# Venturi effect

The pressure in the first measuring tube (1) is higher than at the second (2), and the fluid speed at "1" is lower than at "2", because the cross-sectional area at "1" is greater than at "2".
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.
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.

When a fluid such as water flows through a tube that narrows to a smaller diameter, the partial restriction causes a higher pressure at the inlet than that at the narrow end. This pressure difference causes the fluid to accelerate toward the low pressure narrow section, in which it thus maintains a higher speed. The Venturi meter uses the direct relationship between pressure difference and fluid speeds to determine the volumetric flow rate.

### Relationship between pressure and flow speed

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.

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:

$p_1 - p_2 = \frac{\rho}{2}\left(v_2^2 - v_1^2\right)$

where $\scriptstyle \rho\,$ is the density of the fluid, $\scriptstyle v_1$ is the (slower) fluid velocity where the pipe is wider, $\scriptstyle v_2$ 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.

### 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. 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.

## Experimental apparatus

Venturi tube demonstration apparatus built out of PVC pipe and operated with a vacuum pump
A pair of venturi tubes on a light aircraft, used to provide airflow for air-driven gyroscopic instruments

### 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.

Venturi tubes are available in various sizes from 100 mm to 813 mm with flow coefficient value of 0.984 for all diameter ratios.They are widely used due to low permanent pressure loss. They are more accurate over wide flow ranges than orifice plates or flow nozzles. However it is not used where the Reynolds number is less than 150,000.[1]

Venturi tubes are used in processes where permanent pressure loss is required and where maximum accuracy is needed in case of high viscous liquids.

### 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.[2]

## Instrumentation and measurement

Venturis 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, $\scriptstyle Q$.

Since

\begin{align} Q &= v_1A_1 = v_2A_2\\ p_1 - p_2*h1 &= \frac{\rho}{2}(v_2^2 - v_1^2) \end{align}

then

$Q = A_1\sqrt{\frac{2}{\rho} \cdot \frac{\left(p_1 - p_2\right)}{\left(\frac{A_1}{A_2}\right)^2 - 1}} = A_2\sqrt{\frac{2}{\rho} \cdot \frac{\left(p_1 - p_2\right)}{1 - \left(\frac{A_2}{A_1}\right)^2}}$

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]

## Examples

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

The Bernoulli 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 differentials that create suction as demonstrated and measurable by gas/fluid pressure and velocity equations derived from the Bernoulli Principle 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.[2]