Settling Velocity Calculator

✖Density of Particle is defined as the mass of a unit volume of sediment solids. A simple example is that if 1 cm3 of solid material weighs 2.65 g, the particle density is 2.65 g/cm3.ⓘ Density of Particle [ρ_p]			+10% -10%
✖Liquid Density is mass per unit volume of the liquid.ⓘ Liquid Density [ρ_liquid]			+10% -10%
✖The Effective Particle Diameter is the diameter of the particles in a granular sample for which 10 percent of the total grains are smaller and 90 percent larger on a weight basis.ⓘ Effective Particle Diameter [D_E]			+10% -10%
✖Drag Coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.ⓘ Drag Coefficient [C_D]			+10% -10%

✖Settling velocity is defined as the terminal velocity of a particle in still fluid.ⓘ Settling Velocity [v_s]

⎘ Copy

👎

Formula

✖

Settling Velocity

Formula

`"v"_{"s"} = sqrt((4*"[g]"*("ρ"_{"p"}-"ρ"_{"liquid"})*"D"_{"E"})/(3*"C"_{"D"}*"ρ"_{"liquid"}))`

Example

`"32.67088m/s"=sqrt((4*"[g]"*("12g/mm³"-"49kg/m³")*"10mm")/(3*"30"*"49kg/m³"))`

Calculator

LaTeX

Reset

👍

Download Environmental Engineering Formula PDF PDF Image

Settling Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Settling Velocity = sqrt((4*[g]*(Density of Particle-Liquid Density)*Effective Particle Diameter)/(3*Drag Coefficient*Liquid Density))
v_s = sqrt((4*[g]*(ρ_p-ρ_liquid)*D_E)/(3*C_D*ρ_liquid))
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Settling Velocity - (Measured in Meter per Second) - Settling velocity is defined as the terminal velocity of a particle in still fluid.
Density of Particle - (Measured in Kilogram per Cubic Meter) - Density of Particle is defined as the mass of a unit volume of sediment solids. A simple example is that if 1 cm3 of solid material weighs 2.65 g, the particle density is 2.65 g/cm3.
Liquid Density - (Measured in Kilogram per Cubic Meter) - Liquid Density is mass per unit volume of the liquid.
Effective Particle Diameter - (Measured in Meter) - The Effective Particle Diameter is the diameter of the particles in a granular sample for which 10 percent of the total grains are smaller and 90 percent larger on a weight basis.
Drag Coefficient - Drag Coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.

STEP 1: Convert Input(s) to Base Unit

Density of Particle: 12 Gram per Cubic Millimeter --> 12000000 Kilogram per Cubic Meter (Check conversion here)
Liquid Density: 49 Kilogram per Cubic Meter --> 49 Kilogram per Cubic Meter No Conversion Required
Effective Particle Diameter: 10 Millimeter --> 0.01 Meter (Check conversion here)
Drag Coefficient: 30 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_s = sqrt((4*[g]*(ρ_p-ρ_liquid)*D_E)/(3*C_D*ρ_liquid)) --> sqrt((4*[g]*(12000000-49)*0.01)/(3*30*49))

Evaluating ... ...

v_s = 32.6708756797146

STEP 3: Convert Result to Output's Unit

32.6708756797146 Meter per Second --> No Conversion Required

FINAL ANSWER

32.6708756797146 ≈ 32.67088 Meter per Second <-- Settling Velocity

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Environmental Engineering » Treatment of Water 1: Sedimentation » Settling Velocity » Settling Velocity

Credits

Created by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has created this Calculator and 500+ more calculators!

Verified by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has verified this Calculator and 600+ more calculators!

