# Investigating Stokes Law: Different Formulas, Different Results?

• LaurenG
In summary, Stokes Law is a mathematical equation used to calculate the drag force on a small particle in a fluid and its terminal velocity. The two main formulas used are the standard and modified formulas, which differ in their assumptions and calculations. Scientists choose which formula to use based on the properties of the particle and fluid. Real-world applications of Stokes Law include fluid dynamics, particle physics, and environmental science, as it helps understand the behavior of particles in liquids and is used in various industrial processes.
LaurenG
Hello all.

I'm investigating a little bit about stokes law in order to understand the settling velocity of falling particles and on the net i encountered with 2 different formulas and i simply can't find the reason why they are different. every formula gives me a different answer.
The 2 formulas are :
1. Vt=gd^2(Pp-Pm)/18u -

2. V=2/9*d^2*g*(Pp-Pm)/u -

Any idea why they are different ?
Thanks.

Last edited:
d=2R

davieddy said:
d=2R

Silly me, i knew it's something stupid.
Thanks :)

## 1. What is Stokes Law and why is it important in scientific investigations?

Stokes Law is a mathematical equation that describes the relationship between the drag force on a small spherical particle in a viscous fluid and the properties of the particle and the fluid. It is important in scientific investigations because it allows for the calculation of the terminal velocity of a particle in a fluid, which is a crucial factor in many natural and industrial processes.

## 2. What are the different formulas used in Stokes Law and how do they differ?

There are two main formulas used in Stokes Law: the standard Stokes Law formula and the modified Stokes Law formula. The standard formula assumes that the particle is small enough that its motion is unaffected by the fluid, while the modified formula takes into account the effects of the fluid on the particle's motion. The two formulas differ in their calculations of the drag coefficient, resulting in slightly different results.

## 3. Why do different formulas in Stokes Law yield different results?

The different results obtained from using different formulas in Stokes Law can be attributed to the assumptions made in each formula. The standard formula assumes that the particle is small enough to not be affected by the fluid, while the modified formula considers the effects of the fluid on the particle's motion. Additionally, the modified formula includes a correction factor for non-spherical particles, which can also affect the results.

## 4. How do scientists determine which formula to use in a given situation?

The choice of formula to use in a given situation depends on the specific properties of the particle and the fluid being studied. If the particle is small and the fluid is not highly viscous, the standard formula may be appropriate. However, if the particle is larger or the fluid is highly viscous, the modified formula should be used. In some cases, a combination of both formulas may be necessary to accurately calculate the terminal velocity.

## 5. What are some real-world applications of Stokes Law?

Stokes Law has many real-world applications, including in the fields of fluid dynamics, particle physics, and environmental science. It is used to understand the behavior of particles in liquids, such as in the purification of water or the separation of different components in a mixture. It also plays a role in the movement of microscopic organisms in the ocean and the dispersion of pollutants in air and water. In addition, Stokes Law is used in the design and optimization of industrial processes, such as in the production of pharmaceuticals and the development of new materials.

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