# Stokes Law Calculator

Table of Contents:

## Formula

**Fall or Settling Velocity :**

V_{t} = gd^{2} (ρ_{p} - ρ_{m})/18μ

**Acceleration of Gravity :**

g= 18 μ V_{t} /d^{2}(ρ_{p} - ρ_{m})

**Particle Diameter :**

d= √18 μ V_{t} /g (ρ_{p} - ρ_{m})

**Density of Medium :**

ρ_{m} = ρ_{p} - 18 μ V_{t}/ d^{2}

**Particle Density :**

ρ_{p} = 18 μ V_{t} /d^{2}+ ρ_{m}

**Viscosity of Medium :**

μ = g_{d}^{2}( ρ_{p} - ρ_{m})/18 V_{t}

**Where,**

V_{t} = Fall or Settling Velocity,

g = Acceleration of Gravity,

d = Particle Diameter,

ρ_{m} = Density of Medium,

ρ_{p} = Particle Density,

μ = Viscosity of Medium.

Stoke's law states that at low velocities the frictional force on a spherical body moving through a fluid at constant velocity is equal to 6 π times the product of the velocity, the fluid viscosity, and the radius of the sphere.

In short, a sphere moving through a viscous fluid is directly proportional to the velocity of the sphere as well as the radius of the sphere, and the viscosity of the fluid.

Stoke's Law is defined as the basis of the falling - sphere viscometer. In the viscometer the fluid is stationary in a vertical glass tube. This online Stokes Law Calculator is useful in calculating various parameters of fluid in viscometer.

**Example:**

Calculate the fall or settling velocity (Vt) for the given details through Stoke's Law formula.

Acceleration of Gravity (g) = 25 m/s^{2}

Particle Diameter (d) = 15 m

Density of Medium (ρ_{m}) = 5 kg/m^{4}

Particle Density (ρ_{p}) = 10 kg/m^{3}

Viscosity of Medium (μ) = 20 kg/m-s

**Solution:**

**Apply formula:**

V_{t} = gd^{2} (ρ_{p} - ρ_{m})/18μ

V _{t}= 25*15 (10-5)/18*20

**Fall or Settling Velocity (V _{t}) =**

**78.13 m/s**