Abhishek

Hi ....I am Abhishek Khambhata, have pursued B. Tech in Mechanical Engineering. Throughout four years of my engineering, I have designed and flown unmanned aerial vehicles. My forte is fluid mechanics and thermal engineering. My fourth-year project was based on the performance enhancement of unmanned aerial vehicles using solar technology. I would like to connect with like-minded people.

Is Mechanical Energy Conserved in an Elastic Collision?

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is mechanical energy conserved in an elastic collision

In an elastic collision, the total mechanical energy, which is the sum of kinetic energy and potential energy, is conserved. This means that the total mechanical energy before the collision is equal to the total mechanical energy after the collision. The kinetic energy may be transformed between the colliding objects, but the total mechanical energy remains constant.

Theoretical Explanation

Elastic collisions are characterized by the conservation of both momentum and kinetic energy. During an elastic collision, there are no external forces acting on the system, and the collision does not involve any energy dissipation mechanisms, such as friction or heat generation. As a result, the total kinetic energy of the system is preserved, and it is simply redistributed between the colliding objects.

The conservation of mechanical energy in an elastic collision can be expressed mathematically as:

$KE_i + PE_i = KE_f + PE_f$

where $KE_i$ and $PE_i$ are the initial kinetic and potential energies, respectively, and $KE_f$ and $PE_f$ are the final kinetic and potential energies, respectively.

In the case of a pure elastic collision, where there is no change in potential energy, the conservation of mechanical energy simplifies to:

$KE_i = KE_f$

Mathematical Formulation

is mechanical energy conserved in an elastic collision

For a head-on elastic collision between two objects, A and B, the initial and final kinetic energies can be calculated using the following equations:

$KE_i = \frac{1}{2}m_A v_{Ai}^2 + \frac{1}{2}m_B v_{Bi}^2$

$KE_f = \frac{1}{2}m_A v_{Af}^2 + \frac{1}{2}m_B v_{Bf}^2$

where $m_A$ and $m_B$ are the masses of objects A and B, and $v_{Ai}$, $v_{Bi}$, $v_{Af}$, and $v_{Bf}$ are their initial and final velocities, respectively.

For the conservation of mechanical energy to hold, the following condition must be satisfied:

$KE_i = KE_f$

Examples and Data Points

  1. Elastic Collision Example:
  2. Two trolleys, A and B, collide head-on.
  3. Trolley A has a mass of 2 kg and an initial velocity of 4 m/s.
  4. Trolley B has a mass of 3 kg and an initial velocity of 2 m/s.
  5. After the collision, trolley A has a final velocity of 1 m/s, and trolley B has a final velocity of 5 m/s.
  6. The initial and final kinetic energies can be calculated as follows:
    • $KE_i = \frac{1}{2}(2\ kg)(4\ m/s)^2 + \frac{1}{2}(3\ kg)(2\ m/s)^2 = 16\ J + 6\ J = 22\ J$
    • $KE_f = \frac{1}{2}(2\ kg)(1\ m/s)^2 + \frac{1}{2}(3\ kg)(5\ m/s)^2 = 0.5\ J + 37.5\ J = 38\ J$

  7. Since the initial and final kinetic energies are not equal, this collision is not perfectly elastic. However, the difference in kinetic energy is small, indicating that the collision is close to being elastic.

  8. Newton’s Cradle:

  9. A classic example of elastic collisions is a Newton’s cradle, where a series of balls are suspended from strings.
  10. When one ball is lifted and released, it collides with the next ball, causing a chain reaction of elastic collisions.
  11. The kinetic energy is conserved as the balls collide and rebound, demonstrating the conservation of mechanical energy in an elastic collision.

Figures and Data Points

Collision Type Initial Kinetic Energy Final Kinetic Energy Conservation of Mechanical Energy
Perfectly Elastic $KE_i$ $KE_f$ $KE_i = KE_f$
Near-Elastic $KE_i$ $KE_f$ $KE_i \approx KE_f$
Inelastic $KE_i$ $KE_f$ $KE_i > KE_f$

Figure 1: Comparison of different collision types and their impact on the conservation of mechanical energy.

References

  1. Khan Academy. (n.d.). What are elastic and inelastic collisions? Retrieved from https://www.khanacademy.org/science/physics/linear-momentum/elastic-and-inelastic-collisions/a/what-are-elastic-and-inelastic-collisions
  2. Lehman College. (n.d.). Laboratory Manual. Retrieved from https://www.lehman.edu/faculty/kabat/Phy166-168.pdf
  3. Physics Stack Exchange. (2020). Conservation of Mechanical Energy in Collisions. Retrieved from https://physics.stackexchange.com/questions/524964/conservation-of-mechanical-energy-in-collisions
  4. The Physics Classroom. (n.d.). Analysis of Situations in Which Mechanical Energy is Conserved. Retrieved from https://www.physicsclassroom.com/class/energy/Lesson-2/Analysis-of-Situations-in-Which-Mechanical-Energy

Is Mechanical Energy Conserved in an Inelastic Collision?

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is mechanical energy conserved in an inelastic collision

In the realm of physics, understanding the conservation of mechanical energy is crucial, especially when it comes to the analysis of inelastic collisions. Mechanical energy, which is the sum of kinetic energy and potential energy, is not conserved in an inelastic collision. Instead, a portion of the kinetic energy is converted into other forms of energy, such as heat, sound, and deformation energy.

Momentum Conservation in Inelastic Collisions

One of the fundamental principles in physics is the conservation of momentum. This principle holds true for both elastic and inelastic collisions. In an inelastic collision, the total momentum before the collision is equal to the total momentum after the collision. This means that the sum of the momenta of the colliding objects remains constant, even though the kinetic energy may not be conserved.

The mathematical expression for the conservation of momentum in an inelastic collision is:

m1v1 + m2v2 = m1v'1 + m2v'2

Where:
– m1 and m2 are the masses of the colliding objects
– v1 and v2 are the initial velocities of the colliding objects
– v'1 and v'2 are the final velocities of the colliding objects after the collision

Kinetic Energy Loss in Inelastic Collisions

is mechanical energy conserved in an inelastic collision

In an inelastic collision, some of the kinetic energy is lost and converted into other forms of energy. This results in a decrease in the total kinetic energy after the collision. The amount of kinetic energy lost depends on the nature of the collision and the properties of the colliding objects.

The mathematical expression for the kinetic energy lost in an inelastic collision is:

ΔKE = KE_before - KE_after

Where:
– ΔKE is the change in kinetic energy
– KE_before is the total kinetic energy before the collision
– KE_after is the total kinetic energy after the collision

Energy Transformation in Inelastic Collisions

The lost kinetic energy in an inelastic collision is transformed into other forms of energy, such as heat, sound, and deformation energy. These forms of energy are not considered mechanical energy, as they are not directly related to the motion or position of the objects.

The conversion of kinetic energy into these other forms of energy is due to the internal forces within the colliding objects, such as friction and deformation. These internal forces cause the objects to deform, vibrate, and generate heat, which are not easily recoverable for mechanical purposes.

