Flow Rate Formula: Bernoulli’s Principle & Solved Examples

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Flow Rate is the measure of the quantity of fluid passing through a pipe or channel per unit of time. Flow Rate is an important concept in fluid dynamics and other engineering fields.

Fluid Flow is the tendency of the fluid to move from one place to another.
Flow rate depends on the area of the pipe and the velocity of the liquid.
It is expressed in the units of litres per meter (lpm) or gallons per metre (gpm).

Flow Rate Formula is given as

Q = Av

Here, A is the area of the channel and v is the flow velocity.

Table of Content

What is Flow Rate?
Flow Rate Formula
Bernoulli’s Principle
Things to Remember
Previous Year Questions
Sample Questions

Key Terms: Flow Rate, Flow Rate Formula, Fluids, Bernoulli’s Principle, Velocity, Liquid Flow Rate, Fluid Motion

What is Flow Rate?

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Flow Rate is the measurement of the volume of a fluid that moves in a certain amount of time.

Flow rate depends on the area of the pipe and the velocity of the liquid.
Fluid Flow Rate is the product of area of the pipe and the velocity of the liquid.
It can be articulated either in terms of velocity and area, or time and volume.
It is generally denoted in liters per meter (lpm), or gallons per meter (gpm).

Flow Rate

Flow Rate

Since fluids are generally incompressible, the flow rate into an enclosed region is supposedly equal to the flow of it out of the region.

Read More:

Relevant Concepts
Mechanical Properties of Fluids	Fluid Mechanics Formula	Difference Between Fluid & Liquid
Poiseuille's Law Formula	Continuity Equation	Mechanical Properties of Fluids Formula

Flow Rate Formula

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Flow Rate is defined as the quantity of fluid flowing through channel in the specified period of time. It is the product of the area of the pipe or channel and the velocity of the fluid.

Fluid Flow Rate = Area of Pipe/Channel x Velocity of Fluid

Thus, Flow Rate Formula is given as

Q = Av

Where

Q = Liquid Flow Rate measured in m3/s or L/s.
A = Area of Pipe or Channel Source in m2.
v = Velocity of Liquid in m/s.

Solved Example Example: Water is flowing from a circular pipe that has a radius of 7 m with a velocity of 5 m/s. Calculate the flow rate of water that flows from the pipe in liters per second (L/s). Solution: Given that Radius of Pipe: 7 m Velocity of Water: 5 m/s Area of the circular pipe can be calculated using the formula, A = πr² A = π (7 m)² A = π (49 m²) = 154 m² Using the Flow Rate Formula, Q = Av Q = (154 m²) (5 m/s) = 770 m³/s Converting into liters per second, 1 m³/s = 1000 L/s. Q = 770 m³/s x \(\frac{1000 L/s}{1 m3/s}\) Q = 770000 L/s. Hence, the flow rate of water through a circular pipe is 770000 L/s.

Bernoulli’s Principle

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Bernoulli’s Principle was discovered by Daniel Bernoulli, a Swiss Mathematician in 1738. Bernoulli’s Principle states that

“Total mechanical energy of a moving fluid along with the gravitational potential energy of elevation, the energy related to the fluid pressure and the kinetic energy of the fluid motion, remains constant.”

Bernoulli’s Principle generally gives an overview of fluid dynamics in a nutshell.
It specifies that as the speed of the fluid tends to increase, the pressure is seen to decrease simultaneously.
The amount of fluid that enters the pipe or an enclosed area, if presuming a steady flow, then it must be equivalent to the amount of fluid that actually leaves the pipe, leading the fluid speed to increase in the thin region.
Bernoulli’s principle expresses the energy conservation of every ideal fluid in a steady flow.

Bernoulli’s Theorem Detailed Explanation

Check More:

Related Topics
Properties of Fluids	Dynamic Viscosity	Froude Number Formula
Fluid Friction	Viscosity	Pitot Tube

Things to Remember

Flow rate is the measure of the volume of a fluid moving through a channel within a certain amount of time.
Flow Rate of a fluid depends on the area of the pipe and the velocity of the liquid.
Fluid Flow Rate = Area of Pipe/Channel x Velocity of Fluid
Flow Rate Formula is expressed as Q = Av, where A is the area of the pipe and v is the velocity of fluid.
Bernoulli’s principle states that as the speed of the fluid tends to increase, the pressure evidently decreases.

Previous Years’ Questions

An ideal fluid flows (laminar flow) through a pipe of… (JEE Main - 2020)
Under a constant pressure head, the rate of flow of orderly… (COMEDK UGET - 2015)
Liquid of density ρ flows along a horizontal pipe of…
The equation of continuity in incompressible fluid flow… (KEAM - 2016)
An ideal fluid flows through a pipe of circular cross-section…
The flow of liquid in a tube is laminar, when the value of… (KEAM - 2016)
Streamline flow is more likely for liquids with…
Specific gravity of a fluid is a dimensionless quantity… (AIIMS - 2005)
Bernoulli’s principle is based on the law of conservation… (UPSEE - 2010)
Bernoulli's theorem is applicable in the case of…

Sample Questions

Ques. Assume that a source of water is flowing from a circular pipe that has a radius of 0.0800 m with a velocity of 3.30 m/s. Calculate the flow rate of water that flows from the pipe in liters per second (L/s)? (5 Marks)

Ans. It is given that,

Radius of Pipe: 0.0800 m
Velocity of Water: 3.30 m/s

Area of the circular pipe will be calculated as
A = πr²
A = π (0.0800 m)²
A = π (0.00640 m²) = 0.0201 m²

Using the Flow Rate Formula,

Q = Av
Q = (0.0201 m²) (3.30 m/s) = 0.663 m³/s

Therefore, it can now be converted into liters per second = 1 m³/s = 1000 L/s.

