What is Bernoullis Principle | Vision Science Academy Kalyan
What is Bernoullis Principle
Could you please explain the underlying physics behind the following scenario: When air is directed upward from a hair dryer and a hanging ball is placed in the path of the airflow, the ball moves upward and remains suspended in the air stream?
The phenomenon described above, where air from a hair dryer lifts a ball hanging in the path of the airflow, is a result of both Bernoulli’s principle and Newton’s third law of motion.
- Bernoulli’s Principle: As air flows faster over the top surface of an object, it creates an area of lower pressure compared to the air on the bottom surface. This pressure difference generates an upward force, commonly known as lift. In the case of a ball placed in the path of the air from a hair dryer, the faster-moving air over the top of the ball creates lower pressure, while the slower-moving air below the ball has higher pressure. This pressure difference pushes the ball upward, creating lift.
- Newton’s Third Law of Motion: This law states that for every action, there is an equal and opposite reaction. When the hair dryer expels a high-speed stream of air downward, the air pushes against the ball in an upward direction. Simultaneously, the ball pushes the air downward, due to Newton’s third law. This action-reaction pair of forces propel the ball upward.
The combination of the pressure difference created by the faster-moving air over the ball and the reaction force from the air being expelled by the hair dryer results in the ball being lifted upward. This is similar to how an airplane wing generates lift, as the air moving over the curved upper surface of the wing creates lower pressure, causing the wing (and the airplane attached to it) to lift.
Bernoulli’s theorem states that in an ideal fluid (one that is incompressible and has no viscosity), as the speed of a fluid increases, its pressure decreases, and vice versa. This principle is often applied to explain various phenomena, such as the lift generated by an airplane wing, the flow of blood through arteries, and the behavior of fluids in pipes.
The mathematical expression of Bernoulli’s theorem is:
P + 0.5ρv^2 + ρgh = constant
Where:
- P is the pressure of the fluid
- ρ is the density of the fluid
- v is the velocity of the fluid
- g is the acceleration due to gravity
- h is the height above a reference point
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