Venturi effect

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

The Venturi effect is the fluid pressure that results when an incompressible fluid flows through a constricted section of pipe. The Venturi effect may be derived from a combination of Bernoulli's principle and the equation of continuity. 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 supplied by a drop in pressure or a pressure gradient force.

The limiting case of the Venturi effect is choked flow, in which a constriction in a pipe or channel limits the total flow rate through the channel, because the pressure cannot drop below zero in the constriction. Choked flow is used to control the delivery rate of water and other fluids through spigots and other valves.

Referring to the diagram to the right, using Bernoulli's equation in the special case of incompressible fluids (such as the approximation of a water jet), the theoretical pressure drop (p1p2) at the constriction would be given by \frac{\rho}{2}(v_2^2 - v_1^2).

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 fluid with air. If a pump forces the fluid 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), air will be sucked in through the small hole because of changes in pressure. At the end of the system, a mixture of fluid and air 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.

See also

Wikipedia content modification information:

  • This page was last modified on 4 December 2008, at 15:43.

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