Bernoulli’s Principle is a very important concept in Fluid Mechanics which is the study of fluids (like air and water) and their interaction with other fluids. Bernoulli’s principle is also referred to as Bernoulli’s Equation or Bernoulli Theorem.
This principle was first stated by Daniel Bernoulli and then formulated in Bernoulli’s Equation by Leonhard Euler in 1752, which provides the relationship between the pressure (P) of the fluid flowing, at a height (h) of the container having kinetic and gravitational potential energy.
The conservation of energy was found to be true for flowing fluids by the statement of Bernoulli’s Principle. It may seem contradictory, but Bernoulli’s principle describes how a fluid’s velocity and pressure are related to each other.
In this article, we have provided what is Bernoulli’s principle, Bernoulli’s equation, its derivation, examples, and proof.
What is Bernoulli’s Principle?
Bernoulli’s Principle says that when a fluid is flowing horizontally, the points where the speed is higher exhibit low pressure, while the points where the speed is lower exhibit high pressure. According to Bernoulli’s principle, the gravitational potential energy of elevation, the energy related to fluid pressure, and the kinetic energy of the fluid motion combine up to give the total mechanical energy of a flowing fluid and are all constant.
In real life, Bernoulli’s principle can be observed in rivers. In some places, the width of the river was found to be changed. When the width of the river increases the speed of the water flowing through it decreases. While the speed of water increases in the narrower regions.
Bernoulli’s Principal Definition
Bernoulli’s principle is a fundamental principle in fluid dynamics that relates the pressure within a fluid to the speed of the fluid’s motion
Check: Application of Bernoulli’s Theorem
Bernoulli’s Principle is formulated into an equation called Bernoulli’s Equation. Bernoulli’s Equation is a relationship between kinetic energy, gravitational potential energy, and the pressure of the fluid inside the container.
Thus, Bernoulli’s Principle Formula is stated as:
[Tex]\bold{P+\dfrac{1}{2}\rho v^2+\rho gh=\text{Constant}}
[/Tex]
where,
- P is the Pressure exerted by the fluid,
- ρ is the Density of the fluid,
- v is the Velocity of the fluid,
- g is the Acceleration due to gravity and
- h is the Height of the container.
Bernoulli’s Equation Derivation
Let us consider a container in the shape of a pipe, whose two edges are placed at different heights and varying diameters. The relationship between the areas of cross-sections A, the flow speed v, height from the ground y, and pressure P at two different points 1 and 2 are given in the figure below.
As illustrated in the diagram, the pipe should be at various heights. According to the equation of continuity, its velocity must fluctuate. To achieve this acceleration and force are required, which is produced by the fluid surrounding it, and the pressure in different places must be different.
Before, deriving Bernoulli’s Equation, we assume that the fluid has no viscous forces, so the fluid’s energy will be conserved. Also, the density of the fluid flowing at both points of the container must be uniform.
To determine Bernoulli’s equation, we must first determine how much work done experienced by the fluid,
The work done at point 1 where the force F1 is exerted to displace the fluid to dx1 is
dW1 = F1 dx1
Here, the force exerted at point 1 is given by, F1 = P1A1
where P1 and A1 are the pressure exerted and cross-sectional area at point 1.
This implies,
dW1 = P1A1 dx1
⇒ dW1 = P1 dv
Similarly, the work done by the fluid at point 2 is:
dW2 = P2A2 dx2
⇒ dW2 = P2 dv
Now, the total work done by the fluid flowing through the container is,
dW = P1 dv – P2 dv
⇒ dW = (P1 – P2) dv . . .(1)
Now, the change in the kinetic energy of the fluid is given by,
[Tex]\begin{aligned}\text{d}K&=\dfrac{1}{2}m_2v^2_2-\dfrac{1}{2}m_1v^2_1\end{aligned}
[/Tex]
But, the mass m of the fluid can be written as,
m = ρ dv
Therefore,
[Tex]\begin{aligned}\text{d}K=\dfrac{1}{2}\rho dv (v^2_2-v^2_1)\end{aligned}
[/Tex] . . . (2)
Similarly, the change in gravitational potential energy is given by,
[Tex]\begin{aligned}\text{d}U&=\dfrac{1}{2}m_1gy_2-\dfrac{1}{2}m_2gy_1\\\Rightarrow \text{d}U&=\dfrac{1}{2}\rho dv g(y_2-y_1)\end{aligned}
[/Tex] . . . (3)
According to the law of conservation of energy:
dW = dK + dU
[Tex]\begin{aligned}&(P_1 – P_2) dv=\dfrac{1}{2}\rho dv (v^2_2-v^2_1)+\dfrac{1}{2}\rho dv g(y_2-y_1)\\ \Rightarrow & (P_1-P_2)=\dfrac{1}{2}\rho (v^2_2-v^2_1)+\dfrac{1}{2}\rho g(y_2-y_1)\\ &\Rightarrow P_1+\dfrac{1}{2}\rho v_1^2+\rho gy_1=P_2+\dfrac{1}{2}\rho v_2^2+\rho gy_2\end{aligned}
[/Tex]
This is Bernoulli’s equation and this can be written as a general expression,
[Tex]\bold{P+\frac{1}{2}\rho v^2+\rho gh=\text{Constant} }
[/Tex]
Bernoulli’s Equation at Constant Depth
As the name suggests, let us suppose any fluid is moving at some constant depth, so h1 = h2, under this condition Bernoulli’s equation be
[Tex]P_1+\frac{1}{2}\rho v_1^2+\rho gh_1 = P_2+\frac{1}{2}\rho v_2^2+\rho gh_2
[/Tex]
[Tex]\Rightarrow P_1+\frac{1}{2}\rho v_1^2= P_2+\frac{1}{2}\rho v_2^2
[/Tex] (As h1 = h2 ⇒ ρgh1 = ρgh2)
Bernoulli’s Equation for Static Fluids
Any fluid is said static if there is no motion in it, for example, oil in a container, a calm lake, the air in a room with no air current, etc. For static fluid there is no velocity gradient throughout the fluid, thus v1 = v2. So, under this condition Bernoulli’s equation be.
