9 hloubky za vtokem do mostn\u00edho otvoru. Rovn\u011b\u017e zpracov\u00e1v\u00e1 z\u00e1vislost pr\u016ftokov\u00e9ho sou\u010dinitele na \u0159ad\u011b faktor\u016f, je\u017e je prezentov\u00e1na pomoc\u00ed graf\u016f a\u00a0rovnic. Z\u00e1v\u011br pr\u00e1ce d\u00e1v\u00e1 doporu\u010den\u00ed pro volbu pr\u016ftokov\u00e9ho sou\u010dinitele p\u0159i v\u00fdpo\u010dtech v\u00a0softwaru Hec-Ras.<\/p>\n

\u00davod<\/h2>\n

Hydraulick\u00fd v\u00fdzkum proud\u011bn\u00ed mostn\u00edm objektem pro p\u0159\u00edpad zatopen\u00e9ho vtoku a\u00a0voln\u00e9ho v\u00fdtoku byl \u0159e\u0161en na Fakult\u011b stavebn\u00ed \u010cVUT v\u00a0Praze v\u00a0letech 2017 a\u017e 2019 v\u00a0r\u00e1mci projektu studentsk\u00e9 grantov\u00e9 sout\u011b\u017ee SGS17\/171\/OHK1\/3T\/11, jeho\u017e hlavn\u00ed \u0159e\u0161itelkou byla Ing. Petra Pode\u0161vov\u00e1. Tento \u010dl\u00e1nek byl naps\u00e1n za podpory tohoto projektu.<\/p>\n

Z\u00e1kladem \u0159e\u0161en\u00ed byl fyzik\u00e1ln\u00ed v\u00fdzkum, p\u0159i kter\u00e9m byl vyu\u017eit st\u00e1vaj\u00edc\u00ed sklen\u011bn\u00fd \u017elab v\u00a0hydraulick\u00e9 laborato\u0159i fakulty. Vzhledem k\u00a0rekonstrukci haly v\u00a0posledn\u00edm roce \u0159e\u0161en\u00ed byl v\u00fdzkum dopln\u011bn i\u00a0o\u00a0simulace na 3D matematick\u00e9m modelu.<\/p>\n

Souhrn dosavadn\u00edch poznatk\u016f<\/h2>\n

V\u00fdtok pod stavidlem<\/h3>\n

Proud\u011bn\u00ed mostn\u00edm otvorem se zatopen\u00fdm vtokem a\u00a0voln\u00fdm v\u00fdtokem je bl\u00edzk\u00e9 v\u00fdtoku pod stavidlem. Charakteristick\u00fd pod\u00e9ln\u00fd profil hladiny pro p\u0159\u00edpad v\u00fdtoku pod stavidlem, kdy proud\u011bn\u00ed nen\u00ed ovlivn\u011bno doln\u00ed vodou, je zn\u00e1zorn\u011bn na obr. 1<\/em>.<\/p>\n\"\"<\/a>\n

Obr. 1. Pod\u00e9ln\u00fd profil hladiny p\u0159i v\u00fdtoku pod stavidlem neovlivn\u011bn\u00fd doln\u00ed vodou
\nFig. 1. Water level profile at sluice gate flow not affected by the downstream flow<\/h6>\n

P\u0159i nezatopen\u00ed doln\u00ed vodou se vytv\u00e1\u0159\u00ed z\u00fa\u017een\u00e1 hloubka y<\/em>c<\/sub> \u2248 0,6a<\/em>. Bernoulliho rovnice pro dan\u00fd p\u0159\u00edpad je:<\/p>\n\"\"<\/a>\n\n\n\n\n\n\n\n\n\n\n
kde<\/td>\nEh<\/sub><\/em> [m]<\/td>\nje<\/td>\nenergetick\u00e1 v\u00fd\u0161ka p\u0159ed vtokem do objektu,<\/td>\n<\/tr>\n
<\/td>\n y<\/em>h<\/sub> [m]<\/td>\n<\/td>\nhloubka p\u0159ed vtokem do objektu,<\/td>\n<\/tr>\n
<\/td>\nv<\/em>h<\/sub> [m\u00b7s-1<\/sup>]<\/td>\n<\/td>\npr\u016f\u0159ezov\u00e1 rychlost proud\u011bn\u00ed p\u0159ed vtokem do objektu,<\/td>\n<\/tr>\n
<\/td>\ny<\/em>c<\/sub> [m]<\/td>\n<\/td>\nz\u00fa\u017een\u00e1 hloubka za v\u00fdtokov\u00fdm profilem,<\/td>\n<\/tr>\n
<\/td>\nv<\/em>c<\/sub> [m\u00b7s-1<\/sup>]<\/td>\n<\/td>\npr\u016f\u0159ezov\u00e1 rychlost v\u00a0profilu z\u00fa\u017een\u00e9 hloubky,<\/td>\n<\/tr>\n
<\/td>\na\u00a0<\/em>[-]<\/td>\n<\/td>\nCoriolisovo \u010d\u00edslo,<\/td>\n<\/tr>\n
<\/td>\n \u03be<\/em>Z<\/sub> [-]<\/td>\n<\/td>\nsou\u010dinitel m\u00edstn\u00ed ztr\u00e1ty z\u00fa\u017een\u00edm proudu,<\/td>\n<\/tr>\n
<\/td>\n\u03c6 <\/em>[-]<\/td>\n<\/td>\nrychlostn\u00ed sou\u010dinitel.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

