# Venturi effect

The pressure at "1" is higher than at "2" because the fluid speed at "1" is lower 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.

The Venturi effect is the reduction in fluid pressure that results when a fluid flows through a constricted section of pipe. The fluid velocity must increase through the constriction to satisfy the equation of continuity, while its pressure must decrease due to conservation of energy: the gain in kinetic energy is balanced by a drop in pressure or a pressure gradient force. An equation for the drop in pressure due to venturi effect may be derived from a combination of Bernoulli's principle and the equation of continuity.

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 convergent-divergent 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 low speed flow of gas), the theoretical pressure drop (p1p2) at the constriction would be given by $\rho(v_2^2 - v_1^2)/2$.

The Venturi effect is named after Giovanni Battista Venturi, (1746–1822), an Italian physicist.

## Experimental apparatus

This is a 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.
A venturi can be used to measure the volumetric flow rate.
Since
$\begin{cases} Q = v_1A_1 = v_2A_2\\ p_1 - p_2 = \frac{\rho}{2}(v_2^2 - v_1^2) \end{cases}$
Then
$Q = A_1\sqrt{\frac{2\left(p_1 - p_2\right)}{\rho\left(\left(\frac{A_1}{A_2}\right)^2-1\right)}} = A_2\sqrt{\frac{2\left(p_1 - p_2\right)}{\rho\left(1-\left(\frac{A_2}{A_1}\right)^2\right)}}$
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 water 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.
• 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.

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.

## Practical uses

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

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.