What is Stokes equation?
Navier-Stokes equation, in fluid mechanics, a partial differential equation that describes the flow of incompressible fluids. The equation is a generalization of the equation devised by Swiss mathematician Leonhard Euler in the 18th century to describe the flow of incompressible and frictionless fluids.
How is Stokes drag calculated?
He found what has become known as Stokes’ Law: the drag force F on a sphere of radius a moving through a fluid of viscosity η at speed v is given by: F=6πaηv. Note that this drag force is directly proportional to the radius.
What is the Stokes equation to determine particle size?
Stokes diameter is the diameter of a sphere that has the same density and settling velocity as the particle. Aerodynamic diameter is the diameter of the unit density sphere that has the same settling velocity as the particle. – V ts = 0.003 x SG x d2 at NTP. – This equation gives V ts in cm/sec using d in microns.
What is stokes law in water treatment?
If a specific gravity of the particle is greater than the specific gravity of the water i.e., 1, then the particle will settle down under the action of gravity. The velocity of the particle is calculated using stoke’s law. Now, let us understand more about Stoke’s law.
What is stokes law and its application?
Stokes Law gives the relation between the velocity and frictional force acting on a spherical body moving in a viscous fluid. This law also gives the settling or terminal velocities of spherical objects moving in a viscous fluid column. The Law. Proof. Terminal velocity.
What is Stokes law write the formula and importance of it?
In Stokes’s law, the drag force F acting upward in resistance to the fall is equal to 6πrηv, in which r is the radius of the sphere, η is the viscosity of the liquid, and v is the velocity of fall. Key People: Sir George Gabriel Stokes, 1st Baronet …(Show more) Related Topics: viscosity fluid flow …(Show more)
What are the four conditions of Stokes law?
Conditions under which Stoke’s law is valid are: The fluid through which the body moves must have infinite extension. The body is perfectly rigid and smooth. There is no slip between the body and the fluid. The motion of the body does not give rise to turbulent motion.
What is stokes law write its condition?
What is Stokes’ law? Stokes’ law is a law in physics that states that the force that resists a sphere’s fall in a viscous fluid is directly proportional to the velocity of the sphere, the radius of the sphere, and the viscosity of the fluid.
Which is the practical examples of stokes law?
Applications of Stoke’s law are as follows: 1. Rain drop do not acquire alarmingly high velocity during their free fall. If this does not happen a person moving in rain would get hurt.
What is stokes law write the formula and importance of it?
What is Stokes law write its condition?
Why do we use Stokes Theorem?
Stokes’ theorem can be used to turn surface integrals through a vector field into line integrals. This only works if you can express the original vector field as the curl of some other vector field. Make sure the orientation of the surface’s boundary lines up with the orientation of the surface itself.
What are the limitations of Stokes equation?
Limitations of the Stoke’s Law. Negative density difference in Stoke’s equation: Stokes’ equation is invalid if the density difference in the equation is negative that is when the particles are lighter than the dispersion medium.
What is stokes law and application?
Stoke’s law explains why the speed of a raindrop is below a freely dropping body with continuous velocity, from the height of clouds. Stokes’ law, with a modified form of Ladenburg’s wall-correction factor, has been applied to determine the viscosity of glass from the velocity of a freely falling platinum sphere.
Which type of operation is used in Stokes theorem?
2. The flux of the curl of a vector function A over any surface S of any shape is equal to the line integral of the vector field A over the boundary C of that surface i.e. It converts a line integral to a surface integral and uses the curl operation. Hence Stokes theorem uses the curl operation.
What are the limitations of Stokes law?
What factors affect Stokes law?
Stoke’s Law Derivation The viscous force acting on a sphere is directly proportional to the following factors: Coefficient of viscosity (η). The radius of the sphere (r). The velocity of the object (v).