How to Calculate and Solve for Newton’s Drag Force for Turbulent Resistance | Mineral Processing

November 23, 2021 Loveth Idoko

Last Updated on May 17, 2024

The image above represents newton’s drag force for turbulent resistance. To calculate newton’s drag force for turbulent resistance, three essential parameters are needed and these parameters are Particle Diameter (d), Terminal Velocity (v) and Density of Fluid (ρ_f).

The formula for calculating newton’s drag force for turbulent resistance:

D = 0.055π.d²v²ρ_f

Where:

D = Newton’s Drag Force for Turbulent Resistance
d = Particle Diameter
v = Terminal Velocity
ρ_f = Density of Fluid

Let’s solve an example;
Find the newton’s drag force for turbulent resistance when the particle diameter is 8, the terminal velocity is 4 and the density of fluid is 2.

This implies that;

d = Particle Diameter = 8
v = Terminal Velocity = 4
ρ_f = Density of Fluid = 2

D = 0.055π.d²v²ρ_f
D = 0.055π.(8)²(4)²(2)
That is, D = 0.055π.(64)(16)(2)
D = 0.055π.(2048)
D = 353.86

Therefore, the newton’s drag force for turbulent resistance is 353.86 N.

Calculating the Particle Diameter when the Newton’s Drag Force for Turbulent Resistance, the Terminal Velocity and the Density of Fluid are Given

d = √(^D / _{0.055π.v²ρ_f})

Where:

d = Particle Diameter
D = Newton’s Drag Force for Turbulent Resistance
v = Terminal Velocity
ρ_f = Density of Fluid

Let’s solve an example;
Find the particle diameter when the newton’s drag force for turbulent resistance is 42, the terminal velocity is 2 and the density of fluid is 4.

This implies that;

D = Newton’s Drag Force for Turbulent Resistance = 42
v = Terminal Velocity = 2
ρ_f = Density of Fluid = 4

d = √(^D / _{0.055π.v²ρ_f})
That is, d = √(⁴² / _{0.055π.(2²)(4)})
d = √(⁴² / _0.055π.16)
d = √(⁴² / _2.76)
So, d = √15.2
d = 3.89

Therefore, the particle diameter is 3.89.

Calculating the Terminal Velocity when the Newton’s Drag Force for Turbulent Resistance, the Particle Diameter and the Density of Fluid are Given

v = √(^D / _{0.055π.d²ρ_f})

Where:

v = Terminal Velocity
D = Newton’s Drag Force for Turbulent Resistance
d = Particle Diameter
ρ_f = Density of Fluid

Let’s solve an example;
Find the terminal velocity when the newton’s drag force for turbulent resistance is 50, the particle diameter is 5 and the density of fluid is 2.

This implies that;

D = Newton’s Drag Force for Turbulent Resistance = 50
d = Particle Diameter = 5
ρ_f = Density of Fluid = 2

v = √(^D / _{0.055π.d²ρ_f})
Then, v = √(⁵⁰ / _{0.055π.(5²)(2)})
v = √(⁵⁰ / _0.055π.50)
v = √(⁵⁰ / _8.64)
So, v = √5.78
v = 2.40

Therefore, the terminal velocity is 2.40.

Calculating the Density of Fluid when the Newton’s Drag Force for Turbulent Resistance, the Particle Diameter and the Terminal Velocity are Given

ρ_f = ^D / _{0.055π.d²v²}

Where:

ρ_f = Density of Fluid
D = Newton’s Drag Force for Turbulent Resistance
d = Particle Diameter
v = Terminal Velocity

Let’s solve an example;
Find the density of fluid when the newton’s drag force for turbulent resistance is 35, the particle diameter is 6 and the terminal velocity is 3.

This implies that;

D = Newton’s Drag Force for Turbulent Resistance = 35
d = Particle Diameter = 6
v = Terminal Velocity = 3

ρ_f = ^D / _{0.055π.d²v²}
This means, ρ_f = ³⁵ / _{0.055π.(6²)(3²)}
ρ_f = ³⁵ / _{0.055π.(36)(9)}
ρ_f = ³⁵ / _0.055π.324
So, ρ_f = ³⁵ / _55.9
ρ_f = 0.626

Therefore, the density of fluid is 0.626.

How to Calculate Newton’s Drag Force for Turbulent Resistance Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the newton’s drag force for turbulent resistance.

To get the answer and workings of the newton’s drag force for turbulent resistance 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 Newton’s Drag Force for Turbulent Resistance under Mineral Processing

The screenshot below displays the page or activity to enter your values, to get the answer for the newton’s drag force for turbulent resistance according to the respective parameter which is the Particle Diameter (d), Terminal Velocity (v) and Density of Fluid (ρ_f).

Now, enter the values appropriately and accordingly for the parameters as required by the Particle Diameter (d) is 8, Terminal Velocity (v) is 4 and Density of Fluid (ρ_f) is 2.

Finally, Click on Calculate

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