Question 5: Write and explain any three applications of Bernoulli’s equation.
Applications of Bernoulli’s equation
- The velocity of the fluid can be increased by narrowing the cross-sectional area of the flow of the fluid. (Equation of continuity).
- Bernoulli’s equation is (When the velocity of the fluid is increased, the pressure drops.
So both these ideas when combined, has important applications in our life.
(1) Aerofoil an Bernoulli’s Equation
Aerofoil is the mechanism by which a particular shape creates an aerodynamic force. It is designed in such a way that the fluid (for example air, and particularly in the case of aeroplan) flows faster on its upper surface than its bottom. In this way the pressure below the aerofoil is greater than the pressure above it. An up thrust acts upon the body as consequence of this unbalanced force. Aerofoils are employed on aircrafts in the form of wings that creates a normal upward thrust in the air.
Explanation: The shape of an aerofoil is shown in the figure. The flow of fluid (say air) is faster at the top surface as compared to the bottom surface. Let v1 is the speed of air above the aerofoil and v2 is below it, v1 > v2. Bernoulli’s equation gives P2 > P1, where P1 is pressure above the aerofoil and P2 is pressure below it. The difference in the pressures produces a force in the upward direction that provides an up thrust or lift to the aerofoil (or airplane).
(2) Jets and nozzles and Bernoulli’s Equation
Jets and nozzles work on the principle of Bernoulli’s’ equation. A slow stream of a fluid is converted to a fast jet by narrowing the exit of the fluid. The phenomenon enables us to suck water, oil or air from a container.
Take a filter pump as an example for explanation. It consists of a narrow section in the middle called jet. As water emerges from the jet, its speed increases due to small cross-sectional area (equation of continuity). The increased speed of water reduces the pressure in the surrounding area. The vessel to be evacuated is connected at this area through a pipe. The decreased pressure makes the air to rush there and the air and water is forced out through the tube at the bottom.
(3) Cricket ball and Bernoulli’s Equation
When the bowler through the ball in such a way that the ball spins as it moves forward, the speed of air on the opposite sides of the ball is different. The speed of air is more on the side where the spin in the ball and speed of air are in one direction. Similarly, the speed of air is less on the side where the spin in the ball and the speed of air are in opposite directions. According to Bernoulli’s equation, the pressure on the ball will be greater on the side where the speed of air is greater. Therefore, there is a resultant pressure on one side of the ball. The extra pressure on one side means an extra force on the ball on that side. This makes the path of the ball a little curved. The batsman is, sometimes, deceived with the line of the ball and looses his/her wicket.