Volumetric Flow Rate
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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:
volumetric flow rate = ^{volume}/_{time}
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 cm^{3} or 12 litres (30 cm x 20 cm x 20 cm = 12,000 cm^{3}). 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 cm^{3} or 30 litres (30 cm x 20 cm x 50 cm = 30,000 cm^{3}). 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 |
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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 cm^{3} | 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 cm^{2} x 10 cm / second |
Q = 6,000 cm^{3}/second | Q = 6,000 cm^{3}/second |
So, the volumetric flow rate is 6,000 cm^{3}/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 cm^{3} / 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 cm^{3} / second
Moving on
In the next tutorial we'll apply what we've learned about volumetric flow rate to explore the equation of continuity.