< 19 Settling Velocity Calculators

Settling Velocity

Go Settling Velocity = sqrt((4*[g]*(Density of Particle-Liquid Density)*Effective Particle Diameter)/(3*Drag Coefficient*Liquid Density))

Settling Velocity with respect to Kinematic Viscosity

Go Settling Velocity = [g]*(Specific Gravity of Material-Specific Gravity of Fluid)*Diameter^2/18*Kinematic Viscosity

Settling Velocity with respect to Dynamic Viscosity

Go Settling Velocity = [g]*(Density of Particle-Liquid Density)*Effective Particle Diameter^2/18*Dynamic Viscosity

Settling Velocity using Temperature in Fahrenheit

Go Settling Velocity = 418*(Specific gravity of particle-Specific Gravity of Fluid)*Effective Particle Diameter^2*((Outside Temperature+10)/60)

Settling Velocity with respect to Specific Gravity of Particle

Go Settling Velocity = sqrt((4*[g]*(Specific Gravity of Material-1)*Diameter)/(3*Drag Coefficient))

Settling Velocity given Celsius for diameter greater than 0.1mm

Go Settling Velocity = 418*(Specific gravity of particle-Specific Gravity of Fluid)*Diameter*(3*Temperature in Fahrenheit+70)/100

Settling Velocity given Fahrenheit for diameter greater than 0.1mm

Go Settling Velocity = 418*(Specific gravity of particle-Specific Gravity of Fluid)*Diameter*(Temperature in Fahrenheit+10)/60

Settling Velocity given degree Celsius

Go Settling Velocity = 418*(Specific gravity of particle-Specific Gravity of Fluid)*Diameter^2*((3*Temperature+70)/100)

Settling Velocity given Frictional Drag

Go Settling Velocity = sqrt(2*Drag Force/(Area*Drag Coefficient*Liquid Density))

Settling Velocity given Specific Gravity of Particle and Viscosity

Go Settling Velocity = [g]*(Specific gravity of particle-1)*Diameter^2/18*Kinematic Viscosity

Settling Velocity given Particle Reynold's Number

Go Settling Velocity = Dynamic Viscosity*Reynolds Number/(Liquid Density*Diameter)

Settling Velocity given Drag Force as per Stokes Law

Go Settling Velocity = Drag Force/3*pi*Dynamic Viscosity*Diameter

Settling Velocity at 10 degree Celsius

Go Settling Velocity = 418*(Specific gravity of particle-Specific Gravity of Fluid)*Diameter^2

Settling Velocity given Displacement Velocity for Fine Particles

Go Settling Velocity = Displacement velocity/sqrt(8/Darcy Friction Factor)

Settling Velocity given Height at Outlet Zone with respect to Settling Velocity

Go Settling Velocity = Falling Speed*Height of Crack/Outer Height

Settling Velocity given Surface Area with respect to Settling Velocity

Go Settling Velocity = Falling Speed*Cross-Sectional Area/Area

Settling Velocity given Ratio of Removal with respect to Settling Velocity

Go Settling Velocity = Falling Speed/Removal Ratio

Surface Loading with respect to Settling Velocity

Go Surface loading rate = 864000*Settling Velocity

Settling Velocity given Displacement Velocity with Settling Velocity

Go Settling Velocity = Displacement velocity/18

Settling Velocity Formula

Settling Velocity = sqrt((4*[g]*(Density of Particle-Liquid Density)*Effective Particle Diameter)/(3*Drag Coefficient*Liquid Density))
v_s = sqrt((4*[g]*(ρ_p-ρ_liquid)*D_E)/(3*C_D*ρ_liquid))

What is sedimentation?

Sedimentation is the tendency for particles in suspension to settle out of the fluid in which they are entrained and come to rest against a barrier.

How to Calculate Settling Velocity?

Settling Velocity calculator uses Settling Velocity = sqrt((4*[g]*(Density of Particle-Liquid Density)*Effective Particle Diameter)/(3*Drag Coefficient*Liquid Density)) to calculate the Settling Velocity, The Settling Velocity is defined as the terminal velocity of a particle in still fluid. It gives the settling velocity for a spherical particle settling under the action of gravity under the condition that Re ≪ 1 and diameter ≫ mean free path. Settling Velocity is denoted by v_s symbol.

