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1 Delft Universit of Technolog Drukken en draaien Basisfsica, Coriolis en -interacties (PPT) Mosselman, Erik Publication date 2016 Document Version Final published version Citation (APA) Mosselman, E. (2016). Drukken en draaien: Basisfsica, Coriolis en -interacties (PPT) WMCN-kennisdag, Lelstad, Netherlands. Important note To cite this publication, please use the final published version (if applicable). Please check the document version above. Copright Other than for strictl personal use, it is not permitted to download, forward or distribute the tet or part of it, without the consent of the author(s) and/or copright holder(s), unless the work is under an open content license such as Creative Commons. Takedown polic Please contact us and provide details if ou believe this document breaches coprights. We will remove access to the work immediatel and investigate our claim. This work is downloaded from Delft Universit of Technolog. For technical reasons the number of authors shown on this cover page is limited to a maimum of 10.
2 Basisfsica h h u h t Drukken en draaien Basisfsica, Coriolis en -interacties Erik Mosselman WMCN-kennisdag Water Management Centre of the Netherlands Lelstad, Coriolis Ooit Coriolis-krachten gevoeld? 1
3 Coriolis Coriolis-krachten Afwijking naar rechts op het noordelijk halfrond: draaiing tegen de wijzers van de klok Gustave-Gaspard Coriolis Afwijking naar links op het zuidelijk halfrond Coriolis Coriolis Coriolis-krachten Zeestromingen en luchtstromingen Noodzakelijk ingrediënt voor orkanen Middagsessie over orkanen door Femke Davids Waar op de wereld zijn orkanen het sterkst?? 2
4 Basisprincipes van waterbeweging Continuïteit Basisprincipes: Wet van Behoud van Massa (continuïteit) Antoine Lavoisier q t h q q t hqt Wet van Behoud van Impuls () h q t Isaac Newton Continuïteit h q t Stationaire stroming:../t = 0 q 0 q constant hu constant massabalans: sterkere stroming boven ondiepten F ma Per eenheid van massa: F m Dt Werking van verschillende krachten: F Dt m F F Dt m V z w b g wind Dt h h Welke krachten werken er op een watervolume? Zwaartekracht (via drukgradiënt) Stromingsweerstand (bodemwrijving, vegetatie, overlaten) Wind F wind wind m h F m druk zw g gi m h F resist b 3
5 z w b g wind Dt h h z w b g wind Dt h h z w b g wind Dt h h z w b g wind Dt h h z w b g wind Dt h h z w b g wind Dt h h 4
6 z u g w b wind t h h b wind gi t h h Euler Stationaire stroming:../t = 0 Uniforme stroming:../ = 0 Empirisch: b = gu 2 /C 2 Geen wind 2 gu gi Ch u C hi 2 0 impulsbalans: sterkere stroming in diepe delen Basisprincipes van waterbeweging Beschrijving per eenheid van massa Alleen geldig voor constante massadichtheid Niet geschikt voor -interactie Beschrijving per eenheid van massa Alleen geldig voor constante massadichtheid Niet geschikt voor -interacties Waterdruk = gewicht waterkolom erboven per m 2 Hdrostatische drukverdeling Lineair p gh p gh p H g gh H z w H 1: g Alzijdige druk: druk even groot in alle richtingen H 5
7 = 1025 kg/m 3 = 1000 kg/m 3 Wat gebeurt er als je de kraan open draait? Wat is de eindsituatie? Wat gebeurt er als je de kraan open draait? Wat is de eindsituatie? = 1025 kg/m 3 = 1000 kg/m 3 40 cm? p gh gh H rechts links links rechts rechts 1,025H 41 cm links 6
8 Coördinaattransformaties Kromlijnig rekenrooster: coördinatenstelsel aangepast aan de vorm van de rivier Correctie met schijnkrachten Met aarde meedraaiend coördinatenstelsel: > Coriolis-versnelling s Een baan langs een gebogen coördinaatlijn lijkt ten onrechte rechtdoor Kromlijnig coordinatenstelsel voor rivierbochten: > Centrifugale versnelling u 2 / R n Coördinaattransformatie: correctie van vergelijkingen voor nietcartesische coördinaten, b.v. met term voor centrifugale versnelling Coördinaattransformaties Einstein deed het omgekeerde! In werkelijkheid etra aantrekkende krachten door grote massa s Coördinatenstelsel zo vervormen dat deze etra krachten gelijk aan nul worden Albert Einstein Gekromde ruimte-tijd met eenvoudiger vergelijkingen 7
9 8
10 met tong Barranquilla met tong Estuarium van de Río Magdalena Getijamplitude ~0.3 m Laagwaterafvoer ~3,000 m 3 /s Zouttong in grote bocht R s 6200 m met tong met tong met tong 9
11 met tong met tong met tong met tong Computerberekeningen laten zien: Twee cellen van spiraalstromen boven elkaar Sterkere spiraalstromen bij stratificatie Stratificatie beïnvloedt secundaire stromingen en, dus, de morfologische ontwikkeling van de rivierbodem Dank! Vragen? 10
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