For finding the flow rate,

Q = 0.663 m³/s x \(\frac{1000 L/s}{1 m3/s}\)

Q = 66.3 L/s.

Hence, the value of the flow rate through a circular pipe is 66.3 L/s.

Ques. Determine the flow rate of fluid presuming that it is moving with a velocity of 20 m/s through a certain pipe that has a diameter of 0.03 m. (3 Marks)

Ans. Given that,

Velocity, v = 20 m/sDiameter, d = 0.03 m

Consider that the cross-sectional area of the pipe is,

A = \(\frac{\pi}{4}\)d²

Hence, A = [(3.14)/4] (0.03)(0.03) A = (0.785)(0.0009)
A = 0.000706 m²

Using the Flow Rate Formula,

Q = Av

Q = (20)(0.000706)Q = 0.014139 m³/s

Thus, the flow rate of the liquid is 0.14139 m³/s.

Ques. Find a mass flow rate of the material, assuming that 20 ml of it is acquired in 20 seconds. Additionally, consider that it has a density of 0.5 gm/ml. (3 Marks)

Ans. We know that,

Mass Flow Rate= Mass/Time

Thus, Mass = Volume x DensityMass = 20 x 0.5 = 10

Mass Flow Rate = 10/20 = 0.5

Ques. State Bernoulli’s Principle. (3 Marks)

Ans. Bernoulli’s Principle was given by Daniel Bernoulli, a Swiss Mathematician, in 1738. It states that the mechanical energy in a fluid, alongside the associative energy of its pressure, and the kinetic energy of the motion involved in the fluid is seen to remain constant.

Bernoulli’s Principle offers an outlook of fluid dynamics in a nutshell. It states that as the speed of the fluid increases, the pressure is seen to decrease at the same time.

Ques. Consider that you can acquire 100 grams of liquid in about 10 seconds. Determine the mass flow rate of the liquid that passes through a pipe. (3 Marks)

Ans. To determine the mass flow rate, first we need to convert 100 grams to kilograms.

Thus, 100 grams = 0.1 Kg

Now,

Mass = 0.1 Kg
Time = 10 Seconds

Therefore, Mass Flow Rate = 0.1/10 = 0.01 Kg/s

Ques. Define Flow Rate. (2 Marks)

Ans. Flow rate can be defined as the amount of fluid that seemingly passes through a specific point, completely based on the temperature and pressure.

Ques. What is a mass flow rate of a material of 40 ml if it is obtained in 40 seconds? The substance has a density of 0.25 gm/ml. (2 Marks)

Ans. We know,

Mass Flow Rate= Mass/Time

Thus, Mass = Volume x Density

Mass = 40 x 0.25 = 10

Mass Flow Rate = Mass/Volume

Mass Flow Rate = 10/40 = 0.25

Ques. At what flow rate, is the 500 grams of liquid passing through a pipe obtained in 10 seconds? (2 Marks)

Ans. Converting 100 grams in terms of kilograms, we get,

Mass = 500 grams = 0.5 kg
Time = 10 seconds

Mass Flow Rate = Mass/Volume

Therefore, Mass Flow Rate = \(\frac{0.5}{10}\) = 0.05 Kg/s

Ques. Assume that an incompressible fluid is flowing through an enclosed region, like a pipe. Now, consider that at point 1 in it, the volume flow rate is recorded to be 10 m3/s. However, at point 2 along the pipe, the area is witnessed to half. Determine the volume flow rate at point 2. (2 Marks)

Ans. Assuming that the area is seen to half, the fluid’s velocity will seemingly double. But, at the same time, the volume flow rate, which is the product of these two quantities, will supposedly stay constant. In simple terms, the volume of water that flows through point 1 per second is equivalent to the volume of water flowing through point 2 per second.

Ques. Determine Equation of Continuity. (3 Marks)

Ans. Equation of continuity expresses that, for a steady flow, the fluid that flows from one point to another should be equivalent to the amount of fluid that passes past another location. Here, the mass flow rate usually remains constant. It occurs since both liquids and gasses are considered fluids.

In a nutshell, according to the continuity equation, the mass of air that enters an encompassed pipe system is equivalent to the mass of air that exits the pipe system. It generally exhibits the law of conservation of mass.

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Flow Rate Formula: Bernoulli’s Principle & Solved Examples

What is Flow Rate?

Flow Rate Formula

Solved Example

Bernoulli’s Principle

Things to Remember

Previous Years’ Questions

Sample Questions

CBSE CLASS XII Related Questions

1.
This ‘average velocity’ is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ?

3.
The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

5.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.
Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

Similar Physics Concepts

Comments

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Flow Rate Formula: Bernoulli’s Principle & Solved Examples

What is Flow Rate?

Flow Rate Formula

Solved Example

Bernoulli’s Principle

Things to Remember

Previous Years’ Questions

Sample Questions

CBSE CLASS XII Related Questions

1.This ‘average velocity’ is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ?

3. The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

5.Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
This ‘average velocity’ is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ?

3.
The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

5.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.
Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?