State Bernoulli's principle. From conversation of energy in a fluid flow through a tube arrive at Bernoulli's equation. Give an application of Bernoulli's therom.
Bernoulli's principle states that as the speed of a fluid (liquid or gas) increases, its pressure decreases, and vice versa. The principle is based on the conservation of energy in fluid flow.
Starting with the conservation of energy in a fluid flowing through a tube, we can consider the potential energy, kinetic energy, and pressure energy. The total energy per unit volume is constant along a streamline. The equation for this principle is expressed as:
This equation is known as Bernoulli's equation and represents the conservation of energy in a streamline flow of an incompressible, non-viscous fluid.
An application of Bernoulli's theorem is in the aviation industry. The principle helps explain how an airplane generates lift. As air flows over the curved upper surface of an airplane wing, its speed increases, leading to a decrease in pressure according to Bernoulli's equation. The higher pressure beneath the wing provides lift, allowing the aircraft to stay airborne.
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Bernoulli's principle states that as the speed of a fluid (liquid or gas) increases, its pressure decreases, and vice versa. The principle is based on the conservation of energy in fluid flow.
Starting with the conservation of energy in a fluid flowing through a tube, we can consider the potential energy, kinetic energy, and pressure energy. The total energy per unit volume is constant along a streamline. The equation for this principle is expressed as:
\[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} \]
where:
- \( P \) is the pressure,
- \( \rho \) 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.
This equation is known as Bernoulli's equation and represents the conservation of energy in a streamline flow of an incompressible, non-viscous fluid.
An application of Bernoulli's theorem is in the aviation industry. The principle helps explain how an airplane generates lift. As air flows over the curved upper surface of an airplane wing, its speed increases, leading to a decrease in pressure according to Bernoulli's equation. The higher pressure beneath the wing provides lift, allowing the aircraft to stay airborne.