Derivation and Applications of the Bernoulli Principal www

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

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

Derivation and Applications of the Bernoulli Principal NIS Taldykorgan Grade 11 Physics Lesson Objective: Daniel Bernoulli (1700 – 1782) 1. To apply Bernoulli’s equation to solve problems 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

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

p large p small v small A 1 v large v 1 Low speed Low KE High pressure v 2 high speed high KE www. assignmentpoint. com low pressure A 2 v small A 1 v 1 Low speed Low KE High pressure

Equation of Continuity www. assignmentpoint. com

Bernoulli’s Equation in terms of Fluid Energy “for any point along a flow tube or streamline” P + ½ v 2 + g h = constant Each term has the dimensions of energy / volume or energy density. ½ v 2 KE of bulk motion of fluid rgh 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/meter 3= energy/volume: P [Pa] = [N m-2] = [N m m-3] = [J m-3] ½ v 2 [kg m-3 m 2 s-2] = [kg m-1 s-2] = [N m m-3] = [J m-3] gh [kg m-3 m s-2 m] = [kg m s-2 m m-3] = [N m m-3] = [J m-3] www. assignmentpoint. com

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

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

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

Bernoulli’s equation: www. assignmentpoint. com

BERNOULLI’S EQUATION Constant • In a moving fluid p+½ V 2 = 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

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

Airplane Wing is curved on top www. assignmentpoint. com

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 crosssectional area – Mass continuity r. AV=constant, velocity must increase www. assignmentpoint. com

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

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

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