Flow Rate Formula

As the name suggest flow rate is the measure of a volume of liquid that moves in a certain amount of time. Also, its current depends on the diameter of the pipe. Moreover, in this topic, you will learn about the flow rate, flow rate formula, formula’s derivation, and solved example.

Flow Rate

What is the difference that distinct fluid from solid? The answer is that in everyday experience with fluids like water and air and slid like onion and potatoes. Moreover, you may have sensed that a major distinction among these two categories of the matter is in the way they move.

Objects like potatoes and onions are solids since they retain their shape when they are thrown. On the other hand, the air does not retain its shape while moving in and out of your lungs. Furthermore, the matter which is not solid is fluid and their main property is that they can flow. In addition, fluids can move and when they move they change shape and volumes. But, their mass remains the same even when they are moving. Besides, the motion of the fluid is known as flow rate.

In simple words, the tendency of the fluid to move from one place to another is its flow rate.

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Flow Rate Formula

Flow rate is the measure of the volume of liquid that moves in a certain amount of time. Moreover, the flow rate depends upon the channel from which the liquid is passing or the area of the pipe, and the velocity of the liquid. Besides, the formula is
Fluid flow rate = area of the pipe or channel × velocity of the liquid

Q = Av

Derivation of the Flow Rate Formula

Q = refers to the liquid flow rate measured as \(m^{3}\)/s or L/s
A = refers to the area of the pipe or channel in \(m^{2}\)
v = refers to the velocity of the liquid in m/s

Solved Example on Flow Rate 

Example 1

Suppose water is flowing from a circular pipe that has a radius of 0.0800 m. Furthermore, its velocity is 3.30 m/s. So, calculate the flow rate of water that flows from the pipe in liters per second (L/s)?

Solution:

For finding the flow rate first we need to find the area of the circular pipe:

A = \(\pi r^{2}\)
A = \(\pi (0.0800 m)^{2}\)
A = \(\pi (0.00640 m^{2}\)) = 0.0201 \(m^{2}\)

So, the area of the pipe is 0.201 \(m^{2}\). Now we can find the flow rate

Q = Av
Q = (0.0201 \(m^{2}\)) (3.30 m/s) = 0.663 \(m^{3}/s\)

Furthermore, we can convert it into liters per second: 1 \(m^{3}/s\) = 1000 L/s.

Q = 0.663 \(m^{3}/s\) × \(\frac{1000 L/s}{1 m^{3}/s}\)

Q = 66.3 L/s

So, the flow rate through a circular pipe is 66.3 L/s.

Example 2

Another example, water is flowing through an open rectangular chute. Also, the width of the chute is 1.20 m and the depth of water flowing inside it is 0.200 m. Moreover, the velocity of water is 5.0 m/s. Then find out the flow rate of the water through the chute in liters per second (L/s)?

Solution:

First of all, we need the find the area of the chute.

A = wh
A =( 1.20 m) (0.200 m) = 0.240 \(m^{2}\)

So, now we can find the flow rate using the flow rate formula

Q = Av
Q =(0.240 \(m^{2}\)) (5.00 m/s) = 1.20 \(m^{3}/s\)

For the answer in L/s we need to convert 1.20 \(m^{3}/s\) in L/s using 1 \(m^{3}/s\) = 1000 L/s

Q = 1.20 \(m^{3}/s\) × \(\frac{1000 L/s}{1 m^{3}/s}\)

Q = 1200 L/s

The flow rate of the chute is 1200 L/s.