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Stokes’ law is concerned with the active force exerted on a body when it is immersed in a liquid. Because of the low viscous force, the falling body’s velocity initially remains low. However, as the spherical body falls with its effective weight, it gains acceleration, and the body’s velocity gradually increases. This causes the liquid in contact to move at the same rate as this body. The movement of an object in this fluid with increasing velocity causes motion in the liquid layers, which results in the formation of viscous force. This force increases with increasing velocity until it reaches the point where it equals the effective force with which this body moves.
In this case, the net force on the body is zero, and it attains a constant velocity known as terminal velocity (Vt). This concept contributed to the formulation of Stokes’ law, and this derivation of frictional force or Stokes’ drag applies to the interface between the body and the fluid. Sir George Stokes stated that “the force acting between the liquid and falling body interface is proportional to velocity, the radius of the spherical object, and fluid viscosity.” Stoke’s law explains why raindrops that fall from the sky do not harm us on the ground. Stokes law is an extremely important physics concept.
Overview:
Stokes’ Law is an equation that describes how small spherical particles settle in a fluid medium. The law is derived by taking into account the forces acting on a specific particle as it sinks through a liquid column under the influence of gravity. The force that retards a sphere moving through a viscous fluid is proportional to the sphere’s velocity, radius, and fluid’s viscosity.
Stokes’ Law is a mathematical equation that describes the behaviour of small spherical particles in a fluid medium. The law is derived by considering the forces acting on a specific particle as it sinks through a liquid column under gravity’s influence. The force that slows a sphere moving through a viscous fluid is proportional to the sphere’s velocity, radius, and viscosity of the fluid.
The force that slows a sphere as it passes through a viscous fluid is proportional to the sphere’s velocity, radius, and fluid viscosity. Stokes’ law has many applications, including sediment settlement in freshwater and determining fluid viscosity. The net force on the body is zero in this case, and it achieves a fixed velocity known as terminal velocity. This definition aided in the formulation of Stokes’ law, and this derivation of frictional force or Stokes’ drag applies at the body-fluid interface.
Stokes’ Law Equation:
In 1851, Stokes devised this formula to calculate the drag force or frictional force of spherical objects immersed in viscous fluids. Sir George G. Stokes, an English scientist, stated the viscous drag force F as follows:
F=6πηr v
Where,
F denotes the drag or frictional force at the interface.
η is the liquid’s viscosity
The radius of the spherical body is denoted by r.
V denotes the flow velocity.
Stokes’ Law Derivation:
The viscous force acting on a sphere is directly proportional to the following parameters, according to Stoke’s Law viscosity equation:
- The coefficient of viscosity of the radius of the sphere
- The object’s velocity
The mathematical representation of Stokes’ assertion regarding the immersion of a spherical body in a viscous fluid is as follows:
F∝ η a r b v c
The Stokes’ law equation can be obtained by solving this proportional expression. We must add a constant to the equation to convert this proportionality sign to equality. Consider that constant to be ‘K,’ and the transformed equation becomes
F=kη a r b v c → equation (1)
In this case, k is the proportionality constant, which is a numerical value with no dimensions.
When we write the parameters’ dimensions on either side of equation (1), we get
M L T-2= [ML-1 T-1 ]a [L]b [ LT-1] c
When we simplify the preceding equation, we obtain
M L T-2=Ma·L-a+b+c·T-a-c → equation(2)
Mass, length, and time are all independent entities in classical mechanics. We get by equating the superscripts of mass, length, and time from equation (2).
a=1 → equation(3)
-a+b+c=1 → equation(4)
-a-c=2 or a+c=2 → equation(5)
Substituting (3) into (5) yields
1+c=2c=1 → equation (6)
Substituting the values of (3) and (6) in (4) yields
-1+b+1=1 b=1 → equation (7)
We get by substituting the values of (3), (6), and (7) in (1).
F= ηk r v
The experimental value of k for a spherical body was found to be 6π.
As a result, the equation gives the viscous force on a spherical body falling through a liquid.
F=6πηr v
Stokes’ Law Applications:
Raindrop Velocity: Raindrops do not travel at extremely high speeds during their free fall. A person walking in the rain will be injured if this does not happen. This is due to the fact that the viscous drag in air opposes the velocity of raindrops as they fall due to gravity. When the viscous force equals the force of gravity, the drop reaches a terminal velocity. As a result, raindrops that fall to the ground have low kinetic energy.
When we jump out of an airplane, we use a parachute to help us land safely on the ground. Because in this case, the person falls with a g acceleration due to gravity, but the acceleration decreases due to viscous drag in the air until the person reaches terminal velocity. The individual then descends at a constant rate and opens his parachute close to the ground at a predetermined time, allowing him to land safely near his destination.
It is used to compute an electron’s charge.
Conditions under which Stokes’ law is valid are:
- The fluid that the body moves through must have an infinite extension.
- The body is both rigid and smooth.
- There is no movement of the body or the fluid.
- The movement of the body does not cause turbulent motion.
- As a result, the motion is streamlined.
- The body is small, but it is larger than the distance between the liquid molecules.
- As a result, the medium for such a body is homogeneous and continuous.
Frequently Asked Questions (FAQs):
Question 1: What is Stokes’ Law?
Answer: In a nutshell, Stoke’s law discusses the active force applied to a body when it is dropped into a substance. The falling body’s velocity initially remains low due to the low viscous impact. When the spherical body sinks with its effective weight, however, it experiences acceleration, and the body’s velocity steadily increases. Stoke’s law explains why raindrops that fall from the sky do not harm us on the ground. Stokes’ law is an extremely important physics concept.
Stokes’ Law is an equation that expresses the drag force that prevents small spherical particles from falling through a fluid medium.
What does Stokes' Law state?
According to Stokes' Law, the force that retards a sphere moving through a viscous fluid is directly proportional to the sphere's velocity, radius, and fluid viscosity.
Question 3: What is the importance of Stokes’ law?
Answer: Stokes’ law is extremely important in a variety of fields. Some important fields where it is used include:
- It aids Millikan in determining the electronic charge in his oil-drop experiment.
- It also aided a man who was parachuting down.
- The law also provides an explanation for cloud formation.