Perfectly Inelastic Collisions

In a perfectly inelastic collision, the maximum possible kinetic energy is lost, and the colliding objects stick together, moving with a shared velocity after the collision. This type of collision represents the scenario where the objects undergo the greatest deformation and energy transformation.

The mathematical expression for the final velocity of the combined objects in a perfectly inelastic collision is:

v' = (m1v1 + m2v2) / (m1 + m2)

Where:
– v' is the final velocity of the combined objects
– m1 and m2 are the masses of the colliding objects
– v1 and v2 are the initial velocities of the colliding objects

Examples and Numerical Problems

  1. Energy Loss Example:
  2. In a head-on collision between two vehicles, the kinetic energy before the collision is 100 J.
  3. After the collision, the kinetic energy is reduced to 60 J.

  4. The lost energy (40 J) is converted into heat and sound.

  5. Momentum Conservation Example:

  6. Two objects with masses 2 kg and 3 kg collide inelastically.
  7. Before the collision, the total momentum is 10 kg m/s.

  8. After the collision, the total momentum remains 10 kg m/s, but the kinetic energy is reduced.

  9. Numerical Problem:

  10. Two objects with masses 5 kg and 3 kg are moving with initial velocities of 4 m/s and 2 m/s, respectively, in the same direction.
  11. They collide inelastically, and the final velocity of the combined objects is 3 m/s.
  12. Calculate the change in kinetic energy due to the inelastic collision.

Given:
– m1 = 5 kg, m2 = 3 kg
– v1 = 4 m/s, v2 = 2 m/s
– v' = 3 m/s

Step 1: Calculate the initial kinetic energy.
Initial kinetic energy = (1/2) * m1 * v1^2 + (1/2) * m2 * v2^2
Initial kinetic energy = (1/2) * 5 * 4^2 + (1/2) * 3 * 2^2 = 40 J + 6 J = 46 J

Step 2: Calculate the final kinetic energy.
Final kinetic energy = (1/2) * (m1 + m2) * v'^2
Final kinetic energy = (1/2) * (5 + 3) * 3^2 = 24 J

Step 3: Calculate the change in kinetic energy.
Change in kinetic energy = Initial kinetic energy – Final kinetic energy
Change in kinetic energy = 46 J – 24 J = 22 J

The change in kinetic energy due to the inelastic collision is a decrease of 22 J.

Conclusion

In summary, mechanical energy is not conserved in an inelastic collision. While momentum is always conserved, a portion of the kinetic energy is lost and converted into other forms of energy, such as heat, sound, and deformation energy. This loss of kinetic energy is a key characteristic of inelastic collisions and is an important concept in the study of physics.

Reference:

  1. https://www.coursehero.com/file/26596054/Lab-09-Momentum-and-Energypdf/
  2. https://www.youtube.com/watch?v=9hJm3ym3EN4
  3. https://www.khanacademy.org/science/physics/linear-momentum/elastic-and-inelastic-collisions/a/what-are-elastic-and-inelastic-collisions
  4. https://www.physicsclassroom.com/class/energy/Lesson-2/Analysis-of-Situations-in-Which-Mechanical-Energy
  5. https://physics.stackexchange.com/questions/402117/when-is-mechanical-energy-ever-conserved-for-inelastic-collisions

Comprehensive Guide to the Diverse Applications of Mechanical Energy

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uses of mechanical energy

Mechanical energy is a fundamental concept in physics that encompasses the energy associated with the motion and position of objects. This form of energy plays a crucial role in various aspects of our daily lives, from simple pendulum experiments to complex industrial applications. In this comprehensive guide, we will delve into the diverse uses of mechanical energy, exploring its principles, transformations, and real-world applications.

1. Conservation of Mechanical Energy

The principle of conservation of mechanical energy is a fundamental law in physics that states that the total mechanical energy of an isolated system remains constant. This means that the sum of the potential energy and kinetic energy of an object remains the same, regardless of the changes in its position or motion.

1.1. Pendulum Example

One of the classic examples of the conservation of mechanical energy is the pendulum experiment. In a pendulum system, the total mechanical energy is the sum of the potential energy and the kinetic energy. When a pendulum is released from rest at a certain height, its potential energy is at its maximum. As the pendulum swings down, the potential energy is converted into kinetic energy, and the total mechanical energy remains constant.

For instance, consider a 0.200-kg pendulum released from rest at a height of 0.5 meters. The potential energy of the pendulum at the highest point can be calculated using the formula:

Potential Energy = m × g × h
Potential Energy = 0.200 kg × 9.8 m/s² × 0.5 m = 0.98 J

As the pendulum swings down, the potential energy is converted into kinetic energy, but the total mechanical energy remains constant at 0.98 J.

1.2. Roller Coaster Energy Transformations

Another example of the conservation of mechanical energy can be observed in the motion of a roller coaster. At the top of the roller coaster hill, the potential energy is at its maximum, and as the roller coaster car descends, the potential energy is converted into kinetic energy.

For instance, consider a roller coaster car with a mass of 500 kg that is lifted to a height of 20 meters. The potential energy of the car at the top of the hill can be calculated using the formula:

Potential Energy = m × g × h
Potential Energy = 500 kg × 9.8 m/s² × 20 m = 98,000 J

As the roller coaster car descends, the potential energy is converted into kinetic energy. If the car reaches a velocity of 20 m/s at the bottom of the hill, its kinetic energy can be calculated using the formula:

Kinetic Energy = 1/2 × m × v²
Kinetic Energy = 1/2 × 500 kg × (20 m/s)² = 100,000 J

The total mechanical energy of the roller coaster car remains constant throughout its motion, with the potential energy being converted into kinetic energy and vice versa.

2. Mechanical Energy in Everyday Life

uses of mechanical energy

Mechanical energy plays a crucial role in various aspects of our daily lives, from the generation of electricity to the motion of automobiles.

2.1. Hydroelectric Power Plants

One of the most significant applications of mechanical energy is in the generation of electricity through hydroelectric power plants. In these plants, the gravitational potential energy of water is converted into electrical energy.

For example, the Agus VI Hydroelectric Power Plant in the Philippines generates approximately 245 MW of power, which is equivalent to 882,000,000 J of mechanical energy per second. This mechanical energy is generated by the flow of water through the turbines, which in turn drive the generators to produce electricity.

2.2. Automobiles

The mechanical energy of a moving car can be calculated using its kinetic energy. For instance, a car with a mass of 1,500 kg traveling at a velocity of 30 m/s has a kinetic energy of:

Kinetic Energy = 1/2 × m × v²
Kinetic Energy = 1/2 × 1,500 kg × (30 m/s)² = 675,000 J

This kinetic energy is the mechanical energy that propels the car forward and allows it to overcome various forces, such as air resistance and rolling friction.

3. Energy Transformations in Sports

Mechanical energy plays a crucial role in various sports, where the conversion between potential energy and kinetic energy is observed.

