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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.
Read More: NCERT Solutions For Class 11 Physics Mechanical Properties of Fluids
| Table of Content |
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
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.
Read More: Mechanical Properties of Fluids Important Questions
Solved ExampleExample: 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
Area of the circular pipe can be calculated using the formula, Using the Flow Rate Formula, Q = Av 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
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| 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.
Read More: Mechanical Properties of Fluids MCQs
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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