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# Stokes Law Calculator

To use Stokes Law Calculator, select the term that you want to calculate, enter the required values, and press calculate button

## Stokes Law Calculator

Stokes Law Calculator is a mathematical tool that is used to find the falling or settling velocity of the small spherical particles of viscous fluid. It is found out by using the particle diameter and density of the particle and medium.

## What is settling velocity?

It is the speed at which the force acting on the particle is balanced by the gravitational force pulling it downwards. Settling velocity represents the velocity at which a particle in a fluid reaches a stable and constant speed under the influence of gravity.

## Formula of settling velocity:

**V _{t} = gd^{2} (ρ_{p} - ρ_{m})/18μ**

Where,

- d = Diameter of the small particles
- V
_{t}= Settling Velocity or Fall velocity of the particles - g = Gravity Acceleration
- ρ
_{m}= Medium density - ρ
_{p}= Density of the particle - μ = medium viscosity

## How to determine the settling velocity of small particles?

**Example 1:**

Determine the settling velocity (V_{t}) of the small particles if the data for particles are given below using the formula of Stoke’s Law.

- Gravity Acceleration (g) = 25 m/s
^{2} - Diameter of the small particles (d) = 15 m
- Medium density (ρ
_{m}) = 5 kg/m^{4} - Density of the particle (ρ
_{p}) = 10 kg/m^{3} - Medium viscosity (μ) = 20 kg/m-s

**Solution:**

**Step 1:**

**Write the data carefully from the above data.**

g = 25 m/s^{2}, d = 15 m, ρ_{m}= 5 kg/m^{4}, ρ_{p} = 10 kg/m^{3}, μ = 20 kg/m-s

**Step 2: **

**Write the formula of the settling velocity.**

V_{t} = gd^{2} (ρ_{p} - ρ_{m})/18μ

**Step 3: **

**Put all the values in the above formula.**

g = 25, d = 15, ρ_{m}= 5, ρ_{p} = 10, μ = 20

V_{t} = gd^{2} (ρ_{p} - ρ_{m})/18μ

V_{t }= {25×15^{2} (10-5)}/(18×20)

V_{t }= {25 × 225 × 5}/(18×20)

V_{t }= {1875}/(360)

**V _{t }= 78.13m/s**

**Example 2:**

Determine the settling velocity (V_{t}) of the small particles if the data for particles are given below using the formula of Stoke’s Law.

- Gravity Acceleration (g) = 20 m/s
^{2} - Diameter of the small particles (d) = 10 m
- Medium density (ρ
_{m}) = 12 kg/m^{4} - Density of the particle (ρ
_{p}) = 15 kg/m^{3} - Medium viscosity (μ) = 22 kg/m-s

**Solution:**

**Step 1:**

**Write the data carefully from the above data.**

g = 20 m/s^{2}, d = 10 m, ρ_{m}= 12 kg/m^{4}, ρ_{p} = 15 kg/m^{3}, μ = 22 kg/m-s

**Step 2: **

**Write the formula of the settling velocity.**

V_{t} = gd^{2} (ρ_{p} - ρ_{m})/18μ

**Step 3: **

**Put all the values in the above formula.**

g = 20, d = 10, ρ_{m}= 12, ρ_{p} = 15, μ = 22

V_{t} = gd^{2} (ρ_{p} - ρ_{m})/18μ

V_{t }= {20×10^{2} (15 -12)}/(18×22)

V_{t }= {20 × 100 × 3}/(18×22)

V_{t }= {6000}/(396)

**V _{t }= 15.15 m/s**