3.1. Downhill Skiing

In downhill skiing, the potential energy of the skier at the top of the hill is converted into kinetic energy as the skier descends. For example, consider a skier with a mass of 70 kg who starts at a height of 500 meters and reaches a velocity of 40 m/s at the bottom of the hill. The potential energy at the top of the hill can be calculated as:

Potential Energy = m × g × h
Potential Energy = 70 kg × 9.8 m/s² × 500 m = 34,300 J

As the skier descends, this potential energy is converted into kinetic energy, which can be calculated as:

Kinetic Energy = 1/2 × m × v²
Kinetic Energy = 1/2 × 70 kg × (40 m/s)² = 112,000 J

The total mechanical energy of the skier remains constant throughout the descent, with the potential energy being transformed into kinetic energy.

4. Mechanical Energy in Industrial Applications

Mechanical energy plays a crucial role in various industrial applications, from the storage of energy to the operation of machinery.

4.1. Flywheels

Flywheels are devices used to store kinetic energy, which can be released as needed. The amount of kinetic energy stored in a flywheel depends on its mass and rotational velocity.

For instance, consider a flywheel with a mass of 500 kg and a rotational velocity of 1,000 rpm (revolutions per minute). The kinetic energy stored in the flywheel can be calculated using the formula:

Kinetic Energy = 1/2 × I × ω²
Where:
I = Moment of Inertia of the flywheel
ω = Angular velocity of the flywheel

Assuming the flywheel has a uniform mass distribution, the moment of inertia can be calculated as:
I = 1/2 × m × r²
I = 1/2 × 500 kg × (1 m)² = 250 kg·m²

The angular velocity (ω) can be calculated as:
ω = 2 × π × N / 60
ω = 2 × π × 1,000 rpm / 60 = 104.72 rad/s

Substituting the values, the kinetic energy stored in the flywheel is:
Kinetic Energy = 1/2 × 250 kg·m² × (104.72 rad/s)² = 1,570,000 J

This stored kinetic energy can be released as needed to power various industrial applications.

5. Mechanical Energy in Renewable Energy Systems

Mechanical energy plays a crucial role in the generation of renewable energy, particularly in wind and hydroelectric power systems.

5.1. Wind Turbines

In wind turbines, the kinetic energy of the wind is converted into mechanical energy, which is then used to generate electrical energy. The amount of mechanical energy generated by a wind turbine depends on the wind speed and the size of the turbine blades.

For example, consider a wind turbine with a blade diameter of 50 meters and a wind speed of 10 m/s. The mechanical power generated by the turbine can be calculated using the formula:

Mechanical Power = 1/2 × ρ × A × v³
Where:
ρ = Density of air (approximately 1.225 kg/m³)
A = Area swept by the turbine blades (π × r²)
v = Wind speed

Substituting the values:
Mechanical Power = 1/2 × 1.225 kg/m³ × (π × (25 m)²) × (10 m/s)³
Mechanical Power = 1,910,000 W or 1.91 MW

This mechanical power can then be converted into electrical energy through the generator in the wind turbine.

5.2. Hydroelectric Power Plants

As mentioned earlier, hydroelectric power plants utilize the gravitational potential energy of water to generate mechanical energy, which is then converted into electrical energy. The amount of mechanical energy generated depends on the height of the water and the flow rate.

For instance, consider a hydroelectric power plant with a water flow rate of 500 m³/s and a height difference of 50 meters. The mechanical power generated can be calculated using the formula:

Mechanical Power = ρ × g × Q × h
Where:
ρ = Density of water (approximately 1,000 kg/m³)
g = Acceleration due to gravity (9.8 m/s²)
Q = Flow rate of water (500 m³/s)
h = Height difference (50 m)

Substituting the values:
Mechanical Power = 1,000 kg/m³ × 9.8 m/s² × 500 m³/s × 50 m
Mechanical Power = 24,500,000 W or 24.5 MW

This mechanical power is then used to drive the turbines and generators, converting the energy into electrical form.

Conclusion

Mechanical energy is a fundamental concept in physics that plays a crucial role in various aspects of our daily lives. From the conservation of energy in simple pendulum experiments to the complex transformations in renewable energy systems, the applications of mechanical energy are diverse and far-reaching.

By understanding the principles of mechanical energy, its transformations, and its quantifiable data, we can better appreciate the underlying physics that govern the world around us. This knowledge can be applied in various fields, from engineering and technology to sports and industrial applications, to optimize the use of mechanical energy and improve the efficiency of systems.

As we continue to explore and harness the power of mechanical energy, the potential for innovation and advancement in various domains remains vast and exciting.

References

  1. Scribd. (n.d.). ES-TG Module 2 Climate Revised. Retrieved from https://www.scribd.com/document/405509820/Es-Tg-Module-2-Climate-Revised
  2. The Physics Classroom. (n.d.). Analysis of Situations in Which Mechanical Energy is Conserved. Retrieved from https://www.physicsclassroom.com/class/energy/Lesson-2/Analysis-of-Situations-in-Which-Mechanical-Energy
  3. Study.com. (n.d.). Conservation of Mechanical Energy. Retrieved from https://study.com/academy/lesson/conservation-of-mechanical-energy.html
  4. CLEAN. (n.d.). Energy Literacy: Essential Principles and Fundamental Concepts for Energy Education. Retrieved from https://cleanet.org/clean/literacy/energy1.html
  5. OpenTextBC. (n.d.). Work and Mechanical Energy. Retrieved from https://opentextbc.ca/foundationsofphysics/chapter/work-mechanical-energy/

Dynamic Equilibrium vs Static Equilibrium: A Comprehensive Guide for Physics Students

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dynamic equilibrium vs static equilibrium

Dynamic equilibrium and static equilibrium are two distinct states of equilibrium that differ in their characteristics and applications. This comprehensive guide will provide you with a deep understanding of the key differences, quantifiable data, and practical applications of these concepts in the field of physics.

What is Dynamic Equilibrium?

Dynamic equilibrium is a state where the forward and reverse reactions of a chemical reaction occur at the same rate, resulting in no net change in the concentrations of reactants and products. This state is characterized by the following:

  1. Rate of Forward Reaction Equals Rate of Backward Reaction: In a dynamic equilibrium, the rate of the forward reaction is equal to the rate of the backward reaction, leading to a constant concentration of reactants and products.

  2. Concentrations of Reactants and Products Remain the Same: The concentrations of the reactants and products in a dynamic equilibrium system remain constant over time, as the forward and backward reactions occur at the same rate.

  3. Both Forward and Backward Reactions are Ongoing: In a dynamic equilibrium, both the forward and backward reactions are continuously occurring, with the rates of these reactions being equal.

  4. Closed System: Dynamic equilibrium typically occurs in a closed system, where the total number of particles (reactants and products) remains constant.

