# Venturi effect

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The Venturi effect is the reduction in fluid pressure that results when a fluid flows through a constricted section (or choke) of a pipe. The Venturi effect is named after Giovanni Battista Venturi (1746–1822), an Italian physicist.

Giovanni Battista Venturi was an Italian physicist, savant, man of letters, diplomat and historian of science. He was the discoverer of the Venturi effect, which was described in 1797 in his Recherches Experimentales sur le Principe de la Communication Laterale du Mouvement dans les Fluides appliqué a l'Explication de Differens Phenomènes Hydrauliques, translated into English by William Nicholson as "Experimental Inquiries Concerning the Principle of the Lateral Communication of a Motion in Fluids," and published in 1836 in Thomas Tredgold's Tracts on Hyraulics. Because of this discovery, he is the eponym for the Venturi tube, the Venturi flow meter and the Venturi pump.

## Background

In fluid dynamics, an incompressible fluid's velocity must increase as it passes through a constriction in accord with the principle of mass continuity, while its static pressure must decrease in accord with the principle of conservation of mechanical energy. Thus, any gain in kinetic energy a fluid may attain due to its increased velocity through a constriction is balanced by a drop in pressure.

In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics and hydrodynamics. Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation,

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction of motion. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.

In fluid mechanics the term static pressure has several uses:

By measuring the change in pressure, the flow rate can be determined, as in various flow measurement devices such as venturi meters, venturi nozzles and orifice plates.

Flow measurement is the quantification of bulk fluid movement. Flow can be measured in a variety of ways. The common types of flowmeters with industrial applications are listed below:

An orifice plate is a device used for measuring flow rate, for reducing pressure or for restricting flow. Either a volumetric or mass flow rate may be determined, depending on the calculation associated with the orifice plate. It uses the same principle as a Venturi nozzle, namely Bernoulli's principle which states that there is a relationship between the pressure of the fluid and the velocity of the fluid. When the velocity increases, the pressure decreases and vice versa.

Referring to the adjacent diagram, using Bernoulli's equation in the special case of steady, incompressible, inviscid flows (such as the flow of water or other liquid, or low speed flow of gas) along a streamline, the theoretical pressure drop at the constriction is given by:

In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. The principle is named after 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 who derived Bernoulli's equation in its usual form in 1752. The principle is only applicable for isentropic flows: when the effects of irreversible processes and non-adiabatic processes are small and can be neglected.

${\displaystyle p_{1}-p_{2}={\frac {\rho }{2}}\left(v_{2}^{2}-v_{1}^{2}\right)}$

where ${\displaystyle \scriptstyle \rho \,}$ is the density of the fluid, ${\displaystyle \scriptstyle v_{1}}$ is the (slower) fluid velocity where the pipe is wider, ${\displaystyle \scriptstyle v_{2}}$ is the (faster) fluid velocity where the pipe is narrower (as seen in the figure).

The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:

### Choked flow

The limiting case of the Venturi effect is when a fluid reaches the state of choked flow, where the fluid velocity approaches the local speed of sound. When a fluid system is in a state of choked flow, a further decrease in the downstream pressure environment will not lead to an increase in the mass flow rate. However, mass flow rate for a compressible fluid will increase with increased upstream pressure, which will increase the density of the fluid through the constriction (though the velocity will remain constant). This is the principle of operation of a de Laval nozzle. Increasing source temperature will also increase the local sonic velocity, thus allowing for increased mass flow rate but only if the nozzle area is also increased to compensate for the resulting decrease in density.

Choked flow is a compressible flow effect. The parameter that becomes "choked" or "limited" is the fluid velocity.

The speed of sound is the distance travelled per unit time by a sound wave as it propagates through an elastic medium. At 20 °C (68 °F), the speed of sound in air is about 343 metres per second, or a kilometre in 2.9 s or a mile in 4.7 s. It depends strongly on temperature, but also varies by several metres per second, depending on which gases exist in the medium through which a soundwave is propagating.

A de Laval nozzle is a tube that is pinched in the middle, making a carefully balanced, asymmetric hourglass shape. It is used to accelerate a hot, pressurized gas passing through it to a higher supersonic speed in the axial (thrust) direction, by converting the heat energy of the flow into kinetic energy. Because of this, the nozzle is widely used in some types of steam turbines and rocket engine nozzles. It also sees use in supersonic jet engines.