P\u0159i uva\u017eov\u00e1n\u00ed:<\/p>\n\"\"<\/a>\n\n\n\n\n
kde<\/td>\na<\/em>\u00a0[m]<\/td>\nje<\/td>\nv\u00fd\u0161ka otvoru,<\/td>\n<\/tr>\n
<\/td>\n\u03b5<\/em>v<\/sub> [-]<\/td>\n<\/td>\nsou\u010dinitel z\u00fa\u017een\u00ed,<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

po dosazen\u00ed rovnice spojitosti do rovnice\u00a0(1) a\u00a0po zaveden\u00ed v\u00fdtokov\u00e9ho sou\u010dinitele dostaneme pro pr\u016ftok:<\/p>\n\"\"<\/a>\n\n\n\n\n
kde<\/td>\nb<\/em> [m]<\/td>\nje<\/td>\n\u0161\u00ed\u0159ka otvoru,<\/td>\n<\/tr>\n
kde<\/td>\n\u03bc<\/em>v<\/sub> [-]<\/td>\n<\/td>\nv\u00fdtokov\u00fd sou\u010dinitel.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

B\u011b\u017en\u011b publikovan\u00e9 z\u00e1vislosti uveden\u00fdch sou\u010dinitel\u016f na pom\u011bru y<\/em>h<\/sub>\/a<\/em>\u00a0jsou vykresleny na obr. 2<\/em>.<\/p>\n\"\"<\/a>\n

Obr. 2. Z\u00e1vislost sou\u010dinitel\u016f \u03b5<\/em>v<\/sub>, \u03bc<\/em>v<\/sub> a\u00a0\u03c6 <\/em>na pom\u011bru y<\/em>h<\/sub>\/a<\/em>
\nFig. 2. Dependence of coefficients \u03b5<\/em>v<\/sub>, \u03bc<\/em>v<\/sub> and \u03c6<\/em> on the ratio y<\/em>h<\/sub>\/a<\/em><\/h6>\n

V\u00fdpo\u010det proud\u011bn\u00ed mostn\u00edm objektem se zatopen\u00fdm vtokem a\u00a0voln\u00fdm v\u00fdtokem<\/h3>\n

Obdobn\u00e9 sch\u00e9ma a v\u00fdpo\u010dtov\u00fd postup jako pro p\u0159\u00edpad v\u00fdtoku pod stavidlem (rovnice (3)) bylo pro p\u0159\u00edpad v\u00fdpo\u010dtu proud\u011bn\u00ed mostn\u00edm objektem se zatopen\u00fdm vtokem a voln\u00fdm v\u00fdtokem publikov\u00e1no Bradleym ve zpr\u00e1v\u011b FHWA [1], z\u00fa\u017een\u00e1 hloubka y<\/em>c<\/sub> je v\u0161ak uva\u017eov\u00e1na jako polovina v\u00fd\u0161ky mostn\u00edho otvoru H<\/em>m<\/sub>\/2. Pod\u00e9ln\u00fd profil pro tento p\u0159\u00edpad je vykreslen na obr. 3<\/em>. Rovnice pro v\u00fdpo\u010det pr\u016ftoku m\u00e1 tvar:<\/p>\n\"\"<\/a>\n\n\n\n\n\n\n
kde<\/td>\nQ <\/em>[m3<\/sup>\u00b7s-1<\/sup>]<\/td>\nje<\/td>\npr\u016ftok,<\/td>\n<\/tr>\n
<\/td>\nC<\/em>D<\/sub> [-]<\/td>\n<\/td>\npr\u016ftokov\u00fd sou\u010dinitel,<\/td>\n<\/tr>\n
<\/td>\n H<\/em>m<\/sub> [m]<\/td>\n<\/td>\nsv\u011btl\u00e1 v\u00fd\u0161ka mostn\u00edho otvoru,<\/td>\n<\/tr>\n
<\/td>\n B<\/em>m<\/sub> [m]<\/td>\n<\/td>\nsv\u011btl\u00e1 \u0161\u00ed\u0159ka mostn\u00edho otvoru (bez pil\u00ed\u0159\u016f).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\"\"<\/a>\n

Obr. 3. Pod\u00e9ln\u00fd profil hladiny p\u0159i proud\u011bn\u00ed mostn\u00edm objektem se zatopen\u00fdm vtokem a\u00a0voln\u00fdm v\u00fdtokem p\u0159i uva\u017eov\u00e1n\u00ed y<\/em>c<\/sub> = H<\/em>m<\/sub>\/2
\nFig. 3. Water level profile at bridge with free and submerged inlet when y<\/em>c<\/sub> = H<\/em>m<\/sub>\/2<\/em><\/h6>\n

V\u00a0t\u00e9to publikaci je uveden graf z\u00e1vislosti pr\u016ftokov\u00e9ho sou\u010dinitele C<\/em>D<\/sub> na parametru y<\/em>h<\/sub>\/H<\/em>m<\/sub>, respektive na y<\/em>h<\/sub>\/y<\/em>d<\/sub>, kter\u00fd je p\u0159ilo\u017een na obr. 4<\/em>. Zde y<\/em>d<\/sub> zna\u010d\u00ed hloubku doln\u00ed vody. Pr\u016fb\u011bh z\u00e1vislosti ukazuje, \u017ee proud\u011bn\u00ed mostn\u00edm objektem se zatopen\u00fdm vtokem a\u00a0voln\u00fdm v\u00fdtokem pro hodnoty y<\/em>h<\/sub>\/H<\/em>m<\/sub> < 1,05 nemus\u00ed b\u00fdt stabiln\u00ed, hodnota pr\u016ftokov\u00e9ho sou\u010dinitele se v\u00a0t\u00e9to oblasti pohybuje kolem hodnoty\u00a00,3, s\u00a0n\u00e1r\u016fstem velikosti pom\u011br\u016f se postupn\u011b zvy\u0161uje a\u017e k\u00a0hodnot\u011b 0,5.<\/p>\n\"\"<\/a>\n