Examples of Dynamic Equilibrium:
– The Haber process for the production of ammonia (N₂ + 3H₂ ⇌ 2NH₃)
– The dissociation of acetic acid in water (CH₃COOH ⇌ CH₃COO⁻ + H⁺)
– The evaporation and condensation of water in a closed container

What is Static Equilibrium?

dynamic equilibrium vs static equilibrium

Static equilibrium is a state where there is no motion or change in a system. This state is characterized by the following:

  1. No Chemical Reactions Taking Place: In a static equilibrium, there are no chemical reactions occurring, as the forward and backward reactions have ceased.

  2. Concentrations of Reactants and Products Remain the Same: The concentrations of the reactants and products in a static equilibrium system remain constant over time, as there are no ongoing reactions.

  3. Neither the Forward nor the Backward Reaction Occurs: In a static equilibrium, neither the forward nor the backward reaction is taking place.

  4. Open or Closed System: Static equilibrium can occur in both open and closed systems, as long as there is no net change in the system.

Examples of Static Equilibrium:
– The solubility of a solid in a liquid, where the rate of dissolution equals the rate of precipitation, resulting in no net change in the amount of solid in solution.
– A book resting on a table, where the force of gravity is balanced by the normal force exerted by the table.
– A person standing still, where the forces of gravity and the normal force are in equilibrium.

Key Differences between Dynamic Equilibrium and Static Equilibrium

  1. Reaction Rates: In dynamic equilibrium, the forward and backward reactions occur at the same rate, while in static equilibrium, there are no ongoing reactions.

  2. System Type: Dynamic equilibrium occurs in closed systems, while static equilibrium can occur in both open and closed systems.

  3. Motion: Dynamic equilibrium involves constant motion, as the forward and backward reactions are continuously occurring, while static equilibrium involves no motion.

Quantifiable Data

  1. Rate Constants: In dynamic equilibrium, the rate constants for the forward and reverse reactions are equal, while in static equilibrium, the rate constants are not applicable.

  2. Concentration Ratios: In dynamic equilibrium, the ratio of reactant to product concentrations can vary depending on the rate constants, while in static equilibrium, the concentration ratio remains constant.

Physics Applications

  1. Net Force: In physics, equilibrium is achieved when the net force acting on an object is zero. This can occur in both static and dynamic equilibrium.

  2. Acceleration: In dynamic equilibrium, the acceleration of an object is zero, indicating constant motion with no change in velocity.

Theorems and Formulas

  1. Le Chatelier’s Principle: This principle states that when a system in dynamic equilibrium is subjected to a change in one of the conditions (concentration, temperature, or pressure), the system will shift to counteract the change and re-establish a new dynamic equilibrium.

Formula: K = [C]^c / ([A]^a * [B]^b)
Where:
– K is the equilibrium constant
– [A], [B], and [C] are the equilibrium concentrations of the reactants and products
– a, b, and c are the stoichiometric coefficients of the reactants and products

  1. Equilibrium Constant Expression: The equilibrium constant (K) is the ratio of the product concentrations raised to their stoichiometric coefficients to the reactant concentrations raised to their stoichiometric coefficients.

Formula: K = [C]^c / ([A]^a * [B]^b)

  1. Gibbs Free Energy: The Gibbs free energy change (ΔG) is related to the equilibrium constant (K) by the following equation:

Formula: ΔG = -RT ln K
Where:
– ΔG is the Gibbs free energy change
– R is the universal gas constant
– T is the absolute temperature
– K is the equilibrium constant

Examples and Numerical Problems

  1. Haber Process Example:
  2. Reaction: N₂ + 3H₂ ⇌ 2NH₃
  3. At equilibrium, the forward and backward reaction rates are equal: r₁ = r₂
  4. Equilibrium concentrations: [N₂] = 0.2 M, [H₂] = 0.6 M, [NH₃] = 0.4 M

  5. Equilibrium constant (K) = [NH₃]^2 / ([N₂] * [H₂]^3) = (0.4)^2 / ((0.2) * (0.6)^3) = 0.444

  6. Solubility Equilibrium Example:

  7. Reaction: AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq)
  8. At equilibrium, the rate of dissolution equals the rate of precipitation: r₁ = r₂
  9. Solubility product constant (Ksp) = [Ag⁺] * [Cl⁻] = 1.8 × 10⁻¹⁰
  10. If [Ag⁺] = 1.3 × 10⁻⁵ M, then [Cl⁻] = Ksp / [Ag⁺] = 1.8 × 10⁻¹⁰ / (1.3 × 10⁻⁵) = 1.3 × 10⁻⁵ M

Figures and Diagrams

Dynamic Equilibrium vs Static Equilibrium
Figure 1: Comparison of Dynamic Equilibrium and Static Equilibrium

Le Chatelier's Principle
Figure 2: Illustration of Le Chatelier’s Principle

Conclusion

In summary, dynamic equilibrium and static equilibrium are two distinct states of equilibrium that differ in their characteristics and applications. Dynamic equilibrium involves ongoing forward and backward reactions with equal rates, while static equilibrium involves no chemical reactions. Understanding the key differences, quantifiable data, and practical applications of these concepts is crucial for physics students to excel in their studies and research.

References

  1. Vaia. (n.d.). The Dance of Balance: Understanding Dynamic Equilibrium. Retrieved from https://www.vaia.com/en-us/explanations/chemistry/physical-chemistry/dynamic-equilibrium/
  2. LibreTexts. (2022). 11.1: Introduction to Chemical Equilibrium. Retrieved from https://chem.libretexts.org/Bookshelves/General_Chemistry/Chem1_%28Lower%29/11:_Chemical_Equilibrium/11.01:_Introduction_to_Chemical_Equilibrium
  3. Reddit. (2018). Difference between dynamic and static equilibrium? Retrieved from https://www.reddit.com/r/Mcat/comments/7wi3nm/difference_between_dynamic_and_static_equilibrium/
  4. ScienceReady. (n.d.). Understanding Equilibrium and Net Force – HSC Physics. Retrieved from https://scienceready.com.au/pages/equilibrium-in-physics
  5. Chemistry Community. (2023). Dynamic vs Static Equilibrium. Retrieved from https://lavelle.chem.ucla.edu/forum/viewtopic.php?t=104061

Is Dynamic Equilibrium A Diffusion: What ,Why, When And Detailed Facts

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Dynamic equilibrium 2

Dynamic equilibrium, in simple words, means equilibrium of bodies that are in motion. In this article we will read about the topic “is dynamic equilibrium a diffusion?”

The pre-requisite for understanding this article is to know about the concept of dynamic equilibrium. Although we will discuss about it in brief to make sure we don’t miss out any detail. We shall start this article by discussing about dynamic equilibrium first and then diffusion.

What is dynamic equilibrium?

Dynamic equilibrium in simple words is a equilibrium of bodies in motion. In chemistry, it relates to reactants and products being used up and being formed at the same rate.

Dynamic equilibrium, in Physics, refers to a closed system where all the forces are continuously acting and are in opposite nature such that the sum of all forces is constant or zero always. The system appears to be stagnant or still but in actual the contents are continuously changing.

