Stokes law in chemical engineering is an equation that is used to calculate the terminal velocity of an object, such as a particulate, in a fluid medium, such as a liquid or a gas. It is named after George Gabriel Stokes who developed the equation in 1851.
Stokes’ law is the basis for many practical calculations in chemical engineering, such as sedimentation and filtration, where particulate matter such as sediment, colloids and crystals, are moved through a fluid medium.
The equation captures the combined effects of all forces acting on the particle in the fluid. The equation states that the terminal velocity of a particle is inversely proportional to the square of its particle diameter, and directly proportional to the force generated by the acceleration of gravity and the density of the fluid.
This equation can be used to calculate the velocity of the particle as a function of the particle diameter, fluid density, fluid viscosity, and accelerates due to gravity. As such, it is an important equation for any engineering application involving the movement of particles in a liquid medium.
What is Stokes law derive its formula?
Stokes law is a useful equation that describes how a particulate object, such as a particle suspended in a liquid, will settle from the liquid’s surface due to the apparent weight of the particle. The equation was formulated by George Stokes in 1851.
Stokes’ law states that, for small Reynolds numbers, the settling velocity of a small sphere in a viscous fluid is proportional to the particle’s mass-to-surface area ratio and the viscosity of the fluid.
This means the settling velocity of a particle is inversely proportional to its radius, making smaller particles have higher velocities. The full equation is written as follows:
U=(-2*(Δρ*G*r^2))/(9*η)
Where U is the particle’s settling velocity; Δρ is the difference in density between the particle and the medium (usually air or water); G is acceleration due to gravity; r is the particle’s radius; and η is the dynamic viscosity of the medium.
Stokes’ law holds true for particles whose diameter is less than around 2 mm, and for fluids of low viscosity, such as water and air.
Which lesson is Stokes law?
Stokes law is a law in fluid dynamics that provides the frictional force between the moving particles in a fluid given the fluid’s viscosity, diameter of the objects, and the speed at which they are moving.
It was proposed by George Stokes in 1851 and was later refined by Horace Lamb in 1908. In its simplest form, Stokes law states that the force, F, on a sphere is proportional to the velocity, v, squared and to the radius, r, squared: F=6πηrv, where η is the dynamic viscosity of the fluid.
It is one of the fundamental laws of fluid dynamics and has applications in many engineering fields, such as particle deposition, sedimentation, and the study of layered fluid flows. It can also be used to calculate drag forces on objects, such as those encountered in sailing and flight.
What is Stokes method physics?
Stokes Method Physics is a method in hydrodynamics that was developed by George Gabriel Stokes in the 19th century. It is used to solve problems dealing with flows of thin, viscous fluids such as water, oil, and air.
The method is first used to divide a flow field into individual elements, then calculate the forces created on each element. These forces are then used to solve the equations of motion for each element.
This results in calculating the velocity, pressure, and other properties of the flow. Stokes Method Physics is useful in engineering applications such as airfoils and turbine blades, as well as in studying ocean currents, wave motion, and other fluid dynamics.
What is the two application of Stokes law?
Stokes law is used in a variety of fields, particularly in the realm of fluid dynamics, where it can predict the motion of large particles in a fluid. One of the most common applications of Stokes Law is to calculate drag force in a fluid.
This can be used to analyze the motion of objects through the air or water, such as a rocket or boat, and to optimize the design of streamlined objects so that they move with minimum drag. Another important application of Stokes Law is in sedimentation, where it is used to calculate the speed at which solid particles sink in a fluid.
This has applications in fields such as environmental engineering, for example for calculating the rate of settling of pollutants in water reservoirs.
What is terminal velocity Class 11?
Terminal velocity Class 11 is a type of vertical acceleration a diver can reach when falling in a non-constant gravitational environment such as through the water. This vertical acceleration is called terminal velocity and is equal to the weight of the object divided by its projected area in the direction of motion.
For an object falling through a fluid, such as water, the fluid drag is proportional to the velocity of the object and is in the opposite direction to the motion of the object. This is why, when a diver jumps from a diving board, they can reach a certain terminal velocity, meaning that the acceleration of the falling object slows down as the forces of drag reach a balance with the force of gravity on the object.
In Class 11, the terminal velocity that can be reached when a diver is falling in water without other influences is 10 meters per second.
What is the study of the properties of fluids in motion is called?
The study of the properties of fluids in motion is called fluid dynamics. Fluid dynamics is the scientific study of how fluids of all types – including liquids, gases, and complex mixtures such as slurries and foam – behave when they are subjected to forces.
Fluid dynamics is concerned with the motion of fluids and the exchange of energy and momentum with their surroundings. It also looks at the ways in which forces and torques act on the boundaries of a fluid, which can be either solid or other fluids.
Many of the phenomena studied are common in everyday life, such as the flow of air over a wing of an airplane or the movement of water in a river. Other applications of this field include the behavior of Earth’s atmosphere and oceans, the atmospheric surface layer, geophysical and oceanographic flows, complex chemical and biological processes, magma flows, and the behavior of transient events, like blowout of an oil well.
When can Stokes law be applied?
