What is Stokes laws derive the formula for this by dimensional method?

What is Stokes laws derive the formula for this by dimensional method?

Suppose that the sphere has radius r and falls through a fluid of viscosity η. Let the terminal velocity be v (Figure 1). We can calculate the viscous drag F on the sphere by dimensional analysis. Solving this gives x = 1, y = 1 and z = 1.

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 the statement of 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.

What is Stokes law and terminal velocity?

Stokes’s law, mathematical equation that expresses the drag force resisting the fall of small spherical particles through a fluid medium. At a constant velocity of fall called the terminal velocity, the upward and downward forces are in balance.

What is Stokes law in physics class 11?

Stokes Law. Stokes Law. The force that retards a sphere moving through a viscous fluid is directly ∝to the velocity and the radius of the sphere, and the viscosity of the fluid.

What is Stokes theorem used for?

Summary. 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.

When can Stokes theorem not be used?

Stokes theorem does not always apply. The first condition is that the vector field, →A, appearing on the surface integral side must be able to be written as →∇×→F, where →F would either have to be found or may be given to you. If →F cannot be found, then Stokes theorem cannot be used.

What’s the unit for viscosity?

newton-second
What is the unit of viscosity? The unit of viscosity is newton-second per square metre, which is usually expressed as pascal-second in SI units.

How do you find terminal velocity in Stokes law?

Solution: The terminal velocity of a sphere of radius r and density ρ , immersed in a liquid of density σ and viscosity η , is given by v=29(ρ−σ)r2gη.

When did Stokes come up with the Stokes law formula?

Stokes Law Formula Stokes came up with this formula in 1851 to calculate this drag force or frictional force of spherical objects immersed in viscous fluids. Here, look at the formula mentioned below. F = 6 * πηrv

How is the Stokes law of motion derived?

The law is derived considering the forces acting on a particular particle as it sinks through the liquid column under the influence of gravity. The force that retards a sphere moving through a viscous fluid is directly proportional to the velocity and the radius of the sphere, and the viscosity of the fluid.

What is the net downward force of Stokes law?

Stokes’ law describes the settling of spheres in a Newtonian fluid. A spherical particle placed in a Newtonian fluid will sink if the buoyant force does not match or exceed the gravitational force on the sphere. The net downward force on a sphere is the difference between the settling force and the buoyant force.

What happens to the viscous force in Stokes law?

The viscous force acting on the body, according to Stokes law, can be given as F = 6 π η r v; as the velocity increases, so does the force acting on the body. When the body’s weight gets balanced by the sum of the upthrust and viscous force, no net force acts on the body. Hence its acceleration becomes zero.