Is Dynamic Equilibrium a diffusion
Image: Dynamic Equilibrium

Image credits: Wikipedia

What is diffusion?

Diffusion is related to movement of particles from one location to other. It has a particular condition only then the particles will be able to move. Let us see about this condition in the section given below.

The condition should be that the particles will move only from an area of high concentration to an area of low concentration, if the movement has to take place from low concentration to high concentration then external influence is necessary.

What happens when the concentration of both systems are equal?

Diffusion takes place on its own until there is a difference in concentration of quantities. As soon as the concentration of both systems are equal, equilibrium is achieved.

The movement of particles will not stop, instead the particles will start moving from one system to another at equal rates. This state is called as dynamic equilibrium.  In simple words, the rates at which forward reaction and backward reaction are taking place are equal.

How is diffusion related to dynamic equilibrium?

We can say that diffusion results into dynamic equilibrium. Equilibrium is achieved once the concentrations at both the ends become equal. Let us see what happens to both the systems that are interacting with each other.

The particles still as well be moving from one side to other but at equal rates. That is the amount of particles moving out of one location will be equal to the amount of particles moving in the same location.

Is dynamic equilibrium a diffusion?

Now we are well aware of the meanings of diffusion and equilibrium. It is an easy guess from here onward for the question “is dynamic equilibrium a diffusion?”

In dynamic equilibrium we see that the particles are transferred at equal rates from both the systems such that the net quantities remain same. This is a diffusion process in which the quantities move from one location to another at equal rates.

Types of diffusion

There are two types of diffusion commonly known. We shall discuss about these two types in the section given below.

The two most common types of diffusion are-

  • Simple diffusion– It is a process in which the particles move through the semi permeable membranes without any significant help from transport proteins hence it is termed as simple diffusion.
  • Facilitated diffusion– As the name suggests, facilitated diffusion is the movement of particles across the boundary of the system or the cell membrane with the help of a carrier molecule which acts as the host. Unlike simple diffusion, here the particles need help of other molecules for transport.

Examples of diffusion

Diffusion is very important in day to day activities. We see diffusion in daily lives and also it takes place inside our bodies as well. Lets see examples of diffusion-

  • A tea bag immersed in hot water– The color of water will change after some time because of diffusion.
  • Air freshener– When we spray air freshener in the room, the particles of air freshener will diffuse in the room which is why we can sense the odour.
  • Dissolution of sugar- When sugar dissolves in water/milk or any liquid, the liquid becomes sweet. This is a result of diffusion of sugar in the liquid.
  • Osmosis- Plants take minerals from roots by the process of Osmosis. If plants don’t take minerals from roots then there would have been no life possible on Earth.
  • Incense stick– The scent of incense stick comes after the diffusion of the smoke with the air molecules of the room. This way the pleasant smell of incense stick reaches to us.
  • Adding water to noodles– The noodles become soft after addition of water because water content inside the noodles increases as diffusion takes place.
  • Dialysis- Diffusion of solutes through a semi permeable membrane. Dialysis is a very important breakthrough in medical history.

Factors affecting diffusion

There are various factors affecting diffusion. By changing these factors one by one or simultaneously, we can change the rate of diffusion taking place.

The factors affecting diffusion are given below-

  • Temperature– Increase in temperature leads to increase in movement of particles (higher kinetic energy). Thus, the rate of diffusion will increase with increase in temperature.
  • Area of interaction– Higher the area of interaction, higher will be the rate of diffusion.
  • Size of the particle– If the size of particles are small enough so that they can pass through the membrane easily, the rate of diffusion will be more.
  • The steepness of the concentration gradient– The concentration gradient is directly proportional to the rate of diffusion. Hence, if the concentration gradient is more then the rate at which diffusion is taking place will also be faster.  

Significance of diffusion

From the examples of diffusion given in above sections, we can make out that diffusion is very important. Without diffusion (osmosis), life would not have been possible on Earth.

The most important significance of diffusion is that it helps the substances to move in and out of cells. Which means that through diffusion we can cut out waste from our bodies. Even plants take use of diffusion to collect nutrients and minerals from the roots.

Also Read:

Is Dynamic Equilibrium A System: What, Why, When And Detailed Facts

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Dynamic equilibrium 1

This article discusses about the topic “is dynamic equilibrium a system?”. We do not observe any significant change in a system that is under dynamic equilibrium.

Dynamic equilibrium is a type of equilibrium in which the rate of change of substances inside the system are happening at the same rate that is reactants and products are being formed and used at the same rate. Such that we cannot observe any net change in the quantities.

What is dynamic equilibrium?

As we have discussed in above section, dynamic equilibrium is a state of system in which the reactants and products are being formed and used at the same rate.

This happens in such a way that we observe no change in the contents but they continuously changing in reality. On a system, when the opposing forces are acting continuously such that the difference between them is constant or zero then the system is said to be under dynamic equilibrium.

Is dynamic equilibrium a system
Image: Image: % concentrations of species in isomerization reaction

Image credits: Wikipedia

When a system is at dynamic equilibrium?

There are various cases where dynamic equilibrium is taking place. But when is the system actually considered under dynamic equilibrium? Lets see it in the section given below.

  • For a chemical reaction, the contents inside the reaction are said to be in dynamic equilibrium when the reaction is occuring reversibly in such a way that the products and reactants are being used up and being formed at the same rate. Such that the contents of the reaction seem to have constant quantities.
  • For a system under the application of forces, it is considered to be in dynamic equilibrium when the opposing forces are acting continuously and at the same rate such that the difference between them is constant or zero.

Why is dynamic equilibrium a system?

Dynamic equilibrium refers to space in 3D coordinates where the rates of forward and backward reactions are same. That is the net change inside these coordinates is zero.

Anything happening beyond these coordinates does not relate to dynamic equilibrium. So we can say that these set of coordinates form a system which is under dynamic equilibrium or in simple words dynamic equilibrium is an example of a system.

Is dynamic equilibrium a closed system?

Yes. Dynamic equilibrium is an example of a closed system. The rates at which forward and backward reactions are happening are equal and hence we can say that the system is under steady state.

The contents of the system do not go out of the system except the energies. This is a well known characteristic of a closed system. Hence, we can say that dynamic equilibrium is an example of a closed system.

Can dynamic equilibrium occur in an open system?

In real life, dynamic equilibrium does not occur in open systems. Open systems tend to lose the contents inside the system.

For a system to be in dynamic equilibrium, the contents inside the system cannot leave the system. The container has to be sealed for a reaction to occur under dynamic equilibrium. Hence, we can say that in real life dynamic equilibrium cannot be achieved in an open system.

Can an open system be at equilibrium?

Closed systems are easier to reach the state of equilibrium because the contents do not go out of the system nor any contents enter the system hence minimum change occurs.

As the change is minimum, it takes lesser time to reach equilibrium whereas in open systems, the change is constantly taking place so it gets difficult to reach equilibrium. Usually the open systems are under non equilibrium conditions.

What does not happen during dynamic equilibrium?

