# Volumetric Flow Rate

## Description

This is an introductory tutorial for a series that explores Volumetric Flow Rate. The video tutorial is still to come.

## Introduction

The velocity with which a liquid flows through a pipe is of interest because it influences the way the liquid flows. Also of interest is the amount of liquid which flows through the pipe in a given time period i.e. the volumetric flow rate. In this tutorial we're going to explore what that is, and how it differs to velocity.

## What is Volumetric Flow Rate?

Volumetric flow rate describes the volume of liquid that moves past a point (a cross-sectional area) in a given time unit (e.g. a second). It is represented by the letter Q. We can use either of the following equations to calculate flow rate:

or

### volumetric flow rate = cross-sectional area x velocity

Importantly volumetric flow rate is not the same as speed or velocity. Let's explore how with an example.

## Example: Volumetric Flow Rate vs. Velocity

A volume of water (labelled A in the image below) and a boat are travelling down a river. The volume of the cube of water is 12,000 cm3 or 12 litres (30 cm x 20 cm x 20 cm = 12,000 cm3). Both A and the boat move 50 cm East (to cross-section B) in 5 seconds. This means that the velocity of both is 10 cm East / second (50 cm E / 5 seconds = 10 cm East / second).

In those same 5 seconds, the volume of water that passes through cross-section B is more than that contained in the dimensions of A. It is 30,000 cm3 or 30 litres (30 cm x 20 cm x 50 cm = 30,000 cm3). This is the volume measurement that we use in the volumetric flow-rate calculation. We'll use both formulae in the calculation below to show you that both methods result in the same answer.

volumetric flow rate = volume/time volumetric flow rate = area x velocity

Let's calculate volume first. Let's calculate area first.
volume = width x height x depth area = width x height
volume = 50 cm x 20 cm x 30 cm area = 20 cm x 30 cm
volume = 30,000 cm3 area = 600 cm 2

Now calculate velocity.
velocity = displacement / time
velocity = 50 cm / 5 seconds
velocity = 10 cm / second

Now calculate Flow Rate. Now calculate Flow Rate.
Q = volume/time Q = area x velocity
Q = 30,000 cm3/5 seconds Q = 600 cm2 x 10 cm / second
Q = 6,000 cm3/second Q = 6,000 cm3/second

So, the volumetric flow rate is 6,000 cm3/second (or 6 litres/second).

In the below image, we have increased the cross-sectional dimension of the waterway. Although the water is still travelling with the same velocity (10 cm / second to the East) in this second example, the volumetric flow rate has now increased (to 10,000 cm3 / second).

Q = volume / time
Q = height x width x depth / time
Q = 20 cm x 50 cm x 50 cm / 5 seconds
Q = 50,000 cm3 / 5 seconds
Q = 10,000 cm3 / second

## Moving on

In the next tutorial we'll apply what we've learned about volumetric flow rate to explore the equation of continuity.