Obr. 4. Z\u00e1vislost pr\u016ftokov\u00e9ho sou\u010dinitele C<\/em>D<\/sub> na pom\u011bru y<\/em>h<\/sub>\/H<\/em>m<\/sub> a\u00a0y<\/em>h<\/sub>\/y<\/em>d<\/sub> podle Bradleyho [1]
\nFig. 4. Dependence of discharge coefficient C<\/em>D<\/sub> on ratio y<\/em>h<\/sub>\/H<\/em>m<\/sub> and y<\/em>h<\/sub>\/y<\/em>d<\/sub> according to Bradley [1]<\/h6>\n

Rovnice (4) pro v\u00fdpo\u010det proud\u011bn\u00ed mostn\u00edm objektem se zatopen\u00fdm vtokem a\u00a0voln\u00fdm v\u00fdtokem byla d\u00e1le publikov\u00e1na v\u00a0dal\u0161\u00ed publikaci FHWA [2], graf pro stanoven\u00ed C<\/em>D<\/sub> ji\u017e v\u0161ak obsahuje jen z\u00e1vislost na y<\/em>h<\/sub>\/H<\/em>m<\/sub> s\u00a0\u00fapravou v\u00a0oblasti hodnot y<\/em>h<\/sub>\/H<\/em>m<\/sub> < 1,08, graf je uveden na obr. 5<\/em>.<\/p>\n\"\"<\/a>\n

Obr. 5. Z\u00e1vislost pr\u016ftokov\u00e9ho sou\u010dinitele C<\/em>D<\/sub> na pom\u011bru y<\/em>h<\/sub>\/H<\/em>m<\/sub> podle Zevenbergena [2]
\nFig. 5. Dependence of discharge coefficient C<\/em>D<\/sub> on ratio y<\/em>h<\/sub>\/H<\/em>m<\/sub> according to Zevenbergen [2]<\/h6>\n

Rovnici (4) uv\u00e1d\u00ed bez grafu ke stanoven\u00ed C<\/em>D<\/sub> ve sv\u00e9 monografii Hamill [3], postup uveden\u00fd v\u00a0publikaci [2] pak pou\u017e\u00edv\u00e1 beze zm\u011bny u\u00a0n\u00e1s hojn\u011b vyu\u017e\u00edvan\u00fd software Hec-Ras [4].<\/p>\n

V\u00fdpo\u010det tlakov\u00e9ho proud\u011bn\u00ed mostn\u00edm objektem<\/h3>\n

Problematikou proud\u011bn\u00ed mostn\u00edm otvorem p\u0159i tlakov\u00e9m proud\u011bn\u00ed se v\u00a0r\u00e1mci sv\u00e9ho v\u00fdzkumu velmi podrobn\u011b zab\u00fdval Picek [5]. Typick\u00fd pod\u00e9ln\u00fd profil hladiny pro tento sc\u00e9n\u00e1\u0159 je zobrazen na obr. 6<\/em>.<\/p>\n\"\"<\/a>\n

Obr. 6. Sch\u00e9ma pod\u00e9ln\u00e9ho profilu pro p\u0159\u00edpad tlakov\u00e9ho proud\u011bn\u00ed mostn\u00edm objektem
\nFig. 6. Water level profile at bridge with pressurized flow<\/h6>\n