[Tex]P_1+\frac{1}{2}\rho v_1^2+\rho gh_1 = P_2+\frac{1}{2}\rho v_2^2+\rho gh_2
[/Tex]
[Tex]\Rightarrow P_1+\rho gh_1 = P_2+\rho gh_2
[/Tex]
Now, to simplify it much further, h2 = 0 (any height can be chosen for the reference height to be zero)
[Tex]\Rightarrow P_2 = P_1+\rho gh_1
[/Tex],
This equation tells us that the static pressure increase from point 1 to 2 by ρgh1.
Principle of Continuity
The primary consideration when representing the flow of fluids or gases is continuity. It shows how mass conservation applies to gases and liquids. The law of conservation of mass in fluid dynamics is demonstrated using the continuity equation.
The principle of continuity is stated as, when a incompressible fluid is flowing in a streamline flow then mass passing through the system at different cross-sectional areas are equal.
The flow and behavior of fluids in a pipe are explained by the continuity equation. This formula is used to explain the flow of liquids and gases through pipes, ducts, rivers, etc.
Consider a pipe as shown above, with different cross-sectional areas A1 and A2. Let the rate of mass entering and leaving the given system be M1 and M2 respectively, with a speed of flow v, and density ρ of the fluid.
Then, according to the principle of continuity, the rate of mass of fluid entering must be equal to the rate of mass of fluid leaving the system.
Since, the rate of mass entering, M1 = ρA1V1 Δt and
The rate of mass entering, M2 = ρA2V2 Δt
Therefore,
ρA1V1 Δt = ρA2V2 Δt
ρA1V1= ρA2V2
The above equation is now termed as Equation of Continuity.
Applications of Bernoulli’s Principle and Equation
The following are the important applications of Bernoulli’s Principle:
Venturi Meter
A venturi meter is a device used to measure the rate of flow in a pipe with a non-uniform cross-section.
To the wide and narrow sections of the pipe, we apply Bernoulli’s equation, where h1=h2. The pressure P2 is less than P1 because A1 is bigger than A2, and v2 is greater than v1. The fluid is accelerated as it enters the tube, which is narrow, and slowed as it exits by a net force to the left.
The venturi meter formula is stated as,
[Tex]\bold{v_1=\sqrt{\dfrac{2gh}{\left(\dfrac{A_1}{A_2}\right)^2-1}}}
[/Tex]
where,
- v1 is the rate of fluid flowing,
- g is the acceleration due to gravity,
- h is the difference in liquid level in the two tubes,
- A1 and A2 are the cross-sectional areas of the tube.
Principle of Lifting an Aircraft
Bernoulli’s theorem governs the operation of aeroplanes. The plane’s wings have a certain form. When the plane is moving, the air flows past it at a high rate, despite the plane’s low surface wig.
There is a variation in the flow of air above and below the wings due to Bernoulli’s principle. As a result of the flow of air on the wing’s up surface, this concept causes a change in pressure. If the force is greater than the plane’s mass, the plane will ascend as shown in the figure below:
Action of Atomizer or Spray Gun
When the piston is pulled, air flows out of the horizontal tube, causing the pressure to drop which is less than the container’s pressure. The consequence is that the liquid in the vertical tube rises. When it runs into the fast air in the tube, it dissipates into a thin mist. The same idea governs filter pumps, Bunsen burners, and sprayers used to apply pesticides or scents.