### Expansion of the section

The Bernoulli equation is invertible, and pressure should rise when a fluid slows down. Nevertheless, if there is an expansion of the tube section, turbulence will appear and the theorem will not hold. Notice that in all experimental Venturi tubes, the pressure in the entrance is compared to the pressure in the middle section. The output section is never compared with them.

## Experimental apparatus

A pair of venturi tubes on a light aircraft, used to provide airflow for air-driven gyroscopic instruments

### Venturi tubes

The simplest apparatus is a tubular setup known as a Venturi tube or simply a venturi (plural: "venturis" or occasionally "venturies"). Fluid flows through a length of pipe of varying diameter. To avoid undue aerodynamic drag, a Venturi tube typically has an entry cone of 30 degrees and an exit cone of 5 degrees. [1]

Venturi tubes are used in processes where permanent pressure loss is not tolerable and where maximum accuracy is needed in case of highly viscous liquids.[ citation needed ]

### Orifice plate

Venturi tubes are more expensive to construct than simple orifice plates, and both function on the same basic principle. However, for any given differential pressure, orifice plates cause significantly more permanent energy loss. [2]

## Instrumentation and measurement

Both venturis and orifice plates are used in industrial applications and in scientific laboratories for measuring the flow rate of liquids.

### Flow rate

A venturi can be used to measure the volumetric flow rate, ${\displaystyle \scriptstyle Q}$.

Since

{\displaystyle {\begin{aligned}Q&=v_{1}A_{1}=v_{2}A_{2}\\[3pt]p_{1}-p_{2}&={\frac {\rho }{2}}\left(v_{2}^{2}-v_{1}^{2}\right)\end{aligned}}}

then

${\displaystyle Q=A_{1}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1}}}}=A_{2}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{1-\left({\frac {A_{2}}{A_{1}}}\right)^{2}}}}}}$

A venturi can also be used to mix a liquid with a gas. If a pump forces the liquid through a tube connected to a system consisting of a venturi to increase the liquid speed (the diameter decreases), a short piece of tube with a small hole in it, and last a venturi that decreases speed (so the pipe gets wider again), the gas will be sucked in through the small hole because of changes in pressure. At the end of the system, a mixture of liquid and gas will appear. See aspirator and pressure head for discussion of this type of siphon.

### Differential pressure

As fluid flows through a venturi, the expansion and compression of the fluids cause the pressure inside the venturi to change. This principle can be used in metrology for gauges calibrated for differential pressures. This type of pressure measurement may be more convenient, for example, to measure fuel or combustion pressures in jet or rocket engines.

The first large-scale Venturi meters to measure liquid flows were developed by Clemens Herschel who used them to measure small and large flows of water and wastewater beginning at the end of the 19th century. [3] While working for the Holyoke Water Power Company, Herschel would develop the means for measuring these flows to determine the water power consumption of different mills on the Holyoke Canal System, first beginning development of the device in 1886, two years later he would describe his invention of the Venturi meter to William Unwin in a letter dated June 5, 1888. [4]

## Examples

The Venturi effect may be observed or used in the following:

Venturi tubes are also used to measure the speed of a fluid, by measuring pressure changes at different segments of the device. Placing a liquid in a U-shaped tube and connecting the ends of the tubes to both ends of a Venturi is all that is needed. When the fluid flows through the Venturi the pressure in the two ends of the tube will differ, forcing the liquid to the "low pressure" side. The amount of that move can be calibrated to the speed of the fluid flow. [2]

## Related Research Articles

In fluid dynamics, the Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

A pitottube, also known as pitot probe, is a flow measurement device used to measure fluid flow velocity. The pitot tube was invented by the French engineer Henri Pitot in the early 18th century and was modified to its modern form in the mid-19th century by French scientist Henry Darcy. It is widely used to determine the airspeed of an aircraft, water speed of a boat, and to measure liquid, air and gas flow velocities in certain industrial applications.

A turbine is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. The work produced by a turbine can be used for generating electrical power when combined with a generator. A turbine is a turbomachine with at least one moving part called a rotor assembly, which is a shaft or drum with blades attached. Moving fluid acts on the blades so that they move and impart rotational energy to the rotor. Early turbine examples are windmills and waterwheels.