As we know the forward rate and backward rate of reactions are same. So the reactants and products form and get used up at the same rate.

As a result of this, we cannot see any change happening inside the system even though the reaction is taking place inside the system.

What does dynamic mean in dynamic equilibrium?

The term dynamic in general means something in constant motion. In dynamic equilibrium the system looks unchanged and static but in reality the reaction is taking place continuously.

Similarly in static equilibrium the contents are same as well as they are static in nature and don’t change without external factors stepping in.

Also Read:

9 Dynamic Equilibrium Example: Detailed Explanations

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Dynamic equilibrium

This article focuses on dynamic equilibrium example. We have an idea of what equilibrium is, we will read in detail about its type- Dynamic equilibrium in this article.

The word dynamic refers to something which is having mobility. And equilibrium is related to stability and balance. We can say that dynamic equilibrium refers to something which is mobile and stable. We will study further about dynamic equilibrium in this article.

What is dynamic equilibrium?

In Physics/Chemistry, dynamic equilibrium occurs in a reversible chemical reaction. In this type of reaction, the formation of both reactants and products occurs at same rate. In a nutshell, backward and forward reaction occur at same rates.

Hence, the net content of both reactants and products remain same. This is also called as steady state sometimes. Thus we can say that things are dynamic in nature but has a balance too. In thermodynamics, this is called as thermodynamic equilibrium where reactions occur at such a rate that composition of mixture does not change significantly.

Dynamic equilibrium example

We know the meaning of dynamic equilibrium. There are various places where we can see dynamic equilibrium taking place in our every day lives. Lets get a clearer idea of what exactly dynamic equilibrium is by looking at its examples.

Dissociation of acetic acid in an aqueous solution

Rate of formation of reactants is equal to  rate of formation of products hence the net content of the system is same. This is why it is said to be in neutral equilibrium.

dynamic equilibrium example
Image: % concentrations of species in isomerization reaction

Image credits: Wikipedia

Train running with constant speed

When the train running with constant speed, the friction is balanced with the forward force applied by the train. At constant velocity, the magnitude of forces are not changed.

Aeroplane flying at constant speed

The upthrust is equal to the force due to gravity. No other change is observed hence it is dynamic equilibrium.

Car moving at constant velocity

The weight is balanced by reaction force and forward force is balanced by friction. Also the forward force is opposed by friction with equal rate. No other change in force is observed. The net force remains the same hence it is said to be in dynamic equilibrium.

Running on a treadmill at constant speed

The forward movement of legs is equal to the backward movement of treadmill floor leaving the human running at the same place hence these forces balance each other and makes the person running on the treadmill and the treadmill itself are in dynamic equilibrium. (Considering both as one system).

Free falling body after it has achieved terminal velocity

After achieving terminal velocity, all the forces are balanced and do not change even with downward movement of the free falling object.

Number of cars entering and leaving the city at the same rate

Particles entering and leaving the system at the same rate is an example of dynamic equilibrium. Here the number of cars entering and leaving the city are same. Considering city as a system, the city is in dynamic equilibrium.

A steady flow of water in pipe

The rate at which water is entering the pipe is equal to the rate at which water is leaving the pipe. Hence the pipe as a system is in dynamic equilibrium.

Heat transfer in heat exchanger

The heat absorbed by the cold fluid is equal to the heat left by the hotter fluid. Hence the pipes of heat exchanger in terms of heat transfer is in dynamic equilibrium. If we look at the mass flow rates at inlet and outlet and they both are same, we can say that entire heat exchanger is in dynamic equilibrium.

Rectilinear motion of bodies

Like trains and cars, their rectilinear motion makes them in dynamic equilibrium. In rectilinear motion having constant velocity, the net forces acting in the system remain same so the system is in dynamic equilibrium.

Difference between static equilibrium and dynamic equilibrium

The major difference between both these equilibriums is the mobility of particles/objects in the system.

In dynamic equilibrium, the rate of particles/objects entering the system is equal to the rate of particles/objects leaving the system. Here we can say the contents of this system are in continuous state of motion. In static equilibrium, the object is at rest and in equilibrium. This means there is no mobility of the contents in the system.

What is static equilibrium?

Static equilibrium is a state of equilibrium attained by bodies when they are at rest. In this case also, the sum of all forces acting on the body is zero.

If for example, an elephant is pulling one end of an inelastic rope in x direction and a truck is pulling other end in -x direction with the same magnitude of force, then the rope does not displace from its original position. This is the best example of static equilibrium.

Also Read:

7 Neutral Equilibrium Example: Detailed Explanations

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Thermal equilibrium

This article will is based on neutral equilibrium example. When we hear the word equilibrium, we instantly think of balance between objects or forces. This fact is true that equilibrium directly relates to balance between two or more objects.

In this article, we will study further about equilibrium. It is more than just balancing. First we will discuss about different types of equilibrium. We will keep our focus on neutral equilibrium in this article.

What is equilibrium?

As discussed above, equilibrium is a state of system in which all the forces are balanced or cancel each other. Equilibrium is very important in every field, be it chemistry or physics or engineering or in everyday lives. Equilibrium means balance, without balance it will be very difficult for lives to be simple.

Equilibrium can be broadly classified as- Mechanical equilibrium, chemical equilibrium and thermal equilibrium. Mechanical equilibrium is also divided further into sub categories out of which one such type is Neutral equilibrium (other sub types are stable equilibrium and unstable equilibrium). Lets see what is neutral equilibrium.

Neutral equilibrium example
Image: Thermal equilibrium

Image credits: Kku, Thermal equilibrium in closed system, CC BY-SA 4.0

Equation of equilibrium of forces

When multiple forces act, then it gets difficult for an object in a stable path or remain stationary. If the forces act in such a way that these forces cancel each other out then it gets easier to keep the object stable.

Lets consider two forces F1 and F2 acting on a body A. The two forces act horizontally in first case and vertically in other case. For the body to be in equilibrium in both the cases, following conditions should be satisfied-

  • 1st case- For the body to be in equilibrium all the forces should cancel each other that means sum of all horizontal forces should be zero.

Σ Fx = 0

where,

Fx represents all the forces in X direction

  • 2nd case- For the body to be in equilibrium all the forces should cancel each other that means sum of all vertical forces should be equal to zero.

Σ Fx = 0

where,

Fy represents all the forces in Y direction

What is neutral equilibrium?

Neutral equilibrium is the type of equilibrium in which the body comes to rest in its new position after being slightly displaced by some external force.

The body does not move after attaining neutral equilibrium that means it remains stationary. This is the compulsory condition for neutral equilibrium. If the body moves to its original position then it should have been moved by an external force.

The body does not come back to its original position rather remains stationary at the new position.

Neutral Equilibrium Example

Now we have an idea about neutral equilibrium, lets get a more clear about it by looking at some examples given below.

We experience neutral equilibrium in our daily lives, lets see the examples of neutral equilibrium we see in everyday lives-

A marble lying on a horizontal surface, undisturbed

The marble is not moving as there is no force acting on it. The marble is lying there on its own without any support of external force. It will only move when an external force is applied on it. Hence it is said to be in neutral equilibrium.