Relation between Conservation of Energy and Bernoulli’s Equation
Bernoulli’s theorem states that the total amount of these three energies within a constantly moving fluid, i.e., kinetic energy, potential energy, and pressure energy, will remain steady throughout the pipeline. However, several factors must be understood:
- The movement of the liquid is assumed to be constant, and there should be no alteration with respect to the pressure, speed, and consistency of the liquid at any point in time. However, if the liquid flow is unstable, there will be a change in speed, and in that case, this equation may not hold true.
- The fluid is considered to be incompressible. Since all liquids are incompressible in nature, this principle can be applied to all fluids. However, in the case of gas flow, there should be a constant density, and one can manage with little difference in pressure, velocity, and temperature.
- Another consideration is the irrotational feature of liquids, which means that the overall angular momentum throughout the liquid is zero.
- The fluid should be ideal for this principle to hold true, meaning there should be no loss of energy due to frictional activity. Hence, there is no excess energy production due to internal particle friction.
Limitations of Bernoulli’s Principle
There are several limitations to Bernoulli’s principle:
- Due to friction, the velocity of fluid particles in the middle of a tube gradually decreases in the tube’s direction. As a result, the liquid’s mean velocity must be used, as the velocity of the particles of the liquid is not constant.
- This Bernoulli equation is effective in streamlining liquid supply, but it is ineffective in turbulent or non-steady flow.
- The liquid flow will be affected by the liquid’s external force.
- This theorem is preferably applied to non-viscous fluids, and an incompressible fluid is required.
- When a fluid is travelling in a curved path, the energy generated by centrifugal forces must be taken into account.
- The liquid flow should remain constant over time.
- A small amount of kinetic energy can be converted to heat energy in an unstable flow, and some energy can be lost due to shear stress in a thick flow. As a result, these losses must be overlooked.
- The effect of viscosity must be negligible.
Also, Read
Solved Examples on Bernoulli’s Principle
Example 1: Water is flowing at a rate of 2m/s through a tube with a diameter of 1 m. If the pressure at this point is 80 kPa, what is the pressure of the water after the tube narrows to a diameter of 0.5m? ρwater=1.0 kgl-1
Solution:
According to Bernoulli’s expression:
[Tex]P_{1}+\frac{1}{2}\rho v^2_{1}+\rho gh_{1}=P_{2}+\frac{1}{2}\rho v^2_{2}+\rho gh_{2}
[/Tex]
The height is same (h1=h2), so the expression can be written as
[Tex]P_{2}=P_{1}+\frac{1}{2}\rho \left(v^2_{1}-v^2_{2}\right)
[/Tex]
The expression for the cross-sectional area is
[Tex]A_{1}=\pi\frac{ d^2}{4}\\ \Rightarrow A_{1}=\pi\frac{ 1^2}{4}\text{ m}^2\\ \Rightarrow A_{1}=\frac{\pi}{4}\text{ m}^2\\
[/Tex]
Similarly
[Tex]A_{2}=\pi\frac{ d^2}{4}\\ \Rightarrow A_{2}=\pi\frac{ 0.5^2}{4}\text{ m}^2\\ \Rightarrow A_{2}=\frac{\pi}{16}\text{ m}^2\\
[/Tex]
The expression for the velocity for each diameter is
[Tex]v_1=\frac{V}{A}\\ \Rightarrow v_1=\frac{2}{\frac{\pi}{4}}\frac{\text{m}}{s}\\ \Rightarrow v_1=\frac{8}{\pi}\frac{\text{m}}{s}
[/Tex]
Similarly,
[Tex]v_2=\frac{2}{\frac{\pi}{16}}\frac{\text{m}}{s}\\ \Rightarrow v_2=\frac{32}{\pi}\frac{\text{m}}{s}
[/Tex]
Substitute the value in Bernoulli’s expression:
[Tex]P_{2}=80000\text{ Pa}+\frac{1}{2}\times1000\frac{\text{kg}}{\text{m}^3}\times\left(\frac{8}{\pi}-\frac{32}{\pi}\right)\frac{\text{m}}{s}\\ \Rightarrow P_{2}=76.2\text{ kPa}
[/Tex]
Example 2: Explain why:
(a) The blood pressure in humans is greater at the feet than at the brain.
(b) Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at sea level, though the height of the atmosphere is more than 100 km.
(c) Hydrostatic pressure is a scalar quantity even though the pressure is force divided by area.
Solution:
(a) The height of the blood column in the foot is greater than that in the brain. As a result, human blood pressure is higher in the feet than in the brain.
(b) The relationship between air density and height is not linear. As a result, pressure does not decrease linearly with height. P = P0e–αh gives the air pressure at a height h, where P0 is the pressure of air at sea level and α is a constant.
(c) When a force is applied to a liquid, the pressure is distributed evenly throughout the liquid. As a result, the pressure due to liquid has no definite direction. As a result, hydrostatic pressure is a scalar value.
