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Škola: Gymnázium, Brno, Slovanské náměstí 7

Škola: Gymnázium, Brno, Slovanské náměstí 7 Šablona: III/2 – Inovace a zkvalitnění výuky prostřednictvím ICT Název projektu: Inovace výuky na GSN prostřednictvím ICT Číslo projektu: CZ.1.07/1.5.00/34.0940 Autor: RNDr. Bc. Miroslav Hruška

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Škola: Gymnázium, Brno, Slovanské náměstí 7

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  1. Škola: Gymnázium, Brno, Slovanské náměstí 7 Šablona: III/2 – Inovace a zkvalitnění výuky prostřednictvím ICT Název projektu: Inovace výuky na GSN prostřednictvím ICT Číslo projektu: CZ.1.07/1.5.00/34.0940 Autor: RNDr. Bc. Miroslav Hruška Tematická oblast: Gravitational field and motion of bodies (gravitační pole a pohyb těles) Název DUMu: Hydrodynamics – Bernoulli’s equation Kód: VY_32_INOVACE_FY.4.19 Datum: 27. 4. 2014 Cílová skupina: Žáci středních škol s CLIL výukou fyziky v angličtině Klíčová slova: Hydrodynamics, velocity, pressure, energy, cross-section Anotace: Prezentace popisuje zákon zachování mechanické energie pro proudění kapaliny

  2. Gravitational field and motion of bodies 19. Hydrodynamics – Bernoulli’s equation

  3. Fill in the gaps • When a liquid is flowing ……………, the conditions (……………, pressure and ………-…………) may differ from point to point, but do not change with ……… • The equation of ……………… states that for a liquid …………. in tube of varying cross-section the mass flow …… is the same everywhere in the ……..

  4. Fill in the gaps – solution • When a liquid is flowing steadily, the conditions (velocity, pressure and cross-section) may differ from point to point, but do not change with time • The equation of continuitystates that for a liquidflowing in tube of varying cross-section the mass flow rate is the same everywhere in the tube

  5. Hydrodynamics

  6. Liquid flowing in a horizontal tube V p1 p2 S1 S2 p2 < p1!

  7. Bernoulli’s equation(for a horizontal tube) • … is the law of conservation of mechanical energy for ideal liquids

  8. Bernoulli’s equation • – represents kinetic energy per unit volume of liquid • Ep = pV … pressure potential energy • p – represents pressure (potential) energy per unit volume of liquid

  9. Bernoulli’s equation The sum of kinetic and pressure energy per unit volume is constant at any point of a horizontal pipe • The pressure in the narrow part is less than that in the wide one

  10. Exercise • Water flows at 10 m/s through a cross-section of a pipe of radius 12 cm. Find the change in pressureat a cross-section of radius 8 cm. • v1 = 10 m/s, r1 = 12 cm • r2 = 8 cm • Δp = ? (v2 = ?)

  11. Solution • First, we will use the equation of continuity to find the speed at the narrow cross-section … 22.5 m/s • Second, we will use Bernoulli’s equation: Pa (decrease)

  12. That is all for now Thank you for your attention

  13. Materiál je určen pro bezplatné používání pro potřeby výuky a vzdělávání na všech typech škol a školských zařízeních. Jakékoliv další využití podléhá autorskému zákonu. Zdroje: • Bednařík, M., Široká, M. Fyzika pro gymnázia, Mechanika. Dotisk 3. vyd. Praha: Prometheus, 2004. 288 s. ISBN 80-7196-176-0 • Hornby, A. S. Oxford Advanced Learner’s Dictionary of Current English. 5. vyd. Oxford: Oxford University Press, 1995. 1428 s. ISBN 0-19-431423-5

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