Sliding a book on the table surface, the book comes in neutral equilibrium after coming to rest

As the action of force diminishes, the book attains neutral equilibrium.

A football lying on the ground

When the ball is lying on the ground untouched, it does not move. An external force is required to move the ball. Without any external force, it will keep lying there. Hence it is neutral equilibrium.

A car parked without handbrakes (no external force applied for it to remain stationary)

When handbrakes are not applied it means the car is stationary on its own and no external force is applied to hold it stationary hence it is in neutral equilibrium.

A roller lying stationary on a flat surface

A roller will roll as soon as it is touched by an external force, when it is lying undisturbed the roller is said to be in neutral equilibrium.

Applying viscous cream on hands (for example sunscreen)

Viscous creams/fluids won’t move until an external force is applied on them. Like in the case of sunscreen we need to apply shear force to apply it without which it would not spread by itself.

A flask lying on ground

A flask lying on ground is stationary, it will not move unless a force is applied. Hence it is said to be in neutral equilibrium.

Pushing a heavy box

Once we start pushing a heavy box, the object starts moving but the moment we stop pushing the object stops moving. It does not move any further on its own nor it comes back to where it started moving. Hence it is in neutral equilibrium,

Throwing a heavy object on floor, it comes to rest as soon as it lands on floor

When we throw a heavy object on floor, the object goes down due to the force of gravity. When it lands on the ground, due its own weight it fails to bounce against the gravity. Hence, it stays there without getting lifted from the ground. Hence we can say that the object is in neutral equilibrium.

Neutral equilibrium of floating bodies

 When a body is floating, it is said to be in neutral equilibrium when the body neither returns to its original position nor it moves any further.

M is the meta centre of the body. If it lies exactly at the same point where gravity, G lies then the body is said to be in neutral equilibrium.

What do you mean by stable equilibrium?

We have seen that in neutral equilibrium the body remains in its new position. Now in stable equilibrium the body comes back to its original position after the force is lifted up or is no more acting on it.

The displacement occurs as a result of external force applied on the body. Neutral equilibrium and stable equilibrium may sound similar but are different from each other.

Is stable equilibrium and neutral equilibrium same?

Stable equilibrium and neutral equilibrium might sound similar but they are different from each other. Although there is not much difference between them either.

The primary difference being that in stable equilibrium, the body comes back to its original position but in neutral equilibrium the body remains stationary at the new position without moving back to its original position or moving any further.

What is unstable equilibrium?

Unstable equilibrium is a state of the body where even a small movement in the body will result in a big change. That means the body is so unstable that a slight push will hamper its equilibrium condition.

We can observe unstable equilibrium in everyday lives. For example, if we place a pointed tip on a book and move the book slightly, the pointed top immediately falls down. Likewise if we place a bottle having a narrow cap upside down, it may stay stationary but as soon as a slight force is applied, it will fall down.

Significance of equilibrium

We all have experienced that perfection comes with stability. In Physics, we can observe that every atom experiences certain kind of force.

  • The atom is stable because the inter atomic forces are balanced The moment we try to split an atom, we get an atomic bomb!
  • While using a pair of scissors we find it inconvenient if the object is moving here and there, we can cut easily if it is clamped or held by hand.
  •  Walking on an inclined road is difficult because we are working against the gravity hence equilibrium is disturbed.
  • Aeroplane cruises as a result of balance between force due to gravity and upthrust.
  • Walking is also an example of balanced equilibrium, if the gravity would have been lesser than we could have started floating mid air.

There are numerous examples in daily lives where we can thank equilibrium for existing. Without equilibrium we couldn’t be having such simplicity in our lives.

Also Read:

Mass Flow Rate And Temperature: Effect, Relation ,Problem Examples

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This article discusses about relation between mass flow rate and temperature. For incompressible fluids, volume rate and mass flow rate go side by side.

We will narrow the discussion by defining the system and science happening there. We will consider a system where heat transfer is taking place, lets say water flowing in a pipe. The entire discussion in this article will revolve around this system.

What is heat transfer?

Heat transfer in simple terms is the transfer of energy (or entropy) from one point to other. It is measured by the temperature change taking place between unit length of system.

We can say that heat transfer is directly proportional to temperature change and inversely proportional to length of the system. Mathematically, heat transfer can be given by-

What are different modes/types of heat transfer?

Heat transfer from one substance to another can take place by many means. Sometimes, it needs a medium for transfer and sometimes it doesn’t.

Lets see what are different types of heat transfer-

  • Conduction–  Heat is transferred between two points when the molecules between them collide with each other. The vibrational energy of the atoms is transferred from on atom/molecule to other. This way the heat propagates. This implies, for heat transfer to take place by conduction it needs a medium.
  • Convection– The heat is transferred by the movement of fluid. This fluid can be air or water.
  • Radiation- The heat transfer can take place in absence of a medium. Radiation heat transfer takes place in the form of electromagnetic waves.

Mass flow rate and temperature relation

Lets consider water flowing through a pipe. Water being a incompressible fluid means that volumetric flow and mass flow rate are proportional.

Lets consider two cases-

  • Low mass flow rate/volumetric flow rate: The volumetric flow rate of the water is low that means volume/mass of water flowing through the pipe section per second is less hence the water molecules will get heated up faster.
  • High mass flow rate/volumetric flow rate: If the number of molecules of water flowing through a point is more then it will take more time to heat them up. Hence, we can say that temperature difference in this case will be lesser.

Mass flow rate and temperature equation

As we have discussed above, the temperature difference in the system is inversely proportional to the mass flow rate in the system. That is, as mass flow rate increases the temperature difference decreases.

The relation between mass flow rate and temperature difference is given below-

gif

For same value of heat transfer we can say that the temperature difference is inversely proportional to the mass flow rate.

How does temperature affect mass flow rate?

The temperature increases the velocity of the molecules flowing hence the kinetic energy of the fluid increases with increase in temperature.

How to calculate pressure from mass flow rate?

Hagen Pouisuille law equation says that pressure is directly proportional to the flow rate.

Q is the flow rate and it is the rate of change of volume. For fluids whose density is constant that is incompressible fluids, mass flow rate is directly proportional to volume flow rate. Hence we can say that pressure increases with mass flow rate.

The Hagen Pouisueille equation is given below-

gif

where,

mu is the dynamic viscosity

Q is the flow rate in liters per second

What is a heat exchanger?

As the name suggests, heat exchangers is a device used for exchanging heat between two substances. It can be used to cool or heat the other substance by using a working substance.

Evaporator and condensers are also types of heat exchangers. Condenser and evaporators are discussed in below sections. Heat exchangers find their applications in refrigeration systems, power plants, air conditioning systems etc.

mass flow rate and temperature
Image: Reheat in Heat Exchangers

Types of heat exchangers

On the basis of direction of cold fluid and hot fluid the heat exchangers can be classified into three types. They are given below-

  • Parallel flow heat exchanger- In this type of heat exchanger, both the cold and hot fluid flow in the same direction.
  • Counter flow heat exchanger– In this type of heat exchanger, both hot and cold fluids move in opposite direction to each other.
  • Cross flow heat exchanger– In this type of heat exchanger , hot and cold fluids move perpendicular to each other.