Example 3: Drive the expression for Bernoulli’s principle.
Solution:
The flow of an ideal fluid in a pipe of varying cross-section. The fluid in a section of length v1∆t moves to the section of length v2∆t in time ∆t
Consider the flow at two regions BC and DE. Take a look at the flow in two different regions: BC and DE. Consider the fluid that present between B and D would travelled in an infinitesimal time interval ∆t. If v1 is the speed at B and v2 is the speed at D, the fluid at B has travelled a distance of v1∆t to C i.e.
[Tex]dx_{1}=v_{1}\Delta{t}
[/Tex]
In the same interval ∆t the fluid initially at D moves to E, a distance equal to v2∆t i.e.
[Tex]dx_{2}=v_{2}\Delta{t}
[/Tex]
The areas A1 and A2 has the pressures P1 and P2. The work done on the fluid at BC is
[Tex]W_{1}=P_{1}A_{1}\cdot v_{1}\Delta{t}\\ \Rightarrow W_{1}=P_{1}\Delta{V}
[/Tex]
where ∆V is the volume passes through region BC.
Since the same volume ∆V passes through both the regions BC and DE. therefore the expression for the work done by the fluid at the another end DE is
[Tex]W_{2}=P_{2}A_{2}\cdot v_{2}\Delta{t}\\ \Rightarrow W_{2}=P_{2}\Delta{V}
[/Tex]
So the total work done on the fluid is
[Tex]W_{1}-W_{2}=P_{1}\Delta{V}-P_{2}\Delta{V}\\ \Rightarrow W_{1}-W_{2}=\left(P_{1}-P_{2}\right)\Delta{V}
[/Tex]
Let the density of the fluid is ρ therefore the expression ∆m = ρ∆V is the mass passing through the pipe in time ∆t, then change in gravitational potential energy is
[Tex]\Delta{U} =\rho g\Delta{V}\left(h_{2}-h_{1}\right)
[/Tex]
The change in its kinetic energy is given by
[Tex]\Delta{K}=\frac{1}{2}\rho\Delta{V}\left(v^2_{2}-v^2_{1}\right)
[/Tex]
According to he work – energy theorem’
[Tex]\left(P_{1}-P_{2}\right)\Delta{V}=\frac{1}{2}\rho \Delta{V}\left(v^2_{2}-v^2_{1}\right)+\rho g\Delta{V}\left(h_{2}-h_{1}\right)\\ \Rightarrow \left(P_{1}-P_{2}\right)=\frac{1}{2}\rho\left(v^2_{2}-v^2_{1}\right)+\rho g\left(h_{2}-h_{1}\right)
[/Tex]
Rearrange the above expression,
[Tex]P_{1}+\frac{1}{2}\rho v^2_{1}+\rho gh_{1}=P_{2}+\frac{1}{2}\rho v^2_{2}+\rho gh_{2}
[/Tex]
This is Bernoulli’s equation and this can written as general expression.
P + 1/2ρv2 + ρgh = constant
Example 4: Suppose that a huge tank 50m high and filled with water is open to the atmosphere and is hit by a bullet that pierces one side of the tank, allowing water to flow out. The hole is 2m above the ground. If the hole is very small in comparison with the size of the tank, how quickly will the water flow out of the tank?
Solution:
According to Bernoulli’s expression:
[Tex]P_{1}+\frac{1}{2}\rho v^2_{1}+\rho gh_{1}=P_{2}+\frac{1}{2}\rho v^2_{2}+\rho gh_{2}
[/Tex]
According to question it is assumed that the top of the container as point 1, and the hole where water is flowing out as point 2. Both points are open to the atmosphere. Therefore, the pressure on each side of the above equation is equal to 1 atm, and thus it got cancel. The size of the hole on the side of the tank is so small compared to the rest of the tank, the velocity of the water at point 1 is nearly equal to 0. Hence, we can cancel out the 1/2ρ(v1)2 term on the left side of the equation. The expression can rewrite as,
[Tex]\rho gh_1=\frac{1}{2}\rho v^2_{2}+\rho gh_{2}\\ \Rightarrow gh_1=\frac{1}{2}v^2_{2}+gh_{2}\\ \Rightarrow v^2_{2}=2\left(gh_1-gh_2\right)\\ \Rightarrow v_{2}=\sqrt{2g\left(h_1-h_2\right)}\\
[/Tex]
Substitute the values in the above expression,
v2 = √{2×(9.8)×(50-2)}
v2 = 30.67 ms-1
Practice Problems on Bernoulli’s Theorem
Problem 1: A fluid is flowing steadily through a pipe. At one point in the pipe, the fluid has a velocity of 10 m/s and a pressure of 200,000 Pa. If the pipe narrows downstream, and the velocity of the fluid increases to 15 m/s, what is the pressure at that point?
