Bernoulli's principle in the context of "Venturi meter"

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⭐ Core Definition: Bernoulli's principle

Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. For example, for a fluid flowing horizontally, Bernoulli's principle states that an increase in the speed occurs simultaneously with a decrease in pressure. The principle is named after the Swiss mathematician and physicist Daniel Bernoulli, who published it in his book Hydrodynamica in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler in 1752 who derived Bernoulli's equation in its usual form.

Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of energy in a fluid is the same at all points that are free of viscous forces. This requires that the sum of kinetic energy, potential energy and internal energy remains constant. Thus an increase in the speed of the fluid—implying an increase in its kinetic energy—occurs with a simultaneous decrease in (the sum of) its potential energy (including the static pressure) and internal energy. If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same because in a reservoir the energy per unit volume (the sum of pressure and gravitational potential ρgh) is the same everywhere.

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Bernoulli's principle in the context of Sneezing

A sneeze (also known as sternutation) is a semi-autonomous, convulsive expulsion of air from the lungs through the nose and mouth, usually caused by foreign particles irritating the nasal mucosa. A sneeze expels air forcibly from the mouth and nose in an explosive, spasmodic involuntary action. This action allows for mucus to escape through the nasal cavity and saliva to escape from the oral cavity. Sneezing is possibly linked to sudden exposure to bright light (known as photic sneeze reflex), sudden change (drop) in temperature, breeze of cold air, a particularly full stomach, exposure to allergens, or viral infection. Because sneezes can spread disease through infectious aerosol droplets, it is recommended to cover one's mouth and nose with the forearm, the inside of the elbow, a facial tissue or a handkerchief while sneezing. In addition to covering the mouth, looking down is also recommended to change the direction of the droplets spread and avoid high concentration in the human breathing heights.

The function of sneezing is to expel mucus containing foreign particles or irritants and cleanse the nasal cavity. During a sneeze, the soft palate and palatine uvula depress while the back of the tongue elevates to partially close the passage to the mouth, creating a venturi (similar to a carburetor) due to Bernoulli's principle so that air ejected from the lungs is accelerated through the mouth and thus creating a low pressure point at the back of the nose. This way air is forced in through the front of the nose and the expelled mucus and contaminants are launched out the mouth. Sneezing with the mouth closed does expel mucus through the nose but is not recommended because it creates a very high pressure in the head and is potentially harmful.

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Bernoulli's principle in the context of Teapot dribble

The teapot effect, also known as dribbling, is a fluid dynamics phenomenon that occurs when a liquid being poured from a container runs down the spout or the body of the vessel instead of flowing out in an arc.

Markus Reiner coined the term "teapot effect" in 1956 to describe the tendency of liquid to dribble down the side of a vessel while pouring. Reiner received his PhD at TU Wien in 1913 and made significant contributions to the development of the study of flow behavior known as rheology. Reiner believed the teapot effect could be explained by Bernoulli's principle, which states that an increase in the speed of a fluid is always accompanied by a decrease in its pressure. When tea is poured from a teapot, the liquid's speed increases as it flows through the narrowing spout. This decrease in pressure was what Reiner thought to cause the liquid to dribble down the side of the pot.However, a 2021 study found the primary cause of the phenomenon to be an interaction of inertia and capillary forces. The study found that the smaller the angle between the container wall and the liquid surface, the more the teapot effect is slowed down.

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Bernoulli's principle in the context of Carburetor

A carburetor (also spelled carburettor or carburetter) is a device used by a gasoline internal combustion engine to control and mix air and fuel entering the engine. The primary method of adding fuel to the intake air is through the Venturi effect or Bernoulli's principle or with a Pitot tube in the main metering circuit, though various other components are also used to provide extra fuel or air in specific circumstances.

Since the 1990s, carburetors have been largely replaced by fuel injection for cars and trucks, but carburetors are still used by some small engines (e.g. lawnmowers, generators, and concrete mixers) and motorcycles. In addition, they are still widely used on piston-engine–driven aircraft. Diesel engines have always used fuel injection instead of carburetors, as the compression-based combustion of diesel requires the greater precision and pressure of fuel injection.

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Bernoulli's principle in the context of Propeller

A propeller (often called a screw if on a ship or an airscrew if on an aircraft) is a device with a rotating hub and radiating blades that are set at a pitch to form a helical spiral which, when rotated, exerts linear thrust upon a working fluid such as water or air. Propellers are used to pump fluid through a pipe or duct, or to create thrust to propel a boat through water or an aircraft through air.

The blades are shaped so that their rotational motion through the fluid causes a pressure difference between the two surfaces of the blade by Bernoulli's principle which exerts force on the fluid. Most marine propellers are screw propellers with helical blades rotating on a propeller shaft with an approximately horizontal axis.

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Bernoulli's principle in the context of Diffuser (thermodynamics)

A diffuser is "a device for reducing the velocity and increasing the static pressure of a fluid passing through a system”. The fluid's static pressure rise as it passes through a duct is commonly referred to as pressure recovery. In contrast, a nozzle is used to increase the discharge velocity and lower the pressure of a fluid passing through it.

Frictional effects during analysis can sometimes be important, but usually they are neglected. Ducts containing fluids flowing at low velocity can usually be analyzed using Bernoulli's principle. Analyzing ducts flowing at higher velocities with Mach numbers in excess of 0.3 usually require compressible flow relations.

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