P\u0159i zanedb\u00e1n\u00ed ztr\u00e1t t\u0159en\u00edm je mo\u017en\u00e9 p\u0159i uva\u017eov\u00e1n\u00ed ztr\u00e1t z\u00fa\u017een\u00edm a\u00a0n\u00e1sleduj\u00edc\u00edm roz\u0161\u00ed\u0159en\u00edm proudu napsat tuto Bernoulliho rovnici:<\/p>\n\"\"<\/a>\n\n\n\n\n\n\n
kde<\/td>\ny<\/em>d<\/sub> [m]<\/td>\nje<\/td>\nhloubka za v\u00fdtokem z\u00a0mostn\u00edho objektu,<\/td>\n<\/tr>\n
<\/td>\nv<\/em>d<\/sub> [m\u00b7s-1<\/sup>]<\/td>\n<\/td>\npr\u016f\u0159ezov\u00e1 rychlost proud\u011bn\u00ed v profilu za v\u00fdtokem z mostn\u00edho objektu,<\/td>\n<\/tr>\n
<\/td>\nZ<\/em>Z<\/sub> [m]<\/td>\n<\/td>\nztr\u00e1ta z\u00fa\u017een\u00edm na vtoku do mostn\u00edho otvoru,<\/td>\n<\/tr>\n
<\/td>\nZ<\/em>R<\/sub> [m]<\/td>\n<\/td>\nztr\u00e1ta roz\u0161\u00ed\u0159en\u00edm na v\u00fdtoku z\u00a0mostn\u00edho otvoru.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Ztr\u00e1ty z\u00fa\u017een\u00edm je mo\u017en\u00e9 vyj\u00e1d\u0159it v\u00a0z\u00e1vislosti na pr\u016f\u0159ezov\u00e9 rychlosti ve vtokov\u00e9m profilu mostu, ke stanoven\u00ed ztr\u00e1t roz\u0161\u00ed\u0159en\u00edm je mo\u017en\u00e9 pou\u017e\u00edt v\u00edce postup\u016f (obdoba Bordovy ztr\u00e1ty pro n\u00e1hl\u00e9 roz\u0161\u00ed\u0159en\u00ed pr\u016fm\u011bru potrub\u00ed jako funkci rozd\u00edlu rychlostn\u00edch v\u00fd\u0161ek na za\u010d\u00e1tku a\u00a0konci roz\u0161\u00ed\u0159en\u00ed proudu nebo analogie ztr\u00e1ty na v\u00fdtoku do velk\u00e9 n\u00e1dr\u017ee). Podrobn\u011b se touto problematikou ve sv\u00e9 pr\u00e1ci zab\u00fdvala Jure\u010dkov\u00e1 [6]. Rovnici, kter\u00e1 vyu\u017e\u00edv\u00e1 posledn\u00ed p\u0159\u00edstup, publikoval nap\u0159\u00edklad Hamill [3]:<\/p>\n\"\"<\/a>\n\n\n\n\n
kde<\/td>\nC<\/em>D0<\/sub> [-]<\/td>\nje<\/td>\npr\u016ftokov\u00fd sou\u010dinitel,<\/td>\n<\/tr>\n
<\/td>\nS<\/em>m <\/sub>= B<\/em>m<\/sub>H<\/em>m<\/sub><\/td>\n<\/td>\nplocha vtokov\u00e9ho otvoru.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Picek [5] v\u0161ak doporu\u010duje pro druh\u00fd profil v\u00a0Bernoulliho rovnici pou\u017e\u00edt profil bezprost\u0159edn\u011b za v\u00fdtokem z\u00a0mostn\u00edho otvoru, kde se vytv\u00e1\u0159\u00ed hloubka y<\/em>d<\/sub>*\u00a0<\/em><\u00a0y<\/em>d<\/sub>, pro v\u00fdpo\u010det proud\u011bn\u00ed tlakov\u00fdm mostn\u00edm objektem pak doporu\u010duje u\u017e\u00edvat rovnici:<\/p>\n\"\"<\/a>\n\n\n\n
kde<\/td>\ny<\/em>d<\/sub>* <\/em>[m]<\/td>\nje<\/td>\nhloubka t\u011bsn\u011b za v\u00fdtokem z\u00a0objektu (viz obr. 6<\/em>).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Vyhodnocen\u00ed sou\u010dinitele C<\/em>D0<\/sub> z\u00a0experiment\u016f na fyzik\u00e1ln\u00edm modelu podle obou rovnic je patrn\u00e9 na obr. 7<\/em>.<\/p>\n\"\"<\/a>\n

Obr. 7. Hodnoty pr\u016ftokov\u00e9ho koeficientu C<\/em>D0<\/sub> pro tlakov\u00e9 proud\u011bn\u00ed vyhodnocen\u00e9 na z\u00e1klad\u011b experimentu podle rovnice (6), resp. (7)
\nFig. 7. Values of discharge coefficient C<\/em>D0<\/sub> for pressurized flow obtained during the experiment according to the equation (6), respectively (7)<\/h6>\n

Metodika v\u00fdzkumu<\/h2>\n

Modelov\u00e1 podobnost<\/h3>\n

Hydraulick\u00fd v\u00fdzkum byl zalo\u017een na fyzik\u00e1ln\u00edm modelov\u00e1n\u00ed p\u0159i proud\u011bn\u00ed s\u00a0volnou hladinou. V\u00a0tomto p\u0159\u00edpad\u011b jsou dominantn\u00edmi silami s\u00edly gravita\u010dn\u00ed a\u00a0pro vyhodnocen\u00ed se vyu\u017e\u00edv\u00e1 Froud\u016fv z\u00e1kon modelov\u00e9 podobnosti. Ten vyjad\u0159uje skute\u010dnost, \u017ee ve vz\u00e1jemn\u011b p\u0159\u00edslu\u0161n\u00fdch profilech na modelu a\u00a0ve skute\u010dnosti budou stejn\u00e1 Froudova \u010d\u00edsla. Bezrozm\u011brn\u00e9 Froudovo \u010d\u00edslo Fr<\/em> je definov\u00e1no rovnic\u00ed:<\/p>\n\"\"<\/a>\n\n\n\n\n
kde<\/td>\nv<\/em>\u00a0[m\u00b7s-1<\/sup>]<\/td>\nje<\/td>\npr\u016f\u0159ezov\u00e1 rychlost proud\u011bn\u00ed,<\/td>\n<\/tr>\n
kde<\/td>\ny<\/em>\u00a0 [m]<\/td>\n<\/td>\nst\u0159edn\u00ed hloubka v\u00a0profilu.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Pro bezrozm\u011brn\u00e9 veli\u010diny, na kter\u00e9 se p\u0159i vyhodnocen\u00ed v\u00fdzkumu \u0159e\u0161itel\u00e9 zam\u011b\u0159ili, ov\u0161em plat\u00ed, \u017ee hodnota z\u00a0modelu m\u00e1 stejnou hodnotu i\u00a0pro skute\u010dnost.<\/p>\n

