Venturi effect

speed at "1" is lower than at "2".]] , showing the columns connected in a U-shape (a manometer) and partially filled with water. The meter is "read" as a differential pressure head in cm or inches of water.]]

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

Background

According to the laws governing fluid dynamics, a fluid's velocity must increase as it passes through a constriction to satisfy the conservation of mass, while its pressure must decrease to satisfy the conservation of energy. Thus any gain in kinetic energy a fluid may accrue due to its increased velocity through a constriction is negated by a drop in pressure. An equation for the drop in pressure due to the Venturi effect may be derived from a combination of Bernoulli's principle and the continuity equation.

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. In choked flow the mass flow rate will not increase with a further decrease in the downstream pressure environment.

However, mass flow rate for a compressible fluid can 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.

Referring to the diagram to the right, using Bernoulli's equation in the special case of incompressible flows (such as the flow of water or other liquid, or low speed flow of gas), the theoretical pressure drop ($p\_1\; -\; p\_2$) at the constriction would be given by:

$\backslash tfrac\{\backslash rho\}\{2\}(v\_2^2\; -\; v\_1^2)$

where $\backslash rho\backslash ,$ is the density of the fluid, $v\_1$ is the (slower) fluid velocity where the pipe is wider, $v\_2$ is the (faster) fluid velocity where the pipe is narrower (as seen in the figure). This assumes the flowing fluid (or other substance) is not significantly compressible - even though pressure varies, the density is assumed to remain approximately constant.

Experimental apparatus

Venturi tubes

The simplest apparatus, as shown in the photograph and diagram, is a tubular setup known as a Venturi tube or simply a venturi. Fluid flows through a length of pipe of varying diameter. To avoid undue drag, a Venturi tube typically has an entry cone of 30 degrees and an exit cone of 5 degrees. To account for the assumption of an inviscid fluid a coefficient of discharge is often introduced, which generally has a value of 0.98.

Orifice plate

Venturi tubes are more expensive to construct than a simple orifice plate which uses the same principle as a tubular scheme, but the orifice plate causes significantly more permanent energy loss.

Instrumentation and Measurement

Venturis are used in industrial and in scientific laboratories for measuring the flow of liquids.

Flow rate

A venturi can be used to measure the volumetric flow rate $Q$.

Since :$\backslash begin\{cases\}\; Q\; =\; v\_1A\_1\; =\; v\_2A\_2\backslash \backslash \; p\_1\; -\; p\_2\; =\; \backslash frac\{\backslash rho\}\{2\}(v\_2^2\; -\; v\_1^2)\; \backslash text\{,\}\; \backslash end\{cases\}$ then :$Q\; =\; A\_1\backslash sqrt\{\backslash frac\{2\backslash left(p\_1\; -\; p\_2\backslash right)\}\{\backslash rho\backslash left(\backslash left(\backslash frac\{A\_1\}\{A\_2\}\backslash right)^2-1\backslash right)\}\}\; =\; A\_2\backslash sqrt\{\backslash frac\{2\backslash left(p\_1\; -\; p\_2\backslash right)\}\{\backslash rho\backslash left(1-\backslash left(\backslash frac\{A\_2\}\{A\_1\}\backslash right)^2\backslash right)\}\}\; \backslash text\{.\}$ 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 a 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.

Examples

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

Cargo Eductors on Oil, Product and Chemical ship tankers

Inspirators that mix air and flammable gas in grills, gas stoves, Bunsen burners and airbrushes

Water aspirators that produce a partial vacuum using the kinetic energy from the faucet water pressure

Steam siphons using the kinetic energy from the steam pressure to create a partial vacuum

Atomizers that disperse perfume or spray paint (i.e. from a spray gun).

Foam firefighting nozzles and extinguishers

Carburetors that use the effect to suck gasoline into an engine's intake air stream

Wine aerators, used to infuse air into wine as it is poured into a glass

The capillaries of the human circulatory system, where it indicates aortic regurgitation

Aortic insufficiency is a chronic heart condition that occurs when the aortic valve's initial large stroke volume is released and the Venturi effect draws the walls together, which obstructs blood flow, which leads to a Pulsus Bisferiens.

Protein skimmers (filtration devices for saltwater aquaria)

In automated pool cleaners that use pressure-side water flow to collect sediment and debris

The barrel of the modern-day clarinet, which uses a reverse taper to speed the air down the tube, enabling better tone, response and intonation

Compressed air operated industrial vacuum cleaners

Venturi scrubbers used to clean flue gas emissions

Injectors (also called ejectors) used to add chlorine gas to water treatment chlorination systems

Steam injectors use the Venturi effect and the latent heat of evaporation to deliver feed water to a steam locomotive boiler.

Sand blasters used to draw fine sand in and mix it with air

Emptying bilge water from a moving boat through a small waste gate in the hull—the air pressure inside the moving boat is greater than the water sliding by beneath

A scuba diving regulator to assist the flow of air once it starts flowing

Modern vaporizers to optimize efficiency

In Venturi masks used in medical oxygen therapy

In recoilless rifles to decrease the recoil of firing

Ventilators

The diffuser on an automobile

Large cities where wind is forced between buildings

The leadpipe of a trombone, affecting the timbre

Foam proportioners used to induct Fire fighting foam foam concentrate into fire protection systems

A simple way to demonstrate the Venturi effect is to squeeze and release a flexible hose in which fluid is flowing: the partial vacuum produced in the constriction is sufficient to keep the hose collapsed.

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 though 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.

See also

Venturi flume

Bernoulli's principle

De Laval nozzle

Bunsen burner

Choked flow

Orifice plate

Pitot tube

External links

3D animation of the Differential Pressure Flow Measuring Principle (Venturi meter)

References

Category:Fluid dynamics