Problem 2: An airplane is flying at a constant altitude. The air pressure on the upper surface of the wing is 90,000 Pa, while the air pressure on the lower surface of the wing is 100,000 Pa. If the speed of the air over the top of the wing is 250 m/s, what is the speed of the air under the wing?
Problem 3: Water is flowing through a hose with a diameter of 2 cm at a speed of 4 m/s. If the hose narrows to a diameter of 1 cm, what is the speed of the water at that point? Assume incompressible flow.
Problem 4: A hydraulic lift is used to lift a car weighing 12,000 N. The piston on which the car sits has an area of 0.2 square meters. If a smaller piston connected to the same hydraulic system has an area of 0.02 square meters, how much force must be applied to the smaller piston to lift the car?
Conclusion of Bernoulli’s Principal
Bernoulli’s principle states that a fluid’s pressure increases with slowing down and decreases with increasing speed. This concept aids in our understanding of many fascinating phenomena, like the functioning of automobile carburetors and water flowing through pipes and airplanes.
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Radius of Gyration
Radius of gyration, R, is a measure used in mechanics and engineering to describe the distribution of mass or inertia of an object relative to its axis of rotation. Radius of Gyration, or the radius of a body, is always centered on its rotational axis. It is a geometric characteristic of a rigid bod
11 min read
Moment of Inertia
Moment of inertia is the property of a body in rotational motion. Moment of Inertia is the property of the rotational bodies which tends to oppose the change in rotational motion of the body. It is similar to the inertia of any body in translational motion. Mathematically, the Moment of Inertia is g
15+ min read
Fluid Mechanics
Mechanical Properties of Fluids
Fluids are substances that can flow and adapt to the shape of their container, including liquids and gases like water and air. Mechanical properties of fluids refer to viscosity, density, and pressure, which describe how fluids respond to external forces and influence their behavior in various situa
11 min read
What is Viscosity?
Viscosity is the measurement of the resistance of the flowing liquid. Let us learn more about viscosity with an example suppose we take two bowls, one bowl contains water and the other has honey in it, we drop the content of both bowls then we see that water flows much faster than honey which conclu
12 min read
Buoyant Force
Buoyancy is a phenomenon due to the buoyant force that causes an object to float. When you put an object in a liquid, an upward force is exerted on the object by the liquid. This force is equal to the weight of the liquid that has been displaced. The amount of liquid that has been displaced depends
13 min read
Archimedes Principle
Archimedes Principle is a fundamental concept in fluid mechanics, credited to the ancient Greek mathematician and physicist Archimedes. According to Archimedes' Principle, when an object is immersed in a fluid the object experiences an upward force whose magnitude is equal to the weight of the fluid
12 min read
Pascal's Law
Pascal's law establishes the relation between pressure and the height of static fluids. A static fluid is defined as a fluid that is not in motion. When the fluid is not flowing, it is said to be in hydrostatic equilibrium. For a fluid to be in hydrostatic equilibrium, the net force on the fluid mus
10 min read
Reynolds Number
As liquid runs into a channel, it collides with the pipe. Engineers ensure that the liquid flow through the city's pipes is as consistent as possible. As a result, a number known as the Reynolds number predicts whether the flow of the liquid will be smooth or turbulent. Sir George Stoke was the firs
6 min read
Streamline Flow
The substance that can change its form under an external force is defined as fluid. Whenever an external force is applied to a fluid, it begins to flow. The study of fluids in motion is defined as fluid dynamics. Have you ever noticed a creek flowing beneath the bridge? When you see a streamline, wh
7 min read
Laminar and Turbulent Flow
Laminar flow and turbulent flow describe the movement patterns of fluids. Laminar flow is characterized by smooth, orderly layers of fluid sliding over one another without mixing, ideal for scenarios where minimal resistance is desired. Turbulent flow features chaotic, swirling patterns with irregul
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Bernoulli's Principle
Bernoulli's Principle is a very important concept in Fluid Mechanics which is the study of fluids (like air and water) and their interaction with other fluids. Bernoulli's principle is also referred to as Bernoulli's Equation or Bernoulli Theorem. This principle was first stated by Daniel Bernoulli
15+ min read
Poiseuilles Law Formula
According to Poiseuille's law, the flow of liquid varies depending on the length of the tube, the radius of the tube, the pressure gradient and the viscosity of the fluid. It is a physical law that calculates the pressure drop in an incompressible Newtonian fluid flowing in laminar flow through a lo
4 min read
Stoke's Law
Stoke's Law: Observe a raindrop falling from a height if you look closely you will notice that the speed of all the raindrops is constant and even though it falls from a height under the influence of gravity its velocity seems constant. These questions are answered using Stoke's law Stoke's law was
12 min read
Solid Mechanics
What is Stress?
