# Venturi principle: continuity equation, Bernoulli’s principle

**Venturi principle**

Venturi principle is a special case of Bernoulli’s principle.

**Continuity Equation**

**Continuity Equation**

The continuity equation is an example of the conservation of energy. We know that in a pipe, the total mass of the flowing fluid remains constant. In other words, there is a conservation of energy.

Mathematically,

**AV = constant,** where A= cross-sectional area of the pipe

V= velocity of the fluid flowing at the same cross-sectional area of the pipe

Now, let us consider that the pipe is uneven as shown in the figure above. But, the total energy of the fluid at any point in the pipe remains constant.

So, **A _{1}V_{1 }= A_{2}V**

_{2 }where

**A**

_{1}> A_{2}Thus due to this reason **V _{2}>V_{1}**

In other words, if the cross-sectional area of the pipe decreases then the velocity of the fluid flowing through that point increases.

**Bernoulli’s Principle**

**Bernoulli’s Principle**

A reduction in the pressure of the fluid as a result of an increase in the velocity is known as Bernoulli’s principle.

### Working mechanism of Bernoulli’s principle

The total energy at any point in the fluid is given by three factors.

- Pressure energy: Pressure energy is the pressure exerted by one fluid molecule on another
- Kinetic energy: Energy as a result of the motion of fluid
- Potential energy: Energy as a result of the height of the fluid

We can see the equation in the figure. If h_{1} = h_{2} then, potential energy remains constant. Since, A_{2}< A_{1}, the velocity of the fluid at point 2 is more than at point 1 (V_{2}>V_{1}). So, kinetic energy is more in narrow areas in comparison to the broader area. But total energy on both sides of the equation is constant. So, the pressure in narrow points decreases. Thus when the velocity of the fluid increases pressure decreases.

**Venturi Principle**

**Venturi Principle**

Now, if you make a hole at point 2 in the tube, the atmospheric air enters the tube (due to pressure gradient). This phenomenon is known as the Venturi principle.

**Applications of Venturi principle**

- Venturi mask
- Orifice plate
- Venturi nozzle