Popis modelu<\/h3>\n

V\u00fdzkum byl prov\u00e1d\u011bn ve Vodohospod\u00e1\u0159sk\u00e9 hale Fakulty stavebn\u00ed \u010cVUT v\u00a0Praze. M\u011b\u0159en\u00ed prob\u00edhalo v\u00a0hydraulick\u00e9m \u017elabu s\u00a0nulov\u00fdm pod\u00e9ln\u00fdm sklonem. Jeho rozm\u011bry byly n\u00e1sleduj\u00edc\u00ed: \u0161\u00ed\u0159ka 252 mm, d\u00e9lka 7 300 mm, v\u00fd\u0161ka st\u011bn v\u00a0prvn\u00ed \u010d\u00e1sti 1\u00a0000\u00a0mm, v\u00a0druh\u00e9 \u010d\u00e1sti 500 mm. Za\u010d\u00e1tek \u017elabu byl osazen vo\u0161tinov\u00fdm usm\u011br\u0148ova\u010dem pro rovnom\u011brn\u00e9 rozd\u011blen\u00ed proudu a\u00a0na jeho konci byl um\u00edst\u011bn \u017ealuziov\u00fd uz\u00e1v\u011br slou\u017e\u00edc\u00ed k\u00a0regulaci hloubky doln\u00ed vody.<\/p>\n

Do \u017elabu byly postupn\u011b vkl\u00e1d\u00e1ny modely mostn\u00edho objektu. D\u00e9lka mostn\u00edho objektu byla 100 mm a\u00a0\u0161\u00ed\u0159ka mostn\u00edho otvoru byla 130 mm, p\u0159i\u010dem\u017e byly pou\u017eity t\u0159i verze modelu li\u0161\u00edc\u00ed se sv\u011btlou v\u00fd\u0161kou mostn\u00edho otvoru v\u00a0rozm\u011brech 80 mm, 100 mm a\u00a0120 mm. Jejich p\u0159\u00ed\u010dn\u00e9 \u0159ezy byly p\u0159evzaty z\u00a0diplomov\u00e9 pr\u00e1ce Ad\u00e9ly Dost\u00e1lov\u00e9 [7] a\u00a0jsou p\u0159ilo\u017eeny na obr. 8<\/em>.<\/p>\n\"\"<\/a>\n

Obr. 8. P\u0159\u00ed\u010dn\u00e9 \u0159ezy model\u016f mostn\u00edch objekt\u016f v\u010detn\u011b jejich rozm\u011br\u016f v\u00a0[mm] [7]
\nFig. 8. Cross sections of bridge models including their dimensions in [mm] [7]<\/h6>\n

M\u011b\u0159en\u00ed veli\u010din<\/h3>\n

V\u00a0r\u00e1mci proveden\u00e9ho v\u00fdzkumu byly m\u011b\u0159eny pouze dv\u011b veli\u010diny, a\u00a0to v\u00fd\u0161ka \u00farovn\u00ed hladiny a\u00a0pr\u016ftok modelem. \u00darovn\u011b hladin byly m\u011b\u0159eny pomoc\u00ed posuvn\u00e9ho hrotov\u00e9ho m\u011b\u0159\u00edtka a\u00a0hodnoty byly ode\u010d\u00edt\u00e1ny s\u00a0p\u0159esnost\u00ed 0,1 mm. Pro m\u011b\u0159en\u00ed pr\u016ftok\u016f byla pou\u017eita dv\u011b za\u0159\u00edzen\u00ed\u00a0\u2013 induk\u010dn\u00ed pr\u016ftokom\u011br Magnetoflow Primo a\u00a0m\u011brn\u00fd Thomson\u016fv p\u0159eliv.<\/p>\n

B\u011bhem v\u00fdzkumu bylo zm\u011b\u0159eno celkem 57 pr\u016fb\u011bh\u016f hladin. Pro ka\u017edou variantu mostn\u00edho objektu byly zm\u011b\u0159eny pr\u016fb\u011bhy hladin pro \u010dty\u0159i hodnoty pr\u016ftoku a\u00a0pro ka\u017ed\u00fd z\u00a0nich byly uva\u017eov\u00e1ny \u010dty\u0159i varianty m\u00edry ovlivn\u011bn\u00ed doln\u00ed vodou, celkem tedy 16 m\u011b\u0159en\u00ed pr\u016fb\u011bhu hladin. Na z\u00e1klad\u011b prvotn\u00edho vyhodnocen\u00ed bylo rozhodnuto o\u00a0nutnosti dom\u011b\u0159en\u00ed n\u011bkolika stav\u016f zejm\u00e9na pro vy\u0161\u0161\u00ed hodnoty pr\u016ftok\u016f na vtoku do mostn\u00edho objektu.<\/p>\n

M\u011b\u0159en\u00ed v\u00fd\u0161ky hladiny bylo prov\u00e1d\u011bno v\u00a0bodech rozm\u00edst\u011bn\u00fdch rovnom\u011brn\u011b v\u00a0pod\u00e9ln\u00e9m a\u00a0p\u0159\u00ed\u010dn\u00e9m sm\u011bru, v\u00a0bl\u00edzkosti mostn\u00edho objektu byla s\u00ed\u0165 m\u011b\u0159en\u00fdch bod\u016f zhu\u0161t\u011bna (viz obr. 9<\/em> p\u0159evzat\u00fd z\u00a0diplomov\u00e9 pr\u00e1ce [7]). Ve v\u011bt\u0161in\u011b p\u0159\u00ed\u010dn\u00fdch profil\u016f bylo m\u011b\u0159en\u00ed prov\u00e1d\u011bno v\u00a0p\u011bti bodech, kdy jeden bod byl v\u00a0ose proud\u011bn\u00ed, dal\u0161\u00ed dva v\u00a0jedn\u00e9 a\u00a0t\u0159ech \u010dtvrtin\u00e1ch \u0161\u00ed\u0159ky od kraje \u017elabu a\u00a0posledn\u00ed dva body byly um\u00edst\u011bny u\u00a0kraje \u017elabu. M\u011b\u0159en\u00e9 body jsou zn\u00e1zorn\u011bny na obr. 9<\/em> \u010derven\u011b, zelenou barvou je zde zn\u00e1zorn\u011bno um\u00edst\u011bn\u00ed mostn\u00edho objektu.<\/p>\n\"\"<\/a>\n