Stress in physics is defined as the force exerted on the unit area of a substance. Stress affects the body as strain in which the shape of the body changes if the stress is applied and sometimes it gets permanently deformed. On the basis of the direction of force applied to the body, we can categori
9 min read
Stress and Strain
Stress and Strain are the two terms in Physics that describe the forces causing the deformation of objects. Deformation is known as the change of the shape of an object by applications of force. The object experiences it due to external forces; for example, the forces might be like squeezing, squash
12 min read
Stress-Strain Curve
Stress-Strain Curve is a very crucial concept in the study of material science and engineering. It describes the relationship between stress and the strain applied on an object. We know that stress is the applied force on the material, and strain, is the resulting change (deformation or elongation)
12 min read
Elasticity and Plasticity
You've undoubtedly heard of the idea of elasticity by now. In layman's words, it indicates that after being stretched, some substances return to their former form. You've experimented with a slingshot. Didn't you? That is an elastic substance. Let us go into the ideas of elasticity and plasticity to
9 min read
Modulus of Elasticity
Modulus of Elasticity or Elastic Modulus is the measurement of resistance offered by a material against the deformation force acting on it. Modulus of Elasticity is also called Young's Modulus. It is given as the ratio of Stress to Strain. The unit of elastic modulus is megapascal or gigapascal Modu
12 min read
Modulus of Rigidity
Modulus of rigidity also known as shear modulus, is used to measure the rigidity of a given body. It is the ratio of shear stress to shear strain and is denoted by G or sometimes by S or μ. The modulus of rigidity of a material is directly proportional to its elastic modulus which depends on the mat
11 min read
Young's Modulus
Young's Modulus is the ratio of stress and strain. It is named after the famous British physicist Thomas Young. Young's Modulus provides a relation between stress and strain in any object. Â When a certain load is added to a rigid material, it deforms. When the weight is withdrawn from an elastic mat
12 min read
Bulk Modulus Formula
For every material, the bulk modulus is defined as the proportion of volumetric stress to volumetric strain. The bulk modulus, in simpler terms, is a numerical constant that is used to quantify and explain the elastic characteristics of a solid or fluid when pressure is applied. We'll go over the bu
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Shear Modulus and Bulk Modulus
A rigid body model is an idealised representation of an item that does not deform when subjected to external forces. It is extremely beneficial for evaluating mechanical systems—and many physical items are quite stiff. The degree to which an item may be regarded as stiff is determined by the physica
7 min read
Poisson's Ratio
Poisson's Ratio is the negative ratio of transversal strain or lateral strain to the longitudinal strain of a material under stress. When a material particularly a rubber-like material undergoes stress the deformation is not limited to only one direction, rather it happens along both transversal and
9 min read
Stress, Strain and Elastic Potential Energy
Elasticity, this term always reminds of objects like Rubber bands, etc. However, if the question arises, which one is more elastic- A rubber or an Iron piece? The answer will be an Iron piece. Why? The answer lies in the definition of Elasticity, elasticity is known to be the ability of the object t
9 min read
Thermodynamics
Basics Concepts of Thermodynamics
Thermodynamics is concerned with the ideas of heat and temperature, as well as the exchange of heat and other forms of energy. The branch of science that is known as thermodynamics is related to the study of various kinds of energy and its interconversion. The behaviour of these quantities is govern
12 min read
Zeroth Law of Thermodynamics
Zeroth Law of Thermodynamics states that when two bodies are in thermal equilibrium with another third body than the two bodies are also in thermal equilibrium with each other. Ralph H. Fowler developed this law in the 1930s, many years after the first, second, and third laws of thermodynamics had a
7 min read
First Law of Thermodynamics
First Law of Thermodynamics adaptation of the Law of Conservation of Energy differentiates between three types of energy transfer: Heat, Thermodynamic Work, and Energy associated with matter transfer. It also relates each type of energy transfer to a property of a body's Internal Energy. The First L
8 min read
Second Law of Thermodynamics
Second Law of Thermodynamics defines that heat cannot move from a reservoir of lower temperature to a reservoir of higher temperature in a cyclic process. The second law of thermodynamics deals with transferring heat naturally from a hotter body to a colder body. Second Law of Thermodynamics is one
10 min read
Thermodynamic Cycles
Thermodynamic cycles are used to explain how heat engines, which convert heat into work, operate. A thermodynamic cycle is used to accomplish this. The application determines the kind of cycle that is employed in the engine. The thermodynamic cycle consists of a series of interrelated thermodynamic
15 min read
Thermodynamic State Variables and Equation of State
