How to Calculate and Solve for Drag Force | Stoke’s Formula | Mineral Processing

November 22, 2021 Loveth Idoko

Last Updated on May 17, 2024

The image above represents drag force. To calculate drag force, three essential parameters are needed and these parameters are Particle Diameter (d), Fluid Viscosity (μ) and Terminal Velocity (v).

The formula for calculating drag force:

D = 3π.dμv

Where:

D = Drag Force | Stoke’s Formula
d = Particle Diameter
μ = Fluid Viscosity
v = Terminal Velocity

Let’s solve an example;
Find the drag force when the particle diameter is 21, the fluid viscosity is 7 and the terminal velocity is 3.

This implies that;

d = Particle Diameter = 21
μ = Fluid Viscosity = 7
v = Terminal Velocity = 3

D = 3π.dμv
D = 3π.(21)(7)(3)
That is, D = 3π.(441)
D = 4156.3

Therefore, the drag force is 4156.3 N.

Calculating the Particle Diameter when the Drag Force, the Fluid Viscosity and the Terminal Velocity are Given

d = ^D / _3π.μv

Where:

d = Particle Diameter
D = Drag Force | Stoke’s Formula
μ = Fluid Viscosity
v = Terminal Velocity

Let’s solve an example;
Find the particle diameter when the drag force is 30, the fluid viscosity is 4 and the terminal velocity is 2.

This implies that;

D = Drag Force | Stoke’s Formula = 30
μ = Fluid Viscosity = 4
v = Terminal Velocity = 2

d = ^D / _3π.μv
Then, d = ³⁰ / _3π.(4)(2)
d = ³⁰ / _75.4
d = 0.39

Therefore, the particle diameter is 0.39.

Calculating the Fluid Viscosity when the Drag Force, the Particle Diameter and the Terminal Velocity are Given

μ = ^D / _3π.dv

Where:

μ = Fluid Viscosity
D = Drag Force | Stoke’s Formula
d = Particle Diameter
v = Terminal Velocity

Let’s solve an example;
Find the fluid viscosity when the drag force is 24, the particle diameter is 4 and the terminal velocity is 6.

This implies that;

D = Drag Force | Stoke’s Formula = 24
d = Particle Diameter = 4
v = Terminal Velocity = 6

μ = ^D / _3π.dv
Then, μ = ²⁴ / _3π.(4)(6)
μ = ²⁴ / _226.2
μ = 0.11

Therefore, the fluid viscosity is 0.11.

Calculating the Terminal Velocity when the Drag Force, the Particle Diameter and the Fluid Viscosity are Given

v = ^D / _3π.dμ

Where:

v = Terminal Velocity
D = Drag Force | Stoke’s Formula
d = Particle Diameter
μ = Fluid Viscosity

Let’s solve an example;
Find the terminal velocity when the drag force is 44, the particle diameter is 8 and the fluid viscosity is 3.

This implies that;

D = Drag Force | Stoke’s Formula = 44
d = Particle Diameter = 8
μ = Fluid Viscosity = 3

v = ^D / _3π.dμ
That is, v = ⁴⁴ / _3π.(8)(3)
v = ⁴⁴ / _226.2
v = 0.19

Therefore, the terminal velocity is 0.19.

How to Calculate Drag Force | Stoke’s Formula With Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the drag force.

To get the answer and workings of the drag force using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.

Now, Click on Mineral Processing under Materials and Metallurgical

Now, Click on Drag Force under Mineral Processing

The screenshot below displays the page or activity to enter your values, to get the answer for the drag force according to the respective parameter which is the Particle Diameter (d), Fluid Viscosity (μ) and Terminal Velocity (v).

Now, enter the values appropriately and accordingly for the parameters as required by the Particle Diameter (d) is 21, Fluid Viscosity (μ) is 7 and Terminal Velocity (v) is 3.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the drag force and presents the formula, workings and steps too.