The Venturi effect is the decrease in pressure that occurs when the flow rate of a fluid—a liquid or gas—increases through a constriction in a tube. It is directly related to the Bernoulli effect, which concerns the relationship between pressure and flow rate in more general circumstances.
When a volume of liquid or gas is at rest, the pressure at any point is the sum of any external pressure applied to the sample of fluid and the force per unit area arising from the weight of the fluid above that point. This pressure is therefore the same at all points in a horizontal plane within a given sample of fluid—a key principle of hydrostatics, the science of fluids at rest. When a fluid is in motion, the condition of constant pressure at a given height does not necessarily prevail, and the dynamic pressures of fluids in motion are governed by the laws of aerodynamics (for gases) and hydrodynamics (for liquids).
In 1791, the Italian physicist Giovanni Venturi started to examine the behavior of fluids flowing through constricted channels. He noted that the increases in flow rates caused by constrictions were accompanied by reductions in the pressure of the fluid. This phenomenon, known as the Venturi effect, can be demonstrated by holding two sheets of paper parallel to one another and blowing into the gap between them. The sheets form a constricted channel, and the increase in flow rate produces a reduction in pressure that causes the two sheets to move toward each other.
The Venturi effect has since found many and diverse applications, ranging from the measurement of the flow rates of liquids to the production of aerosols of paint in air brushes.
Bernoulli effect
A theoretical explanation of the Venturi effect was postulated many years before Venturi’s observations by the Swiss mathematician and physicist, Daniel Bernoulli. In 1738, Bernoulli established a connection between the pressure and flow rate of a fluid by applying the principle of conservation of energy to an idealized incompressible fluid of negligible viscosity and streamlined flow.
Bernoulli’s theory can be understood by considering the motion of such a fluid in a horizontal pipe section. If there is a reduction in pressure from one end of the section of tube to the other—from p1 to p2, say—then the fluid will flow from the high pressure to the low pressure. For an interval of time in which the fluid advances through the tube by a distance d, work is done by the more fluid entering that section or by a piston in the tube, for example. According to basic mechanics, work is the product of force, F, and distance. The force is the product of the pressure and the cross section of the tube, A, so the work done on the fluid is p1Ad. More conveniently, the work done per unit volume of fluid is p1, since the volume of fluid that has flowed through the section is the product of the cross section and the distance moved through the tube, Ad.
At the other end of the section of tube, the fluid in the section under consideration does work on the fluid beyond the section or on a piston that is given by p2Ad. Hence, the net work done on the fluid in the section, per unit volume of flow, is the difference: p1 – p2 . The conservation of energy demands that this work done must end up as some other form of energy, and so it does: the result is an increase in kinetic energy.
If the velocity of the flow increases from v1 to v2 through the section, the increase in kinetic energy is ½mv2 – ½mv2, where m is the mass of fluid that has flowed. In terms of the energy change per unit volume of flow, which must be equal to the work done on the fluid, this expression becomes ½ρ(v2 – v2), where ρ is the density (mass per unit volume) of the fluid. Applying the conservation of energy gives the following:
The second of these equations makes it clear that the sum of pressure and kinetic energy per unit volume must remain constant, the implication being that an increase in flow speed (and therefore kinetic energy) must be accompanied by a reduction in pressure, which is the basis of the Venturi effect.
The above description was formulated for a horizontal flow, but it is easily extended to more general cases if one change is made: include the contribution of potential energy to the total energy per unit volume. Since the change in potential energy for a mass m in moving from height h1 to height h2 is mg(h2 – h1)), where g is acceleration due to gravity, the change in potential energy per unit volume is ρg(h2 – h1), and the sum of pressure, kinetic energy per unit volume, and potential energy per unit volume must remain constant:
Bernoulli’s statement of energy conservation is a good approximation for low-viscosity fluids such as air and water. It applies not only to flow through constricted channels—the Venturi effect—but also to the flow around aircraft wings, where the more rapid flow over the upper surface of an airfoil produces lift, and to the flow of air around sails and water around rudders of boats.
