Derivation and Applications of the Bernoulli Principal

1. Derivation and Applications of the Bernoulli Principal www.assignmentpoint.com

2. Lesson Opener: How does a plane fly? How does a perfume spray work? Why does a cricket ball curve? www.assignmentpoint.com

3. Derivation and Applications of the Bernoulli Principal NIS Taldykorgan Grade 11 Physics Lesson Objective: 1.To apply Bernoulli’s equation to solve problems Daniel Bernoulli (1700 – 1782) 2.To describe Bernoulli’s principle and to derive his formula in terms of conservation of energy 3.To present applications of the Bernoulli principle www.assignmentpoint.com

4. Bernoulli’s Principle As the speed of a fluid goes up, its pressure goes down! The pressure in a fast moving stream of fluid is less than the pressure in a slower stream Fast stream = low air pressure www.assignmentpoint.com Slow stream = High air pressure

5. p large p large A1 A1 A2 p small v2 v1 v1 Low speed Low KE High pressure high speed high KE low pressure v small v large Low speed Low KE High pressure v small www.assignmentpoint.com

6. Equation of Continuity www.assignmentpoint.com

7. Bernoulli’s Equation in terms of Fluid Energy • “for any point along a flow tube or streamline” • P + ½ v2 +  g h = constant • Each term has the dimensions of energy / volume or energy density. • ½ v 2 KE of bulk motion of fluid • g h GPE for location of fluid • P pressure energy density arising from internal forces within • moving fluid (similar to energy stored in a spring) • Transformation of SI Units to Joule/meter3= energy/volume: • P [Pa] = [N m-2] = [N m m-3] = [J m-3] • ½ v2 [kg m-3 m2 s-2] = [kg m-1 s-2] = [N m m-3] = [J m-3] •  g h [kg m-3 m s-2 m] = [kg m s-2 m m-3] = [N m m-3] = [J m-3] www.assignmentpoint.com

8. Deriving Bernoulli’s starting with the law of continuity www.assignmentpoint.com

9. Bernoulli’s Equation For steady flow, the velocity, pressure, and elevation of an incompressible and nonviscous fluid are related by an equation discovered by Daniel Bernoulli (1700–1782). www.assignmentpoint.com

10. Deriving Bernoulli’s equation as Conservation of Energy www.assignmentpoint.com

11. Bernoulli’s equation: www.assignmentpoint.com

12. BERNOULLI’S EQUATION Constant • In a moving fluid p+½rV2 = constant everywhere • An increase in velocity of the fluid results in a decrease in pressure • Bernoulli’s equation is an extension of F=ma for fluid flows and aerodynamics www.assignmentpoint.com

13. HOW DOES A WING GENERATE LIFT? • An imbalance of pressure over the top and bottom surfaces of the wing. • If the pressure above is lower than the pressure on bottom surface, lift is generated www.assignmentpoint.com

14. Airplane Wing is curved on top www.assignmentpoint.com

15. HOW DOES A CURVED WING GENERATE LIFT? Flow velocity over the top of wing is faster than over bottom surface • Air over wing is squashed to smaller cross-sectional area • Mass continuity rAV=constant, velocity must increase www.assignmentpoint.com

16. force high speed low pressure force What happens when two ships or trucks pass alongside each other? www.assignmentpoint.com

17. VENTURI EFFECT velocity increased pressure decreased low pressure high pressure (patm) www.assignmentpoint.com

18. artery Flow speeds up at constriction Pressure is lower Internal force acting on artery wall is reduced External forces causes artery to collapse Arteriosclerosis and vascular flutter www.assignmentpoint.com