Obr. 9. S\u00ed\u0165 m\u011b\u0159en\u00fdch bod\u016f v\u00a0hydraulick\u00e9m \u017elabu
\nFig. 9. Mesh of the measured points in the hydraulic flume<\/h6>\n

V\u00fdsledky experiment\u00e1ln\u00edho v\u00fdzkumu<\/h2>\n

Prohl\u00eddka rozs\u00e1hl\u00e9ho souboru dat, kter\u00fd byl b\u011bhem experiment\u00e1ln\u00edch prac\u00ed po\u0159\u00edzen, uk\u00e1zala, \u017ee pro studium sc\u00e9n\u00e1\u0159e se zatopen\u00fdm vtokem a\u00a0voln\u00fdm v\u00fdtokem bylo nezbytn\u00e9 ponechat jen n\u011bkter\u00e9 pokusy, kdy se vyskytovala voln\u00e1 hladina pod celou d\u00e9lkou re\u00e1ln\u00e9 mostn\u00ed konstrukce. V\u00a0souboru dat, kter\u00fd byl d\u00e1le podroben statistick\u00e9 anal\u00fdze, bylo ponech\u00e1no 34 pr\u016fb\u011bh\u016f hladin.<\/p>\n

Typick\u00fd pr\u016fb\u011bh hladiny p\u0159i experimentech je vykreslen na obr. 10<\/em>. Za vtokov\u00fdm profilem doch\u00e1zelo k\u00a0postupn\u00e9mu sni\u017eov\u00e1n\u00ed hladiny na hodnotu y<\/em>c<\/sub>, v\u00a0naprost\u00e9 v\u011bt\u0161in\u011b p\u0159\u00edpad\u016f se tato hloubka objevovala p\u0159ibli\u017en\u011b ve vzd\u00e1lenosti 2\/3 d\u00e9lky mostn\u00edho objektu. Pak se hladina postupn\u011b zvy\u0161ovala a\u017e k\u00a0hodnot\u011b y<\/em>d<\/sub>.<\/p>\n\"\"<\/a>\n

Obr. 10. Pod\u00e9ln\u00fd profil hladiny vyskytuj\u00edc\u00ed se p\u0159i experiment\u00e1ln\u00edm m\u011b\u0159en\u00ed
\nFig. 10. Water level profile observed at the experimental measurements<\/h6>\n

Pro dan\u00e9 sch\u00e9ma je mo\u017en\u00e9 sestavit Bernoulliho rovnici mezi profilem z\u00fa\u017een\u00e9 hloubky y<\/em>c<\/sub> a\u00a0vzdut\u00e9 hloubky nad mostem y<\/em>h<\/sub> ve\u00a0tvaru (1) nebo mezi profilem s\u00a0hloubkou doln\u00ed vody y<\/em>d<\/sub> a\u00a0vzdut\u00e9 hloubky nad mostem y<\/em>h<\/sub> ve tvaru (5). Mo\u017enosti stanoven\u00ed ztr\u00e1t jsou pops\u00e1ny u\u00a0rovnice (5), k\u00a0vy\u010d\u00edslen\u00ed ztr\u00e1t je pot\u0159eba zn\u00e1t velikost rychlosti v<\/em>c<\/sub> v\u00a0profilu z\u00fa\u017een\u00e9 hloubky y<\/em>c<\/sub>. V\u00a0pr\u016fb\u011bhu experiment\u016f v\u0161ak rychlostn\u00ed pole m\u011b\u0159eno nebylo a\u00a0\u0159e\u0161itel\u00e9 aktivn\u00ed \u0161\u00ed\u0159ku proud\u011bn\u00ed v\u00a0z\u00fa\u017een\u00e9m profilu B<\/em>c<\/sub> pouze odhadovali na z\u00e1klad\u011b porovn\u00e1n\u00ed se simulacemi vybran\u00fdch sc\u00e9n\u00e1\u0159\u016f s\u00a0vyu\u017eit\u00edm 3D matematick\u00e9ho modelu. V\u00a0r\u00e1mci navazuj\u00edc\u00edho v\u00fdzkumu se po\u010d\u00edt\u00e1 s\u00a0t\u00edm, \u017ee se \u0159e\u0161itel\u00e9 zam\u011b\u0159\u00ed pr\u00e1v\u011b na vyhodnocen\u00ed rychlosti v<\/em>c<\/sub>, kter\u00e1 bude nezbytn\u00e1 pro vyhodnocen\u00ed ztr\u00e1t z\u00fa\u017een\u00edm i\u00a0roz\u0161\u00ed\u0159en\u00edm proudu.<\/p>\n