How to calculate Settling Velocity using this online calculator? To use this online calculator for Settling Velocity, enter Density of Particle (ρ_p), Liquid Density (ρ_liquid), Effective Particle Diameter (D_E) & Drag Coefficient (C_D) and hit the calculate button. Here is how the Settling Velocity calculation can be explained with given input values -> 32.67088 = sqrt((4*[g]*(12000000-49)*0.01)/(3*30*49)).

FAQ

What is Settling Velocity?

The Settling Velocity is defined as the terminal velocity of a particle in still fluid. It gives the settling velocity for a spherical particle settling under the action of gravity under the condition that Re ≪ 1 and diameter ≫ mean free path and is represented as v_s = sqrt((4*[g]*(ρ_p-ρ_liquid)*D_E)/(3*C_D*ρ_liquid)) or Settling Velocity = sqrt((4*[g]*(Density of Particle-Liquid Density)*Effective Particle Diameter)/(3*Drag Coefficient*Liquid Density)). Density of Particle is defined as the mass of a unit volume of sediment solids. A simple example is that if 1 cm3 of solid material weighs 2.65 g, the particle density is 2.65 g/cm3, Liquid Density is mass per unit volume of the liquid, The Effective Particle Diameter is the diameter of the particles in a granular sample for which 10 percent of the total grains are smaller and 90 percent larger on a weight basis & Drag Coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.

How to calculate Settling Velocity?

The Settling Velocity is defined as the terminal velocity of a particle in still fluid. It gives the settling velocity for a spherical particle settling under the action of gravity under the condition that Re ≪ 1 and diameter ≫ mean free path is calculated using Settling Velocity = sqrt((4*[g]*(Density of Particle-Liquid Density)*Effective Particle Diameter)/(3*Drag Coefficient*Liquid Density)). To calculate Settling Velocity, you need Density of Particle (ρ_p), Liquid Density (ρ_liquid), Effective Particle Diameter (D_E) & Drag Coefficient (C_D). With our tool, you need to enter the respective value for Density of Particle, Liquid Density, Effective Particle Diameter & Drag Coefficient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Settling Velocity?

In this formula, Settling Velocity uses Density of Particle, Liquid Density, Effective Particle Diameter & Drag Coefficient. We can use 17 other way(s) to calculate the same, which is/are as follows -

Settling Velocity = sqrt(2*Drag Force/(Area*Drag Coefficient*Liquid Density))
Settling Velocity = sqrt((4*[g]*(Specific Gravity of Material-1)*Diameter)/(3*Drag Coefficient))
Settling Velocity = Dynamic Viscosity*Reynolds Number/(Liquid Density*Diameter)
Settling Velocity = Drag Force/3*pi*Dynamic Viscosity*Diameter
Settling Velocity = [g]*(Density of Particle-Liquid Density)*Effective Particle Diameter^2/18*Dynamic Viscosity
Settling Velocity = [g]*(Specific Gravity of Material-Specific Gravity of Fluid)*Diameter^2/18*Kinematic Viscosity
Settling Velocity = [g]*(Specific gravity of particle-1)*Diameter^2/18*Kinematic Viscosity
Settling Velocity = 418*(Specific gravity of particle-Specific Gravity of Fluid)*Diameter^2
Settling Velocity = 418*(Specific gravity of particle-Specific Gravity of Fluid)*Effective Particle Diameter^2*((Outside Temperature+10)/60)
Settling Velocity = 418*(Specific gravity of particle-Specific Gravity of Fluid)*Diameter^2*((3*Temperature+70)/100)
Settling Velocity = 418*(Specific gravity of particle-Specific Gravity of Fluid)*Diameter*(Temperature in Fahrenheit+10)/60
Settling Velocity = 418*(Specific gravity of particle-Specific Gravity of Fluid)*Diameter*(3*Temperature in Fahrenheit+70)/100
Settling Velocity = Falling Speed*Height of Crack/Outer Height
Settling Velocity = Displacement velocity/sqrt(8/Darcy Friction Factor)
Settling Velocity = Displacement velocity/18
Settling Velocity = Falling Speed/Removal Ratio
Settling Velocity = Falling Speed*Cross-Sectional Area/Area

Home

FREE PDFs

🔍 Search