Applications of Bernoulli’s equation

Streamline tracing the direction of air flow around a moving vehicleStreamlines are drawn parallel to the direction of flow and show how fluids flow around the surfaces of objects such as vehicles and aircraft. Where streamlines are close together, speed is higher. Where streamlines are farther apart, speed is lower. Energy is conserved only along the same streamline, because a streamline tracks the motion of the same specific mass of fluid as it flows. Read the text aloud
Bernoulli’s equation tells us that along a streamline the variables of height, pressure, and speed are related by energy conservation. If any of these three increases, at least one of the other two must decrease. For example, if the speed of a fluid goes up, the pressure may go down to compensate. Read the text aloud
Flight is an important application of fluid flow in which the fluid is air. In order to fly, a plane in motion must generate a vertical lift force at least equal to its weight. The purpose of a wing is to manipulate airflow in a specific way to create and control lift forces. The cross section of a wing has the shape of an airfoil. As shown in the illustration below, the shape of an airfoil and the angle of attack force air along streamline (A) to be divided into two paths: air flowing across the top of the wing (B) and air flowing under the wing (C). During the same time interval, air flowing over the wing must travel a further distance than air flowing under the wing, so the speed of air over the top surface of the wing (B) is higher than the speed below the wing (C). This difference in the speed of the airflow is the key to flying. Read the text aloud
Streamlines flowing around an airfoil on an airplane's wing
According to Bernoulli’s equation, the sum of energy densities must be equal for both paths that originate along the same streamline at (A). Increasing the speed above the wing therefore means that the pressure on the top surface of the wing is lower than the pressure on the lower surface—since above and below the wing all the other parameters in Bernoulli’s equation (ρ, g, and h) are equal. The difference between the pressures above and below the wing, when multiplied by the area of the wing, generates the lift force. Because the lift force is created by the motion of air over the wing, the force increases as the square of the plane’s speed. That is why planes need to accelerate along a runway until they reach take-off speed. A plane cannot get off the ground until it reaches a speed at which the lift force exceeds the plane’s weight. Read the text aloud Show Calculate the lift force

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