Proto \u0159e\u0161itel\u00e9 v\u00a0t\u00e9to f\u00e1zi v\u00fdzkumu zam\u011b\u0159ili svou pozornost zejm\u00e9na na posouzen\u00ed spr\u00e1vnosti v\u00fdpo\u010dtu vzdut\u00e9 \u00farovn\u011b hladiny nad mostem v\u00a0p\u0159\u00edpad\u011b zatopen\u00e9ho vtoku a\u00a0voln\u00e9ho v\u00fdtoku podle p\u0159\u00edstupu Bradleyho. Zku\u0161enosti s\u00a0u\u017e\u00edv\u00e1n\u00edm softwaru Hec-Ras, kter\u00fd tento postup pou\u017e\u00edv\u00e1, ukazuj\u00ed, \u017ee vypo\u010d\u00edtan\u00e1 hloubka proud\u011bn\u00ed nad mostn\u00edm objektem y<\/em>h<\/sub> d\u00e1v\u00e1 v\u00a0p\u0159\u00edpad\u011b proud\u011bn\u00ed se zatopen\u00fdm vtokem a\u00a0voln\u00fdm v\u00fdtokem \u010dasto vy\u0161\u0161\u00ed hodnotu, ne\u017e pro v\u011bt\u0161\u00ed pr\u016ftok, kdy je proud\u011bn\u00ed objektem ji\u017e pln\u011b tlakov\u00e9. Rovnice vyu\u017e\u00edv\u00e1 diskutabiln\u00ed hodnotu z\u00fa\u017een\u00e9 hloubky za vtokem jako 0,5 \u00b7 H<\/em>m<\/sub>, zat\u00edmco p\u0159i v\u00fdtoku otvorem to b\u00fdv\u00e1 podle obr. 2<\/em> cca 0,6 \u00b7 H<\/em>m<\/sub>. Vyhodnocen\u00ed experiment\u016f pak uk\u00e1zalo, \u017ee vytvo\u0159en\u00ed pr\u016fb\u011bhu hladiny se zatopen\u00fdm vtokem a\u00a0voln\u00fdm v\u00fdtokem bylo dosa\u017eeno \u010dasto jen p\u0159i zatopen\u00ed z\u00fa\u017een\u00e9 hloubky 0,6 \u00b7 H<\/em>m<\/sub> doln\u00ed vodou. Tuto skute\u010dnost dokl\u00e1d\u00e1 graf na obr. 11<\/em>.<\/p>\n\"\"<\/a>\n

Obr. 11. Z\u00e1vislost pom\u011bru y<\/em>c<\/sub>\/H<\/em>m<\/sub> na y<\/em>d<\/sub>\/H<\/em>m<\/sub> pro proveden\u00e9 experimenty se zatopen\u00fdm vtokem a voln\u00fdm v\u00fdtokem
\nFig. 11. Dependence of ratio y<\/em>c<\/sub>\/H<\/em>m<\/sub> on y<\/em>d<\/sub>\/H<\/em>m<\/sub> for experiments with free flow and submerged face of the deck<\/h6>\n

Na obr. 12<\/em> jsou zobrazeny hodnoty pr\u016ftokov\u00e9ho sou\u010dinitele C<\/em>D<\/sub> stanoven\u00e9 z\u00a0rovnice (4) pro zn\u00e1m\u00e9 hodnoty Q<\/em>, E<\/em>h<\/sub>, H<\/em>m<\/sub> a\u00a0B<\/em>m<\/sub> stanoven\u00e9 vyhodnocen\u00edm experiment\u016f. Pr\u016fb\u011bh bod\u016f byl n\u00e1sledn\u011b prolo\u017een k\u0159ivkou, jej\u00ed\u017e pr\u016fb\u011bh je pops\u00e1n rovnic\u00ed (9), fialovou \u010d\u00e1rou je pak vyzna\u010den pr\u016fb\u011bh Bradleyho z\u00e1vislosti. Pouh\u00fdm okem je patrn\u00e9, \u017ee naprost\u00e1 v\u011bt\u0161ina hodnot sou\u010dinitele C<\/em>D<\/sub> je v\u011bt\u0161\u00ed ne\u017e podle Bradleyho.<\/p>\n\"\"<\/a>\n

Obr. 12. Z\u00e1vislost pr\u016ftokov\u00e9ho sou\u010dinitele C<\/em>D<\/sub> na pom\u011bru y<\/em>h<\/sub>\/H<\/em>m
\n<\/sub>Fig. 12. Dependence of discharge coefficient C<\/em>D<\/sub> on ratio y<\/em>h<\/sub>\/H<\/em>m<\/sub><\/h6>\n\"\"<\/a>\n\"\"<\/a>\n
Obr. 13. Z\u00e1vislost pr\u016ftokov\u00e9ho sou\u010dinitele C<\/em>D<\/sub> na pom\u011bru y<\/em>d<\/sub>\/H<\/em>m
\n<\/sub>Fig. 13. Dependence of discharge coefficient C<\/em>D<\/sub> on ratio y<\/em>d<\/sub>\/H<\/em>m<\/sub><\/h6>\n

Jin\u00fd pohled na sou\u010dinitel C<\/em>D<\/sub> d\u00e1v\u00e1 obr. 13<\/em>, kde je zobrazena jeho z\u00e1vislost tentokr\u00e1t na pom\u011bru y<\/em>d<\/sub>\/H<\/em>m<\/sub>. Vzhledem k\u00a0tomu, \u017ee software Hec-Ras neumo\u017e\u0148uje \u0159e\u0161it podrobn\u00fd pr\u016fb\u011bh hladiny v\u00a0profilu mostn\u00edho objektu a\u00a0v\u00a0p\u0159\u00edpad\u011b, \u017ee \u00farove\u0148 hladiny doln\u00ed vody je vy\u0161\u0161\u00ed ne\u017e spodn\u00ed l\u00edc mostovky, program automaticky uva\u017euje tlakov\u00e9 proud\u011bn\u00ed, byl pr\u016fb\u011bh dopln\u011bn o\u00a0prolo\u017een\u00ed bod\u016f s\u00a0men\u0161\u00edmi hodnotami, ne\u017e je y<\/em>d<\/sub>\/H<\/em>m<\/sub> < 0,97 line\u00e1rn\u00ed z\u00e1vislost\u00ed podle rovnice:<\/p>\n\"\"<\/a>\n