Stokes law can be applied whenever the flow of a liquid is slow enough and the particles are small enough that the effects of viscosity can be ignored. It can be used to calculate the frictional force between two objects suspended in a liquid, or the terminal settling velocity of a particle in a liquid.
It also allows us to estimate the size of particles in a suspension. Stokes law is a valuable tool when dealing with colloidal dispersions, such as milk, paint, detergents, and emulsions, since it takes viscosity into account.
It can also be used to calculate the flow rate of a gas through a small orifice, as well as for determining the pumping rate of a gas or liquid through a pipe. Ultimately, when the flow of a liquid is sufficiently slow, and the shape, size, and relative motion of the particles are known, Stokes law can be applied.
Which is the practical examples of Stokes law?
Stokes Law is a fluid dynamics principle that relates the motion of a small solid particle in a fluid (typically a liquid or gas) to the ambient fluid properties and the particle’s characteristics. It is useful for predicting drag forces and calculating terminal settling speed of particles suspended in a fluid.
Some examples of how Stokes Law is applied in practical areas include:
1.In civil engineering for calculating the sedimentation of particles suspended in a flow, or the removal of particles from water source by settling.
2.In determining the settling velocity of solid particles from industrial process effluents.
3.In the pharmaceutical industry, size distribution of drug particles during formulation is determined by the Stokes Law.
4.In oceanography, drift speed of plankton (which affects plankton distribution) can be calculated using Stokes Law.
5.In engineering, settling of grain sizes in a sedimentary basin and fluid viscosity can be determined using Stokes Law.
6.In mining, using Stokes Law to calculate the velocity of a falling particle assists in optimizing particle separation process.
7.In geophysics, Stokes Law is used to calculate the effects of turbulent transport on particles or bubbles in turbulent flow regime.
8.In industrial processes, Stokes Law can be used to calculate the settling velocity of particles in chemical reactors.
9.In the cosmetics industry, particle sizing for the production of different textured products is determined by Stokes Law.
10.In optical microscopy, Stokes Law can be used to calculate the sedimentation time of particles in a flow.
How does Stokes law calculate time?
Stokes law is an equation used to calculate the drag force on an object that is moving through a fluid. It is commonly used to calculate the amount of time it will take for an object to settle down to the bottom of the fluid, such as a sphere settling in a liquid or gas.
The equation is F = 6πrv, where F is the drag force, r is the radius of the sphere, and v is the velocity at which the sphere is moving. By rearranging the equation, it is possible to determine the time it will take for the sphere to settle in the fluid.
To solve for time, t, the equation is t = F/6πrv. This equation can then be used to calculate the amount of time it will take for an object to settle in a fluid given its size, material, and velocity.
What is the Stokes law explain?
The Stokes law is an equation which describes the motion of solid particles in a liquid or gas. It is named after reverend George Gabriel Stokes, who first derived the equation in 1851. In its most general form, the Stokes law states that the force applied to a particle submerged in a fluid, is equal to the product of the friction coefficient of the fluid and the particle’s velocity: F = 6πηrv.
In aerodynamics, the Stokes law is often applied to a falling object in order to predict the shape and speed of its trajectory. The law states that the rate at which the object falls is dependent on the viscosity of the air around the object and the size of the object itself.
With this law, the drag force of a particle is proportional to the velocity of the particle squared, which implies that the greater the velocity, the more drag force the particle will experience. In other words, particles will experience greater drag as they travel faster.
Finally, Stokes law can also be used to calculate the terminal velocity of a particle, which is the maximum speed at which a particle can reach in a given environment. This is important for applications such as aerosols and dust in air, where particles can be suspended in the air and travel in the atmosphere for long periods of time.
Which of the following formula states the Stoke’s law?
Stoke’s law states that the frictional force exerted by a fluid on a particle is directly proportional to the velocity of the particle, and is inversely proportional to the radius of the particle, according to the formula: F = 6πηrv, where F is the frictional force, η is the coefficient of viscosity of the fluid, r is the radius of the particle, and v is the velocity of the particle.
Stoke’s law allows us to calculate the drag coefficient (Cd) associated with the particle, which depends on the shape of the particle. By using the Cd value, Stoke’s law can then be used to calculate the frictional force experienced by the particle in terms of the above variables.
What is stokes law and how is it used in soil science?
Stokes’ Law is a theoretical law that predicts the motion of a solid particle in a fluid medium. It is named after British physicist George Stokes, who developed the law in 1851. The law states that for a solid particle in a fluid, the terminal velocity is proportional to the square of the particle’s diameter and inversely proportional to the fluid’s viscosity.
It can be used to calculate the settling speed of a particle in a fluid and is commonly used to calculate sediment transport in soil science.
In soil science, Stokes’ Law is used to predict the downward movement of soil particles due to gravity. It is used to predict soil erosion and other particle-induced natural phenomena on land and in aquifers.
It is also used to predict the accumulation and deposition of sediment in rivers and lakes. This is especially useful in areas of high turbidity, where sediment accumulates quickly and reduces water clarity.
Stokes’ Law is also used in soil conservation to determine rates of loss and gain of sediment, as well as to help gauge the effectiveness of soil conservation practices. Ultimately, understanding and predicting sediment transport is critical to successful soil conservation, management, and restoration.
