How to Prove Stokes Law?

In this blog post, we will discuss how to prove Stokes Law. This is an important step in understanding the theory behind this law and its applications. We will start with a derivation of the equation and then show how it can be used to calculate various properties of fluids. Finally, we will provide some examples that illustrate how Stokes Law can be applied in practice.

What is stoke’s law definition?

Stoke’s law is the fluid drag force that acts on a small sphere moving through a viscous fluid. The force is proportional to the velocity of the sphere and to the viscosity of the fluid.

What is the history of stokes law?

The Stoke law is named after Sir George Gabriel Stokes, who derived the law in 1851. It is sometimes also referred to as the viscous force law or the Stokes-Einstein law. The Stoke law is a simple physical model that describes the frictional force exerted on spherical objects by a fluid when the objects are in motion.

The Stoke law is valid for small particles, whose radius is much smaller than the characteristic length scale of the flow. The law is also valid for slow-moving objects, whose velocity is much smaller than the characteristic velocity of the flow.

What is the Stokes law derivation?

The Stokes law derivation is relatively simple. We start with the stokes law equation:

F= – μ * dv/dr * (r₁-r₂)/(r₁*r₂)

where F is the force, μ is the viscosity of the fluid and dv/dr is the velocity gradient. The terms in parentheses are the radii of the two particles.

We can rearrange this equation to solve for the force:

F= μ * dv/dr * (r₁-r₂)/(r₁*r₂)

Now we take the limit as r₁→r₂ to get the Stokes drag force:

F= μ * dv/dr * (r₁-r₂)/(r₁*r₂)

Now we can plug in the values for our system. For example, if we have a sphere with radius r₁= 0.01 m and fluid with viscosity μ= 0.01 Pa*s, then the Stokes drag force on the sphere is

F= μ * dv/dr * (r₁-r₂)/(r₁*r₂)

F= 0.01 * (0.01-0)/(0.01*0)

F= 0 N

This means that the sphere will not experience any drag force from the fluid.

We can also use the Stokes law equation to calculate the terminal velocity of a falling object. The terminal velocity is the point at which the force of gravity is equal to the drag force.

How is the Stokes law proved?

The Stokes law is proved by deriving the equation that relates the drag force to the velocity of a particle in a fluid. The derivation is based on the assumption that the fluid is a Newtonian fluid and that the flow is steady and laminar. The equation is derived by considering the balance of forces on a particle in a fluid. The drag force is given by the product of the fluid density, the velocity of the particle and the drag coefficient. The Stokes law is valid for low Reynolds number flows. The derivation of the Stokes law is given above.

Proof of Stokes law by using the Reynolds number flow

In fluid mechanics, Reynolds number flow is characterized by a dimensionless quantity that measures the ratio of inertial forces to viscous forces. This number is named after British physicist Osborne Reynolds, who proposed it in 1883. and is represented by the equation:

Re = uD/ν

Where:

Re is the Reynolds number, a dimensionless quantity

u is the fluid’s velocity with respect to some external frame of reference

D is a characteristic linear dimension of the object or system through which the fluid is flowing (for example, the diameter of a pipe)

ν is the fluid’s kinematic viscosity

The Reynolds number is an important dimensionless quantity in fluid mechanics because it can be used to predict the transition from laminar flow to turbulent flow. It is also used to estimate the drag force on objects moving through a fluid. For example, the drag force on a sphere can be predicted using the equation:

F= 6rv

Where:

F is the drag force on the object

is the pi

r= sphere radius

stands for fluid viscosity

is the viscosity of the sphere

This equation shows that the drag force on an object increases as the Reynolds number decreases. This is because the viscous forces become dominant at low Reynolds numbers and the inertial forces become dominant at high Reynolds numbers.

Analysis of the stokes law equation

The stoke law equation is derived from the equation of motion for a viscous fluid. The stoke law equation is used to calculate the drag force on an object moving through a fluid. The stoke law equation is a function of the object’s velocity, the fluid’s viscosity, and the object’s diameter.

Conclusion

In a nutshell, it can be said that in order to prove Stokes’ law, the following must be true: 1) The flow is steady or at least laminar. This means that the fluid is flowing in a smooth and uninterrupted way. 2) There are no vortices present in the system. A vortex is a whirlpool of fluid that can disrupt the flow pattern. 3) The viscosity of the fluid is constant throughout its volume. Viscosity is a measure of how resistant a liquid is to flow. 4) The density of the fluid remains constant. Density is a measure of mass per unit volume. 5) The cross-sectional area of the pipe remains unchanged over time. If any one of these conditions isn’t present then it does not come under the stoke law.