Stokes law is an equation used to calculate the force created by a particle in a viscous fluid — typically air or water — due to its motion. It is a useful tool for scientists, engineers and researchers who study material and fluid mechanics.
The equation was first described by Irish physicist and mathematician George Gabriel Stokes in 1851 and is used to describe the behavior of objects in a fluid at low Reynolds numbers. In basic terms, the equation can be used to calculate the frictional drag force (also known as viscous force) experienced by a particle when it is moving through a viscous fluid at a given velocity.
The equation is also used assess the behavior of particles of different sizes and shapes. The equation takes into account the size, shape, and velocity of the particle, as well as the viscosity of the fluid, to calculate the dynamic drag force.
It can then be used to calculate the resistance of the particle to motion and assess the nature of the particle’s interactions with the fluid.
How does Stokes law calculate time?
Stokes law is a law of physics that relates the viscous drag force on a small object that is moving through a fluid to the properties of the fluid and the size, shape, and velocity of the object. It is used to calculate the time a particle will take to reach a given state of motion due to the force of drag.
This type of calculation is useful in many physical situations, such as calculating the motion of a sinking or rising particle or determine the motion of a ball rolling down a hill. The mathematical formula used to calculate time via stokes law is:
Time (sec) = 1.11 * x * (V^2) / (d_particle^2 * g * ρ)
Where x is the drag coefficient, V is the velocity of the object, d_particle is diameter of the particle, g is the gravitational acceleration and ρ is the fluid density.
What is Stokes in viscosity?
Stokes in viscosity is the well-known flow rate formula in fluid mechanics. This equation was named after the Irish physicist George Gabriel Stokes, who derived it in 1845. Stokes’s law states that the rate of a liquid flowing in a tube is proportional to the applied pressure and the radius of the tube.
It is also inversely proportional to the viscosity of the liquid. In other words, the viscosity of a liquid affects how quickly it flows. Stokes’ law is used when studying the motion of objects like particles, bubbles, and droplets through a viscous medium like water or oil.
It is especially useful for studying the behavior of small particles less than 1 micron in diameter. This includes applications in areas such as rheology (the study of flow and deformation of matter), sedimentation (the process of particles settling at the bottom of a liquid), and particle dynamics.
What is Stokes method physics?
Stokes’ method physics is an analytical approach to solving problems in fluid mechanics. It is alternatively referred to as the Stokes’ theorem or Stokes’ theorem method. This theory was developed by the British physicist Sir George Gabriel Stokes in 1845.
The concept of Stokes’ method arose when Stokes looked to unify the laws of differential calculus and integral calculus to solve applied problems in fluid mechanics.
Essentially, the method allows engineers to identify exact solutions with fewer approximations. It aims to provide a basis for solving a wide range of fluid mechanics problems, including the motion of small particles, potential flow systems, viscous flow systems, and boundary layer problems.
The underlying principle of Stokes’ method is that it uses appropriate equations of motion, boundary conditions, and constitutive equations to characterize a given problem, based on the initial and boundary conditions.
These then form the framework of the problem that can be used to calculate a final solution.
Due to the nature of this approach, Stokes’ method is especially beneficial for studying complex laminar flows and understanding, predicting, and visualizing fluid movement. It is a common approach for calculating hydrodynamic coefficients such as drag force and lift force in aircraft design, and it is also applied to analyze low-speed flows, turbulence, and wave motion in oceanography.
What are the four conditions of Stokes law?
Stokes’ law is an equation that is used to calculate the drag force, or the force that is produced when an object moves through a fluid medium. It is named after physicist George Gabriel Stokes and is valid for objects that have a diameter much smaller than the length of the path of the fluid (known as slow flow).
It is also applicable for objects that are moving much slower than the speed of sound in the medium.
The four conditions of Stokes’ law are as follows:
1.The viscosity of the fluid must be low. Viscosity refers to the resistance of the fluid to flow, and a low viscosity implies that it flows more easily.
2.The size of the particles must be much smaller than the length of the path taken by the fluid.
3. The Reynolds number must be low. Reynolds number is a dimensionless number that is used to indicate the relative magnitude of inertial forces and viscous forces in a fluid, and a low Reynolds number indicates that the viscous forces are greater than the inertial forces.
4.The speed of the particles must be much slower than the speed of sound in the medium.
What is stock’s force Class 11?
Stock’s Force Class 11 is a program designed to help students in India prepare for their Class 11 exams. It is an online coaching program created by Rahul Stock, a renowned teacher and education mentor, in partnership with Stock’s Learning.
The program offers comprehensive coaching and practice materials covering the board syllabus of Science, Maths and Commerce. The Stock’s Force Class 11 program aims to provide a complete and holistic learning experience, with live class lectures led by Rahul Stock himself, weekly quizzes and assignments, detailed doubt-resolution sessions, recorded 24/7 interactive classes, customised practice materials and more.
By equipping learners with essential problem-solving and analytical skills, the program helps them to tackle the toughest of questions in their exams confidently and come out with flying colours.
