**Venturi effect** is the reduction in pressure (and increase in speed) that a fluid experiences when it flows through a constricted section of a pipe. We are going to use both the continuity equation and the Bernoulli’s equation to explain it. We will assume that all parts of the pipe are at the same height, so there are no variations in potential energy.

Consider the situation depicted in the figure below, where an **incompressible fluid** flows through a pipe which has two different cross-sectional areas, one smaller than the other:

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In order to understand what happens when the fluid flows through the pipe, we are going to apply both the continuity and the Bernoulli’s equations:

Isolating v_{2} from the continuity equation and substituting into Bernoulli’s equation:

Since A_{2} is smaller than A_{1}:

From the previous equation it can be seen that pressure is smaller at A_{2}, where the cross-sectional area is smaller. This effect is behind the principle of operation of the atomizer, the aquarium aerators, and also the so called **Venturi meter**.

The Venturi meter is a tube filled with a fluid of density ρ_{fl}. The tube is connected to the pipe where we want to measure the speed of the fluid (or its rate of flow). The difference in height of the fluid on the two sides of the U-tube is caused by the pressure difference between the two cross-sectional areas of the pipe, and is given by Pascal’s law:

Using the Bernoulli’s equation we can determine the speed of the fluid as a function of h:

If you want to see a solved problem of application of the Venturi effect, click here.

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