Venturi effect

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The pressure at "1" is higher than at "2", and the fluid speed at "1" is lower than at "2", because the cross-sectional area at "1" is greater than at "2".

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A flow of air through a venturi meter, 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.

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Flow in a Venturi tube

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

The Venturi effect is a jet effect; as with a funnel the velocity of the fluid increases as the cross sectional area decreases, with the static pressure correspondingly decreasing. According to the laws governing fluid dynamics, a fluid's velocity must increase as it passes through a constriction to satisfy the principle of continuity, while its pressure must decrease to satisfy the principle of conservation of mechanical 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. Increasing source temperature will also increase the local sonic velocity, thus allowing for increased mass flow rate.

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 at the constriction is given by:

\[p_1 - p_2 = \frac{\rho}{2}(v_2^2 - v_1^2)\]

where \(\rho\,\) 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

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Venturi tube demonstration apparatus built out of PVC pipe and operated with a vacuum pump

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.^[1]

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 \[ \begin{cases} Q = v_1A_1 = v_2A_2\\ p_1 - p_2 = \frac{\rho}{2}(v_2^2 - v_1^2) \text{,} \end{cases} \] then \[ Q = A_1\sqrt{\frac{2\left(p_1 - p_2\right)}{\rho\left(\left(\frac{A_1}{A_2}\right)^2-1\right)}} = A_2\sqrt{\frac{2\left(p_1 - p_2\right)}{\rho\left(1-\left(\frac{A_2}{A_1}\right)^2\right)}} \text{.} \] 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 discussion of this type of siphon.

Differential Pressure

Main article: Pressure head

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 concentrate into fire protection systems

The Bernouli Principle and its corollary, the Venturi effect, are essential to aerodynamic as well as hydrodynamic design concepts. Airfoil and hydrofoil designs to lift and steer air and water vessels (airplanes, ships and submarines) are derived from applications of the Bernouoli Principle and the Venturi effect, as are the instruments that measure rate of movement through the air or water (velocity indicators). Stability indication and control mechanisms such as gyroscopic attitude indicators and fuel metering devices, such as carburetors, function as a result of gas or fluid pressure differntials that create suction as demonstrated and measurable by gas/fluid pressure and velocity equations derived from the Bernouli Principle and and the Venturi Effect.

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.^[1]