Different applications require different types flow directions between the hot and cold fluids. The governing principle is same in all the three types.

What is an evaporator?

An evaporator is a type of heat exchanger used for converting the liquid phase of a substance to its gaseous form. For example, water gets converted into vapor. Entire phase change process occurs with no temperature change.

The heat transferred from the hot fluid is equal to the heat absorbed by the colder fluid. Evaporator is used in refrigeration systems to remove the heat from the food and beverages kept inside the refrigerator.

What is condenser?

A condenser is a type of heat exchanger which used for converting a gaseous phase of a substance to liquid phase of that substance. For example, vapor converting back to liquid form. Entire phase change process occurs with no temperature change.

The heat transferred to the cold fluid is equal to the heat absorbed by the hotter fluid. Condensers are used in power plants where the exhaust steam from the turbine is converted into liquid

What is LMTD?

LMTD also known as Logarithmic Mean Temperature Difference is a term used in heat exchangers. It is the logarithmic average of temperatures of cold fluid and hot fluid.

LMTD is used for finding the overall heat transfer taking place inside the system. It takes into account initial and final temperatures of both hot fluid and cold fluid. The formula for LMTD is given below-

gif

Where,

Delta T1 is the temperature difference between the initial temperatures of both hot and cold fluids.

Delta T2 is the temperature difference between the final temperatures of both hot and cold fluids.

Mass Flow Rate And Pressure: Effect, Relation ,Problem Examples

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This article discusses about mass flow rate and pressure. They both have a direct relation between them (although no direct formula). Lets study more about it.

Anything which flows is bound to have certain mass. The amount of mass which passes through a point per second is called as mass flow rate. The term mass flow rate finds its use in thermal engineering and fluid mechanics. Lets discuss more about mass flow rate in this article. 

What is pressure?

Pressure is the amount of force exerted per unit area. For the same amount of force, if the area is smaller then value of pressure is more and if the area is more then the value of pressure is less.

The units of pressure is N/m^2. Mathematically, pressure can be given by-

P = F/A

Where,

F is the force applied normal to the cross section

A is the area of the cross section

What is mass flow rate?

The term flow means anything pertaining to movement. Mass flow rate refers to an amount of mass passing through a point per second. The mass can be of anything such as gas, water, oil or any other fluid.

The term mass flow rate is very important term used in fluid mechanics and thermal engineering. Its applications lie in turbo machinery, rockets, aeroplane and many other fluid related applications. Mathematically, mass flow rate can be given as,

Mass flow rate and pressure relation

Logically, more the pressure applied to the inlet section will mean more pressure difference is created between inlet and outlet hence more mass will try to rush through the section. Hence, we can say that mass flow rate is directly proportional to pressure (gradient).

Even vice versa is true, when more mass flows through a point per second then the force exerted by the mass molecules on the surface of the section will be greater hence pressure will be more if mass flow rate is more. Hence we can say both are directly proportional to each other. Note that this completely true for incompressible fluids like water.

Does mass flow rate change with pressure?

Note that alone pressure has no effect on mass flow rate, it is the pressure difference created that affects the flow rate.

The value of pressure difference between the inlet section and outlet section affects the mass flow rate. If the pressure difference is more then the mass flow rate will be more and if the pressure difference will be less then the mass flow rate will be less.

Alone greater pressure has no effect on the flow rate, if both the inlet and outlet has high value of pressures and low difference between them then the flow rate will be low due to low pressure difference. We will get more clarity by looking at an example.

Mass flow rate and pressure difference relation example

As discussed in earlier section, pressure difference directly affects the mass flow rate. This can be explained using simple example discussed below.

The aeroplane will generate more lift when there is a larger pressure difference (as in cambered airfoils). If there is large pressure values on both the sides of airfoil then there won’t be any significant change in pressure values and thus no or very less pressure difference will be there. Due to this very less air will flow hence generating lesser lift.

Bernoulli’s equation

The Bernoulli’s principle is meant for incompressible fluids which states that when a fluid is flowing in a streamline flow then velocity increases with decrease in static pressure.

In simple terms, Bernoulli’s principle means- Static pressure+Dynamic pressure= Total pressure and that is said to be constant.

Mathematically, Bernoulli’s principle can be given as-

gif
mass flow rate and pressure
Image: Fluid flowing through a venturi meter

Image credits: user:ComputerGeezer and Geof, VenturiFlow, CC BY-SA 3.0

Hagen Poisueille law

This law given the direct relation between pressure difference and the volumetric flow rate.

This law gives the relation for pressure drop for incompressible Newtonian fluids in a laminar flow. The Hagen Poisueille equation is given as follows-

gif

What are the different types flow?

There are three main types of flows- Laminar, turbulent and transient flow.

Laminar flow

This type of flow is characterized by fluid particles flowing in a smooth manner. Each layer moves past the adjacent layer in such a manner that they don’t mix. We can tell whether the flow is laminar or not by looking at the value of Reynold’s number of the flow. Reynold’s number is discussed in later sections of this article.

Turbulent flow

This type of layer is characterized by mixing of two fluid layers in a flow. The flow is more violent than laminar flow. It is desired when mixing of two fluids is to be done.

Transient flow

Transient flow is simply the transition between laminar and turbulent flow.

Reynold’s number

Reynold’s number is dimensionless number which is used for determining the type of flow in the system.

The ratio of inertial forces to viscous forces is called as Reynold’s number. The general formula for Reynold’s number is given below-

gif

where,

mu is the dynamic viscosity

V is the velocity of flow

Significance of Reynold’s number

As discussed in above section, Reynold’s number is used to find the type of flow in the system. It gives us an idea about the inertial and viscous effects of flow on the system.

For fluid flowing over a flat plate-

  • Laminar flow- Re<3×10^5
  • Turbulent flow- Re>3×10^5

For fluid in a circular pipe-

  • Laminar flow- Re<2000
  • Turbulent flow-Re>4000
  • Transient flow-2000<Re<4000

Prandtl number

Prandtl number is named after the physicist Ludwig Prandtl. It is a dimensionless number which is used for determining the behaviour of heat transfer.

Prandtl number is the ratio of momentum diffusivity to thermal diffusivity. The mass analog of Prandtl number is Schmidt number. Mathematically, it can be written as-

gif

Cp is the specific heat at constant pressure

k is the thermal conductivity

Mass flow rate example

Let us assume following data for a system.

Density of the fluid- 0.2 kg/m^3

Area of the cross section- 1m^2

Volume flow rate- 10m^3/s

Use the following data to calculate the mass flow rate in the system.

Mass flow rate can be found using the formula given below-

gif

From using the formula given above, we get mass flow rate as- 2kg/s.