Na posledn\u00edm obr. 14<\/em> je pak zn\u00e1zorn\u011bn pr\u016fb\u011bh z\u00e1vislosti sou\u010dinitele C<\/em>D0<\/sub>, jeho\u017e hodnoty byly spo\u010d\u00edt\u00e1ny podle rovnice (6), na pom\u011bru y<\/em>d<\/sub>\/H<\/em>m<\/sub>. Zde je nezbytn\u00e9 uv\u00e9st, \u017ee uveden\u00e1 rovnice po fyzik\u00e1ln\u00ed str\u00e1nce nepopisuje proud\u011bn\u00ed mostn\u00edm objektem se zatopen\u00fdm vtokem a\u00a0voln\u00fdm v\u00fdtokem zcela spr\u00e1vn\u011b.<\/p>\n\"\"<\/a>\n

Obr. 14. Z\u00e1vislost sou\u010dinitele C<\/em>D0<\/sub> stanoven\u00e9ho podle rovnice (6) na pom\u011bru y<\/em>d<\/sub>\/H<\/em>m
\n<\/sub>Fig. 14. Dependence of coefficient C<\/em>D0<\/sub> obtained from equation (6) on ratio y<\/em>d<\/sub>\/H<\/em>m<\/sub><\/h6>\n

Pr\u016fb\u011bh z\u00e1vislosti vykreslen\u00fdch bod\u016f na obr. 14<\/em> byl prolo\u017een funkc\u00ed podle rovnice:<\/p>\n\"\"<\/a>\n

Jedn\u00edm z\u00a0dal\u0161\u00edch c\u00edl\u016f \u0159e\u0161itel\u016f bude nal\u00e9zt v\u00fdpo\u010detn\u00ed postupy, kter\u00e9 zajist\u00ed spojit\u00e9 \u0159e\u0161en\u00ed v\u00fdpo\u010dtu vzdut\u00e9 hloubky nad mostem p\u0159i p\u0159echodu ze stavu se zatopen\u00fdm vtokem a\u00a0voln\u00fdm v\u00fdtokem na pln\u011b tlakov\u00e9 proud\u011bn\u00ed, co\u017e software Hec-Ras neposkytuje. Porovn\u00e1n\u00ed grafu na obr. 14<\/em> s\u00a0v\u00fdstupy v\u00fdzkumu Picka podle obr. 7<\/em> na mo\u017en\u00e9 propojen\u00ed ukazuj\u00ed.<\/p>\n

Z\u00e1v\u011br<\/h2>\n

Vyhodnocen\u00ed experiment\u016f na fyzik\u00e1ln\u00edm modelu p\u0159i proud\u011bn\u00ed mostn\u00edm objektem se zatopen\u00fdm vtokem a\u00a0voln\u00fdm v\u00fdtokem uk\u00e1zaly na to, \u017ee v\u00fdpo\u010det vzdut\u00e9 hloubky nad mostem y<\/em>h<\/sub> s\u00a0vyu\u017eit\u00edm rovnice (4) a\u00a0stanoven\u00edm pr\u016ftokov\u00e9ho sou\u010dinitele C<\/em>D<\/sub> podle z\u00e1vislosti podle grafu na obr. 5<\/em> m\u016f\u017ee d\u00e1vat p\u0159\u00edli\u0161 velk\u00e9 hodnoty.<\/p>\n

Na z\u00e1klad\u011b proveden\u00e9 anal\u00fdzy zejm\u00e9na pak grafu na obr. 13<\/em> se v\u00a0p\u0159\u00edpad\u011b u\u017eit\u00ed softwaru Hec-Ras doporu\u010duje nepou\u017e\u00edvat postup, kdy program s\u00e1m ode\u010dte hodnotu C<\/em>D<\/sub> z\u00a0uveden\u00e9 z\u00e1vislosti, ale doporu\u010duje se pro hodnoty y<\/em>d<\/sub>\/H<\/em>m<\/sub> v\u00a0rozsahu od 0,7 do 0,95 pou\u017e\u00edt hodnotu C<\/em>D<\/sub>\u00a0=\u00a00,5, pro hodnotu pom\u011bru men\u0161\u00ed ne\u017e 0,7 p\u0159ibli\u017en\u011b C<\/em>D<\/sub>\u00a0=\u00a00,525.<\/p>\n","protected":false},"excerpt":{"rendered":"

The paper presents the results of hydraulic research of flow through bridge structure with free water surface and submerged inlet on a physical model. It compares current knowledge with measured data and discusses the differences. <\/p>\n","protected":false},"author":8,"featured_media":8138,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[86],"tags":[1921,1790,1922,1924,1923],"coauthors":[1896,1897],"class_list":["post-8264","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hydraulics-hydrology-and-hydrogeology","tag-bridge","tag-discharge-coefficient","tag-free-water-surface","tag-mathematical-modeling","tag-physical-modeling"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/8264","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/comments?post=8264"}],"version-history":[{"count":3,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/8264\/revisions"}],"predecessor-version":[{"id":30589,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/8264\/revisions\/30589"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media\/8138"}],"wp:attachment":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media?parent=8264"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/categories?post=8264"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/tags?post=8264"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/coauthors?post=8264"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}