# Flow Rate Formula

Flow rate is the measurement of how much liquid travels in a given length of time, as the name implies. Its current is also affected by the pipe’s diameter. The flow rate of a fluid is its ability to flow from one point to another.

### What is Flow Rate?

The flow rate of a liquid is defined as the measure of the volume of liquid that moves in a certain amount of time. It is the amount of fluid that moves through a given area in a given amount of time. It can be interpreted as the velocity of the liquid for a cross-sectional area of the pipe.

It varies directly with the area of the pipe and the velocity with which the liquid flows in a pipe.

- It is denoted by the symbol Q.
- Its standard unit of measurement is cubic meters per second (m
^{3}/s) and the dimensional formula is given by [M^{0}L^{3}T^{-1}].

**Flow Rate Formula**

The formula for flaw rate is given as,

Q = Avwhere,

- Q is the flow rate,
- A is area of cross section of pipe,
- v is the velocity of the fluid.
The Flow rate Q can also be defined to be the volume of fluid passing by some position through an area during a period of time.

Q = V / twhere,

- V is the volume of fluid and
- t is the period of time taken.

**Sample Problems**

**Problem 1: Calculate the flow rate of liquid moving in a pipe of cross-section 20 m ^{2} at a velocity of 10 m/s.**

**Solution:**

We have,

A = 20

v = 10

Using the formula we have,

Q = Av

= 20 (10)

=

200 m^{3}/s

**Problem 2: Calculate the flow rate of liquid moving in a pipe of cross-section 15 m ^{2} at a velocity of 12 m/s.**

**Solution:**

We have,

A = 15

v = 12

Using the formula we have,

Q = Av

= 15 (12)

=

180 m^{3}/s

**Problem 3: Calculate the flow rate of a liquid moving in a pipe of radius 2 m at a velocity of 10 m/s.**

**Solution:**

We have,

r = 2

v = 10

Calculate the cross section area.

A = πr

^{2}= 3.14 (2) (2)

= 12.56 m

^{2}Using the formula we have,

Q = Av

= 12.56 (10)

=

125.6 m^{3}/s

**Problem 4: Calculate the velocity of the liquid if its flow rate is 100 m ^{3}/s in a pipe of cross-section 50 m^{2}.**

**Solution:**

We have,

Q = 100

A = 50

Using the formula we have,

Q = Av

or

v = Q/A

= 100/50

=

2 m/s

**Problem 5: Calculate the velocity of the liquid if its flow rate is 144 m ^{3}/s in a pipe of cross-section 36 m^{2}.**

**Solution:**

We have,

Q = 144

A = 36

Using the formula we have,

Q = Av

or

v = Q/A

= 144/36

=

4 m/s

**Problem 6: Calculate the area of the cross-section if its flow rate is 90 m ^{3}/s moving at a velocity of 15 m/s.**

**Solution:**

We have,

Q = 90

v = 15

Using the formula we have,

Q = Av

or A = Q/v

= 90/15

=

6 m^{2}

**Problem 7: Calculate the area of the cross-section if its flow rate is 120 m ^{3}/s moving at a velocity of 45 m/s.**

**Solution:**

We have,

Q = 120

v = 45

Using the formula we have,

Q = Av

or

A = Q/v

= 120/45

=

2.66 m^{2}