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Settling Velocity Formula

GoSettling Velocity given Frictional Drag Formula

GoSettling Velocity with respect to Specific Gravity of Particle Formula

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Settling Velocity of particles refers to the rate at which a particle sinks through a fluid under the influence of gravity. Check FAQs

v s = \sqrt{\frac{4 \cdot [g] \cdot (ρ m - ρ f) \cdot d}{3 \cdot C D \cdot ρ f}}

v_s - Settling Velocity of Particles?ρ_m - Mass Density of Particles?ρ_f - Mass Density of Fluid?d - Diameter of a Spherical Particle?C_D - Drag Coefficient?[g] - Gravitational acceleration on Earth?

Settling Velocity Example

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Here is how the Settling Velocity equation looks like with Values.

Here is how the Settling Velocity equation looks like with Units.

Here is how the Settling Velocity equation looks like.

0.0049 = \sqrt{\frac{4 \cdot 9.8066 \cdot (2700 - 1000) \cdot 0.0013}{3 \cdot 1200 \cdot 1000}}

0.0049m/s = \sqrt{\frac{4 \cdot 9.8066m/s² \cdot (2700kg/m³ - 1000kg/m³) \cdot 0.0013m}{3 \cdot 1200 \cdot 1000kg/m³}}

0.0049 = \sqrt{\frac{4 \cdot 9.8066 \cdot (2700 - 1000) \cdot 0.0013}{3 \cdot 1200 \cdot 1000}}

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Settling Velocity Solution

Follow our step by step solution on how to calculate Settling Velocity?

FIRST Step Consider the formula

v s = \sqrt{\frac{4 \cdot [g] \cdot (ρ m - ρ f) \cdot d}{3 \cdot C D \cdot ρ f}}

Next Step Substitute values of Variables

∴

v s = \sqrt{\frac{4 \cdot [g] \cdot (2700kg/m³ - 1000kg/m³) \cdot 0.0013m}{3 \cdot 1200 \cdot 1000kg/m³}}

Next Step Substitute values of Constants

∴

v s = \sqrt{\frac{4 \cdot 9.8066m/s² \cdot (2700kg/m³ - 1000kg/m³) \cdot 0.0013m}{3 \cdot 1200 \cdot 1000kg/m³}}

Next Step Prepare to Evaluate

∴

v s = \sqrt{\frac{4 \cdot 9.8066 \cdot (2700 - 1000) \cdot 0.0013}{3 \cdot 1200 \cdot 1000}}

Next Step Evaluate

∴

v s = 0.00490721651131157m/s

LAST Step Rounding Answer

∴

v s = 0.0049m/s

Settling Velocity Formula Elements

Variables

Constants

Functions

Settling Velocity of Particles

Settling Velocity of particles refers to the rate at which a particle sinks through a fluid under the influence of gravity.

Symbol: v_s

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Settling Velocity of Particles

Mass Density of Particles

Mass Density of Particles refers to the mass of a particle per unit volume, typically expressed in kilograms per cubic meter (kg/m³).

Symbol: ρ_m

Measurement: Mass ConcentrationUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Mass Density of Particles

Mass Density of Fluid

Mass Density of Fluid refers to the mass per unit volume of the fluid, typically expressed in kilograms per cubic meter (kg/m³).

Symbol: ρ_f

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Mass Density of Fluid

Diameter of a Spherical Particle

The Diameter of a Spherical Particle is the distance across the sphere, passing through its center.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diameter of a Spherical Particle

Drag Coefficient

The Drag Coefficient refers to the dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.

Symbol: C_D

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Drag Coefficient

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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.

Syntax: sqrt(Number)

Other Formulas to find Settling Velocity of Particles

Go Settling Velocity given Frictional Drag

v s = \sqrt{\frac{2 \cdot F D}{a \cdot C D \cdot ρ f}}

Go Settling Velocity with respect to Specific Gravity of Particle

v s = \sqrt{\frac{4 \cdot [g] \cdot (G s - 1) \cdot d}{3 \cdot C D}}

Go Settling Velocity given Particle Reynold's Number

v s = \frac{μ viscosity \cdot Re}{ρ f \cdot d}

Go Settling Velocity given Drag Force as per Stokes Law

v s = \frac{F D}{3 \cdot π \cdot μ viscosity \cdot d}

Other formulas in Settling Velocity category

Go Surface Loading with respect to Settling Velocity

R = 864000 \cdot v s

How to Evaluate Settling Velocity?

Settling Velocity evaluator uses Settling Velocity of Particles = sqrt((4*[g]*(Mass Density of Particles-Mass Density of Fluid)*Diameter of a Spherical Particle)/(3*Drag Coefficient*Mass Density of Fluid)) to evaluate the Settling Velocity of Particles, The Settling Velocity formula 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 of Particles is denoted by v_s symbol.

How to evaluate Settling Velocity using this online evaluator? To use this online evaluator for Settling Velocity, enter Mass Density of Particles (ρ_m), Mass Density of Fluid (ρ_f), Diameter of a Spherical Particle (d) & Drag Coefficient (C_D) and hit the calculate button.

FAQs on Settling Velocity

What is the formula to find Settling Velocity?

The formula of Settling Velocity is expressed as Settling Velocity of Particles = sqrt((4*[g]*(Mass Density of Particles-Mass Density of Fluid)*Diameter of a Spherical Particle)/(3*Drag Coefficient*Mass Density of Fluid)). Here is an example- 0.004907 = sqrt((4*[g]*(2700-1000)*0.0013)/(3*1200*1000)).

How to calculate Settling Velocity?

With Mass Density of Particles (ρ_m), Mass Density of Fluid (ρ_f), Diameter of a Spherical Particle (d) & Drag Coefficient (C_D) we can find Settling Velocity using the formula - Settling Velocity of Particles = sqrt((4*[g]*(Mass Density of Particles-Mass Density of Fluid)*Diameter of a Spherical Particle)/(3*Drag Coefficient*Mass Density of Fluid)). This formula also uses Gravitational acceleration on Earth constant(s) and Square Root (sqrt) function(s).

What are the other ways to Calculate Settling Velocity of Particles?

Here are the different ways to Calculate Settling Velocity of Particles-

Settling Velocity of Particles=sqrt((2*Drag Force)/(Projected Area of A Particle*Drag Coefficient*Mass Density of Fluid))
Settling Velocity of Particles=sqrt((4*[g]*(Specific Gravity of Spherical Particle-1)*Diameter of a Spherical Particle)/(3*Drag Coefficient))
Settling Velocity of Particles=(Dynamic Viscosity*Reynold Number)/(Mass Density of Fluid*Diameter of a Spherical Particle)

Can the Settling Velocity be negative?

No, the Settling Velocity, measured in Speed cannot be negative.

Which unit is used to measure Settling Velocity?

Settling Velocity is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Settling Velocity can be measured.

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Settling Velocity Formula

​GoSettling Velocity given Frictional Drag Formula

​GoSettling Velocity with respect to Specific Gravity of Particle Formula

Settling Velocity Example

Settling Velocity Solution

Settling Velocity Formula Elements

Other Formulas to find Settling Velocity of Particles

Other formulas in Settling Velocity category

How to Evaluate Settling Velocity?

FAQs on Settling Velocity

Variable Name

GoSettling Velocity given Frictional Drag Formula

GoSettling Velocity with respect to Specific Gravity of Particle Formula