A viscometer is an instrument used to measure the viscosity of a fluid. For liquids with viscosities which vary with flow conditions, an instrument called a rheometer is used. Thus, a rheometer can be considered as a special type of viscometer. Viscometers only measure under one flow condition.

A nozzle is a device designed to control the direction or characteristics of a fluid flow as it exits an enclosed chamber or pipe.

A steam injector is typically used to deliver cold water to a boiler against its own pressure using its own live or exhaust steam, replacing any mechanical pump. This was the purpose for which it was originally invented in 1858 by Henri Giffard. Its operation was from the start intriguing since it seemed paradoxical, almost like perpetual motion, but its operation was later explained using thermodynamics. Other types of injector may use other pressurised motive fluids such as air.

Hydraulic head or piezometric head is a specific measurement of liquid pressure above a vertical datum.

An ultrasonic flow meter is a type of flow meter that measures the velocity of a fluid with ultrasound to calculate volume flow. Using ultrasonic transducers, the flow meter can measure the average velocity along the path of an emitted beam of ultrasound, by averaging the difference in measured transit time between the pulses of ultrasound propagating into and against the direction of the flow or by measuring the frequency shift from the Doppler effect. Ultrasonic flow meters are affected by the acoustic properties of the fluid and can be impacted by temperature, density, viscosity and suspended particulates depending on the exact flow meter. They vary greatly in purchase price but are often inexpensive to use and maintain because they do not use moving parts, unlike mechanical flow meters.

A wet gas is any gas with a small amount of liquid present. The term "wet gas" has been used to describe a range of conditions varying from a humid gas which is gas saturated with liquid vapour to a multiphase flow with a 90% volume of gas. There has been some debate as to its actual definition but there is currently no fully defined quantitative definition of a wet gas flow that is universally accepted.

Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing from an orifice to the height of fluid above the opening. The law states that the speed v of efflux of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth h is the same as the speed that a body would acquire in falling freely from a height h, i.e. , where g is the acceleration due to gravity. This expression comes from equating the kinetic energy gained, , with the potential energy lost, mgh, and solving for v. The law was discovered by the Italian scientist Evangelista Torricelli, in 1643. It was later shown to be a particular case of Bernoulli's principle.

A rocket engine nozzle is a propelling nozzle used in a rocket engine to expand and accelerate the combustion gases produced by burning propellants so that the exhaust gases exit the nozzle at hypersonic velocities.

In fluid mechanics, pressure head is the height of a liquid column that corresponds to a particular pressure exerted by the liquid column on the base of its container. It may also be called static pressure head or simply static head. It is mathematically expressed as:

A spray nozzle is a precision device that facilitates dispersion of liquid into a spray. Nozzles are used for three purposes: to distribute a liquid over an area, to increase liquid surface area, and create impact force on a solid surface. A wide variety of spray nozzle applications use a number of spray characteristics to describe the spray.

Flow conditioning ensures that the “real world” environment closely resembles the “laboratory” environment for proper performance of inferential flowmeters like orifice, turbine, coriolis, ultrasonic etc.

Isentropic nozzle flow describes the movement of a gas or fluid through a narrowing opening without an increase or decrease in entropy.

## References

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3. Herschel, Clemens. (1898). Measuring Water. Providence, RI:Builders Iron Foundry.
4. "Invention of the Venturi Meter". Nature. 136: 254. August 17, 1935. doi:10.1038/136254a0 . Retrieved May 15, 2018. [The article] reproduces a letter from Herschel to the late Dr. Unwin describing his invention of the Venturi Meter. The letter is dated June 5, 1888, and addressed from the hydraulic engineer's office of the Holyoke Water Power Co., Mass. In his letter, Herschel says he tested a one-inch Venturi Meter, under 210 ft. head: 'I am now satisfied that here is a new and pregnant principle to be applied to the art of gauging fluids, inclusive of fluids such as compressed air, illuminating or fuel gases, steam, etc. Further, that the shape of the meter should be trumpet-shaped in both directions; such a meter will measure volumes flowing in either direction, which in certain localities becomes a useful attribute...'
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9. Anderson, John (2017). Fundamentals of Aerodynamics (6th ed.). New York, NY: McGraw-Hill Education. p. 218. ISBN   978-1-259-12991-9.