The branch of thermodynamics deals with the process of heat exchange by the gas or the temperature of the system of the gas. This branch also deals with the flow of heat from one part of the system to another part of the system. For systems that are present in the real world, there are some paramete
5 min read
Enthalpy: Definition, Formula and Reactions
Enthalpy is the measurement of heat or energy in the thermodynamic system. It is the most fundamental concept in the branch of thermodynamics. It is denoted by the symbol H. In other words, we can say, Enthalpy is the total heat of the system. Let's know more about Enthalpy in detail below. Enthalpy
13 min read
State Functions
State Functions are the functions that are independent of the path of the function i.e. they are concerned about the final state and not how the state is achieved. State Functions are most used in thermodynamics. In this article, we will learn the definition of state function, what are the state fun
7 min read
Carnot Engine
A Carnot motor is a hypothetical motor that works on the Carnot cycle. Nicolas Leonard Sadi Carnot fostered the fundamental model for this motor in 1824. In this unmistakable article, you will find out about the Carnot cycle and Carnot Theorem exhaustively. The Carnot motor is a hypothetical thermod
5 min read
Heat Engine - Definition, Working, PV Diagram, Efficiency, Types
Heat engines are devices that turn heat energy into motion or mechanical work. Heat engines are based on the principles of thermodynamics, specifically the conversion of heat into work according to the first and second laws of thermodynamics. They are found everywhere, from our cars, power plants to
14 min read
Wave and Oscillation
Introduction to Waves - Definition, Types, Properties
A wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities in physics, mathematics, and related subjects, commonly described by a wave equation. At least two field quantities in the wave medium are involved in physical waves. Periodic waves occur when variables o
11 min read
Wave Motion
Wave Motion refers to the transfer of energy and momentum from one point to another in a medium without actually transporting matter between the two points. Wave motion is a kind of disturbance from place to place. Wave can travel in solid medium, liquid medium, gas medium, and in a vacuum. Sound wa
12 min read
Oscillation
Oscillations are defined as the process of repeating vibrations of any quantity about its equilibrium position. The word “oscillation†originates from the Latin verb, which means to swing. An object oscillates whenever a force pushes or pulls it back toward its central point after displacement. This
8 min read
Oscillatory Motion Formula
Oscillatory Motion is a form of motion in which an item travels over a spot repeatedly. The optimum situation can be attained in a total vacuum since there will be no air to halt the item in oscillatory motion friction. Let's look at a pendulum as shown below. The vibrating of strings and the moveme
3 min read
Amplitude Formula
The largest deviation of a variable from its mean value is referred to as amplitude. It is the largest displacement from a particle's mean location in to and fro motion around a mean position. Periodic pressure variations, periodic current or voltage variations, periodic variations in electric or ma
7 min read
What is Frequency?
Frequency is the rate at which the repetitive event that occurs over a specific period. Frequency shows the oscillations of waves, operation of electrical circuits and the recognition of sound. The frequency is the basic concept for different fields from physics and engineering to music and many mor
9 min read
Amplitude, Time Period and Frequency of a Vibration
Sound is a form of energy generated by vibrating bodies. Its spread necessitates the use of a medium. As a result, sound cannot travel in a vacuum because there is no material to transfer sound waves. Sound vibration is the back and forth motion of an entity that causes the sound to be made. That is
5 min read
Energy of a Wave Formula
Wave energy, often referred to as the energy carried by waves, encompasses both the kinetic energy of their motion and the potential energy stored within their amplitude or frequency. This energy is not only essential for natural processes like ocean currents and seismic waves but also holds signifi
7 min read
Simple Harmonic Motion
Simple Harmonic Motion is a fundament concept in the study of motion, especially oscillatory motion; which helps us understand many physical phenomena around like how strings produce pleasing sounds in a musical instrument such as the sitar, guitar, violin, etc., and also, how vibrations in the memb
15+ min read
Displacement in Simple Harmonic Motion
The Oscillatory Motion has a big part to play in the world of Physics. Oscillatory motions are said to be harmonic if the displacement of the oscillatory body can be expressed as a function of sine or cosine of an angle depending upon time. In Harmonic Oscillations, the limits of oscillations on eit
10 min read
Sound
Production and Propagation of Sound
Have you ever wonder how are we able to hear different sounds produced around us. How are these sounds produced? Or how a single instrument can produce a wide variety of sounds? Also, why do astronauts communicate in sign languages in outer space? A sound is a form of energy that helps in hearing to
6 min read
What are the Characteristics of Sound Waves?