What is Stokes law of viscosity derive expression for terminal velocity?
Stokes law of viscosity is an equation used to describe the relationship between the terminal velocity of a small object and its properties such as size, shape, and density. It was discovered by George Gabriel Stokes in the 19th century and is an important equation in particle dynamics and fluid dynamics.
The equation used to calculate the terminal velocity of a small object is called the Stokes law of viscosity and is represented by the following equation:
V = ((2*g*d*ρ)/(3*μ))⁰.⁵
In the equation, V is the terminal velocity of the object (in m/s); g is the acceleration due to gravity (in m/s²); d is the diameter (in m); ρ is the density (in kg/m³); and μ is the viscosity of the fluid (in Pa s).
To briefly explain how this equation works, the key idea is that since the object-fluid interaction is due to the viscosity of the fluid, the equation takes into account the density, size, and viscosity of the object, as well as the acceleration due to gravity and the viscosity of the fluid.
Ultimately, this equation can be used to accurately calculate the terminal velocity of any given small object.
What is Stokes Law in simple definition?
Stokes Law, named after Sir George Stokes, is an equation that states that the force that is required to keep a small spherical object moving through a fluid is proportional to the velocity of the object times the radius of the object.
It is used to calculate the terminal velocity of an object in a fluid and how friction from the fluid affects the object. Generally, this law states that in a viscous liquid the slowing effect is proportional to the velocity.
This means that, if the velocity is doubled, the frictional effects will also double. Similarly, if the velocity is halved, the frictional effects are also halved. Stokes Law is important in both the study of fluids and in the physical and medical sciences when considering the terminal velocity of a small object falling through a viscous medium like water or air.
How do you use Stokes law?
Stokes law is a formula used to calculate the frictional force due to fluid drag on small spherical objects moving through a fluid. The formula accounts for the viscosity of the fluid and the physical characteristics of the object such as size, shape and density.
Stokes law is useful in a variety of contexts such as particle sedimentation rates, predicting settling velocities in particulate filters, or calculations of drag forces on droplets or bubbles in liquid or gaseous media.
The primary equation used in Stokes law is:
F = 6πηvrd
F = frictional force in dynes (also known as a Newton per square meter)
η = viscosity of the fluid in poise (1 poise = 0.1 Pa·s [pascal second])
v = velocity of the spherical object in cm/s
r = radius of the spherical object in cm
d = density of the solid in gm/cm3
Using this equation, engineers can calculate the frictional force with a given set of conditions. For example, if you want to calculate the frictional force on a particle with a radius of 0.2 cm, travelling at a velocity of 1 cm/s in water, you can solve the equation like this:
F = 6πηvrd
F = 6 * 3.14 * 0.01 * 1 * 0.2 * 1000
F = 37.68 dynes
So the frictional force on this particle in water is 37.68 dynes.
Which lesson is Stokes law?
Stokes law is a law of physics which is also known as the Law of Viscous Drag. This law describes the effects of drag forces on particles in a fluid and states that these drag forces are proportional to the radius of the particle.
It was developed by the physicist George Gabriel Stokes in 1851 and has since been used to describe the motion of fluids in various objects. The law states that the viscosity of a fluid increases the resistance of an object, and the force of drag is proportional to the radius and the terminal velocity of the particles.
This law is commonly used in applications such as engineering, liquid dynamics, electrostatics, and to study the motion of blood cells in the heart. It is also used to analyze/understand the motion of bubbles and particles in liquids, crystallization processes, and the transfer of heat and momentum.
Which of the following formula states the Stokes law?
The Stokes law is stated by the following formula:
F⃗=6πηRv⃗, where F⃗ is the drag force, η is the viscosity of the fluid, R is the radius of the object, and v⃗ is the relative velocity of the fluid to the object. This law explains the drag force of a fluid on a stationary object, taking into consideration the object’s size, surface, and the relative movement of the fluid.
The law was developed in 1851 by Sir George Stokes and is applicable to materials moving in a straight line and assuming the flow is laminar, i. e. , having low to moderate turbulence. The Stokes law is considered to be a good approximation when the object size is much smaller than the characteristic length of the flow.
However, when the object size is comparable to the flow characteristics, the approximation is no longer valid.
When can Stokes law be applied?
Stokes law can be applied when objects are moving in a fluid, such as a liquid or gas, at low Reynolds numbers, meaning the viscous forces are more significant than the inertia of the object. At these situations, objects will experience a viscous force with an instantaneous velocity, which Stokes law can be used to calculate.
This formula can calculate the viscous force for a wide range of vessels and objects, including spheres, disks, ellipsoids, and cylinders, with different Reynolds numbers. It is applicable when the particle/object radius is in the range 10^-5 m and 10^-2 m, and the velocity of the particle is less than 1 mm/s.
The equation can also be used to calculate the sedimentation velocity in fluids or the drag force on objects moving quickly. Stokes law is also applicable in air if the viscosity of air is accounted for.
