Volume flow rate is the term used in physics that describes the flow of some volume of some matter. It means it gives the flow amount in terms of physical dimensions, but not mass moves through space per unit time. This amount is considered as the flow rate. The term “volume flow rate” almost always applies with liquids and gases but not for solids. Although solid even can move with some steady rate. In this article, the student will learn the volume flow rate formula with examples. Let us learn it!

## What is Volume Flow Rate?

Flow is a common phenomenon in physics for liquids and gases. We have heard the term volume flow rate many times. The volume flow rate of a fluid can be defined to be the volume of fluid which is passing through the given cross-sectional area per unit time. Here cross-sectional area means the area through which something is flowing. Because liquids are incompressible, so any portion of liquid flowing through a pipe could change shape, but still, it will maintain the same volume.

Even this is true if the pipe changes its diameter. So, the volume flow rate for an incompressible fluid at any point along a pipe is the same as the volume flow rate at any other point along a pipe.

Source:en.wikipedia.org

As volume flow rate measures the amount of volume that passes through an area per time, therefore equation for the volume flow rate will look like the ratio of volume to time. It turns out that there is a useful alternative for writing the volume flow rate like this. As rate will be high when the pipe becomes narrow. It means that fluids speed up when they reach a narrow section of a pipe and slow down when they reach a wider section of a pipe.

**The Formula for Volume Flow Rate**

Volume flow rate is represented by the symbol Q, with unit as \(m^{3} s^{-1}\) i.e. cubic meters per second. Therefore the Volume Flow Rate Formula can be written as:

\(Volume Flow Rate = \frac{ (variation of volume) } { (variation of time) }\)

Mathematically, \(Q = \frac { \Delta Vol } { \Delta t }\)

Where,

Q | Volume flow rate |

\(\Delta Vol\) | Volume of the fluid that is variating |

\(\Delta t\) | Variation of time |

**Solved Examples for Volume Flow Rate Formula**

Q.1: A fluid is flowing through a tube which has a transverse area of 0.3 square meters. All the fluid in the tube of 30 cm flows to a container in a period of 5 seconds. Determine the volume flow through the tube using Volume Flow Rate Formula.

Solution : The total volume of the fluid flowing is given by the formula as:

\(Q = \frac{\Delta Vol } { \Delta t }\)

Given parameters are:

\(\Delta Vol = 0.3 m^{2} \times 0.30 m\) ( i.e. product of flow length with cross sewctional area )

\(= 0.09 m^{3} = 90 L ( as 1 m^{3} = 1000 liters )\)

\(\Delta t = 5\) seconds

Thus applying formula,

\(Q = \frac{\Delta Vol } { \Delta t }\)

\(= \frac { 90 } {5}\)

= 18 L per second

Therefore the volume flow rate will be 18 liter per sec.

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