Sound is nothing but the vibrations (a form of energy) that propagates in the form of waves through a certain medium. Different types of medium affect the properties of the wave differently. Does this mean that Sound will not travel if the medium does not exist? Correct. It will not, It is impossibl
7 min read
Speed of Sound
Speed of Sound as the name suggests is the speed of the sound in any medium. We know that sound is a form of energy that is caused due to the vibration of the particles and sound travels in the form of waves. A wave is a vibratory disturbance that transfers energy from one point to another point wit
12 min read
Reflection of Sound
Reflection of Sound is the phenomenon of striking of sound with a barrier and bouncing back in the same medium. It is the most common phenomenon observed by us in our daily life. Let's take an example, suppose we are sitting in an empty hall and talking to a person we hear an echo sound which is cre
9 min read
Refraction of Sound
A sound is a vibration that travels as a mechanical wave across a medium. It can spread via a solid, a liquid, or a gas as the medium. In solids, sound travels the quickest, comparatively more slowly in liquids, and the slowest in gases. A sound wave is a pattern of disturbance caused by energy trav
5 min read
How do we hear?
Sound is produced from a vibrating object or the organ in the form of vibrations which is called propagation of sound and these vibrations have to be recognized by the brain to interpret the meaning which is possible only in the presence of a multi-functioning organ that is the ear which plays a hug
7 min read
Audible and Inaudible Sounds
We hear sound whenever we talk, listen to some music, or play any musical instrument, etc. But did you ever wondered what is that sound and how is it produced? Or why do we hear to our own voice when we shout in a big empty room loudly? What are the ranges of sound that we can hear? In this article,
10 min read
Explain the Working and Application of SONAR
Sound energy is the type of energy that allows our ears to sense something. When a body vibrates or moves in a ‘to-and-fro' motion, a sound is made. Sound needs a medium to flow through in order to propagate. This medium could be in the form of a gas, a liquid, or a solid. Sound propagates through a
8 min read
Noise Pollution
Noise pollution is the pollution caused by sound which results in various problems for Humans. A sound is a form of energy that enables us to hear. We hear the sound from the frequency range of 20 to 20000 Hertz (20kHz). Humans have a fixed range for which comfortably hear a sound if we are exposed
8 min read
Doppler Effect - Definition, Formula, Examples
Doppler Effect is an important phenomenon when it comes to waves. This phenomenon has applications in a lot of fields of science. From nature's physical process to planetary motion, this effect comes into play wherever there are waves and the objects are traveling with respect to the wave. In the re
7 min read
Doppler Shift Formula
When it comes to sound propagation, the Doppler Shift is the shift in pitch of a source as it travels. The frequency seems to grow as the source approaches the listener and decreases as the origin fades away from the ear. When the source is going toward the listener, its velocity is positive; when i
3 min read
Electrostatics
Electrostatics
Electrostatics is the study of electric charges that are fixed. It includes an study of the forces that exist between charges as defined by Coulomb's Law. The following concepts are involved in electrostatics: Electric charge, electric field, and electrostatic force. Electrostatic forces are non con
14 min read
Electric Charge
Electric Charge is the basic property of a matter that causes the matter to experience a force when placed in a electromagnetic field. It is the amount of electric energy that is used for various purposes. Electric charges are categorized into two types, that are, Positive ChargeNegative ChargePosit
8 min read
Coulomb's Law
Coulomb’s Law is defined as a mathematical concept that defines the electric force between charged objects. Columb's Law states that the force between any two charged particles is directly proportional to the product of the charge but is inversely proportional to the square of the distance between t
9 min read
Electric Dipole
An electric dipole is defined as a pair of equal and opposite electric charges that are separated, by a small distance. An example of an electric dipole includes two atoms separated by small distances. The magnitude of the electric dipole is obtained by taking the product of either of the charge and
11 min read
Dipole Moment
Two small charges (equal and opposite in nature) when placed at small distances behave as a system and are called as Electric Dipole. Now, electric dipole movement is defined as the product of either charge with the distance between them. Electric dipole movement is helpful in determining the symmet
6 min read
Electrostatic Potential
Electrostatic potential refers to the amount of electrical potential energy present at a specific point in space due to the presence of electric charges. It represents how much work would be done to move a unit of positive charge from infinity to that point without causing any acceleration. The unit
12 min read
Electric Potential Energy
Electrical potential energy is the cumulative effect of the position and configuration of a charged object and its neighboring charges. The electric potential energy of a charged object governs its motion in the local electric field. Sometimes electrical potential energy is confused with electric po
15+ min read
Potential due to an Electric Dipole
The potential due to an electric dipole at a point in space is the electric potential energy per unit charge that a test charge would experience at that point due to the dipole. An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific
7 min read
Equipotential Surfaces
When an external force acts to do work, moving a body from a point to another against a force like spring force or gravitational force, that work gets collected or stores as the potential energy of the body. When the external force is excluded, the body moves, gaining the kinetic energy and losing a
8 min read
Capacitor and Capacitance
Capacitor and Capacitance are related to each other as capacitance is nothing but the ability to store the charge of the capacitor. Capacitors are essential components in electronic circuits that store electrical energy in the form of an electric charge. They are widely used in various applications,
11 min read