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Škola: Gymnázium, Brno, Slovanské náměstí 7

Enhance physics education at Gymnázium Brno with ICT through the project "Inovace výuky na GSN prostřednictvím ICT." Learn about Bernoulli's equation in fluid dynamics emphasizing velocity, pressure, and energy in cross-sections.

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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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