# What is the continuity equation?

## Continuity equation

The main objective of atmospheric chemistry is to understand in a **quantitative** way how the different concentrations of the species depend on the control processes among which we have **emissions** , **transport** , **chemistry** and **deposition** . This dependency is expressed mathematically by means of the **continuity equation** , which is responsible for providing the necessary basis for all **research** models of **chemistry** with respect to the atmosphere.

The continuity equation is the relationship that exists between the **area** and the **speed** that a **fluid** has in a given place and that tells us that the **flow** of a fluid is **constant** throughout a hydraulic **circuit** .

- Explanation of the continuity equation
- What is it for
- Continuity equation applied to fluid mechanics
- Other apps
- Examples

## Explanation of the continuity equation

The continuity equation is an equation that explains that the **amount of fluid** that enters through a tube and that is generally measured in **liters / second** is the same as the amount of flow that leaves the same tube, regardless if it had, it has more or less **radius** along it.

When the tube through which the water passes is in the proper conditions, which means that it does not have holes, the amount of **water** that **enters** per **second** as there are no losses must be the **same amount** as the water that **leaves** per second. It must then be assumed that when the inlet of the tube is smaller, the speed of the water must also be less than when the diameter or the outlet section is larger. In this case, the inlet velocity of the water will be greater than the outlet velocity.

## What is it for

At present, the continuity equation is widely used to perform different analyzes of **nozzles** , **pipes** , the height of **turbine ****blades** and **compressors** . The equation of everyday life or mass conversation is a very useful tool to achieve the **analysis of fluids** that flow through **tubes** or **ducts** which have a variable diameter.

## Continuity equation applied to fluid mechanics

Before explaining the continuity of the equation applied to fluid mechanics, it is also important to know that the **continuity equation** starts from the following ideal **bases** :

- The
**fluid**is**incompressible**. - The fluid
**temperature****does not change**. - The flow is
**continuous**, that is, its**speed**and**pressure**do not depend on time. - The flow is
**laminar**. Not turbulent. - There is no
**rotation**within the mass of the fluid, it is a flow that does not rotate. - There are no
**losses**by**friction**in the fluid, ie no viscosity.

The continuity equation is as follows:

**Q _{1} = Q _{2} ⇒ S _{1}**

**ㆍ v**

_{1}= S_{2}**ㆍ v**

_{2}where:

**S**is the**area**of the cross sections of points 1 and 2 of the duct.**v**is the flow**velocity**at points 1 and 2 of the pipe.

In the equation of continuity it is also important to know who is known for **spending ****metric** or **flow** , quantity A. v, in other words, we can say that the **constant** flow is along the tube. The flow is expressed in **m3 / s** and indicates the **volume** of **liquid** that **flows** per unit of time. Thus, if the flow rate is **1m3 / s it** means that in every second 1m3 flows through each area section.

## Other apps

#### Electromagnetism

Regarding electromagnetic theory, the continuity equation is given from two **Maxwell** equations and establishes that the **divergence** of the current **density** is equal to the negative of the derivative of the charge density with respect to **time** , this means that current flow only occurs when the load varies over time.

#### Quantum mechanics

In fluid mechanics, a continuity equation is an equation for the **conservation** of **mass** and the conservation of **probability** .

#### Relativistic mechanics

With respect to the special theory of **relativity** , a continuity equation must be written in **covariant** form . The continuity equation for the **mass density** or for the mass energy and for the density having the linear momentum is written in terms of **the** energy-impulse **tensor** .

## Examples

A very easy example to observe with respect to the phenomenon of continuity can be observed when someone **irrigates** a little **water** using a **hose** , since there it can be seen how when pressing the outlet of the hose we can observe how the water **jet** comes out more triggered, this is where we check this concept.

When a **faucet** is opened little by little , a small jet of water is formed, the radius of which will **decrease** with distance from the faucet and which eventually breaks into drops.