45.PNG

# Bernoulli's Principle Bernoulli's principle, discovered by Daniel Bernoulli in the 18th century, states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Bernoulli's principle is usuall...

# Bernoulli's Principle Bernoulli's principle, discovered by Daniel Bernoulli in the 18th century, states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Bernoulli's principle is usually applied to inviscid fluids. This principle is often stated as: * Faster moving fluid = Lower pressure * Slower moving fluid = Higher pressure ## Equation $\frac{v^2}{2} + gz + \frac{p}{\rho} = \text{constant}$ Where: * $v =$ fluid flow speed at a point on a streamline * $g =$ acceleration due to gravity * $z =$ elevation of the point above a reference plane * $p =$ pressure at the selected point * $\rho =$ density of the fluid ## Bernoulli's Principle Examples ### Airplane Wing The shape of an airplane wing is designed so that the air flows faster over the top of the wing than under the wing. Because faster moving air means lower pressure, the pressure on top of the wing is less than the pressure on the bottom of the wing. The higher pressure below the wing pushes the wing up toward the lower pressure above the wing. ### Curveball A curveball works because the ball is spinning. The spinning ball drags some air around with it. * The relative speed of the airflow is greater on one side * The relative speed of the airflow is slower on the other side The side with the greater relative speed has lower pressure than the side with slower relative speed. The difference in pressure pushes the ball in the direction of lower pressure, causing the ball to curve.