FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Archimedes Number Formula

Fx Copy

LaTeX Copy

Archimedes Number (Ar), is a dimensionless number used to determine the motion of fluids due to density differences, named after the ancient Greek scientist and mathematician Archimedes. Check FAQs

Ar = \frac{[g] \cdot {L c}^{3} \cdot ρ Fluid \cdot (ρ B - ρ Fluid)}{{(μ viscosity)}^{2}}

Ar - Archimedes Number?L_c - Characteristic Length?ρ_Fluid - Density of Fluid?ρ_B - Density of Body?μ_viscosity - Dynamic Viscosity?[g] - Gravitational acceleration on Earth?

Archimedes Number Example

With values

With units

Only example

Here is how the Archimedes Number equation looks like with Values.

Here is how the Archimedes Number equation looks like with Units.

Here is how the Archimedes Number equation looks like.

154331.157 = \frac{9.8066 \cdot {9.9}^{3} \cdot 1.225 \cdot (15 - 1.225)}{{(1.02)}^{2}}

154331.157 = \frac{9.8066m/s² \cdot {9.9m}^{3} \cdot 1.225kg/m³ \cdot (15kg/m³ - 1.225kg/m³)}{{(1.02Pa*s)}^{2}}

154331.157 = \frac{9.8066 \cdot {9.9}^{3} \cdot 1.225 \cdot (15 - 1.225)}{{(1.02)}^{2}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Chemical Engineering » Category

Fluid Dynamics » fx Archimedes Number

Archimedes Number Solution

Follow our step by step solution on how to calculate Archimedes Number?

FIRST Step Consider the formula

Ar = \frac{[g] \cdot {L c}^{3} \cdot ρ Fluid \cdot (ρ B - ρ Fluid)}{{(μ viscosity)}^{2}}

Next Step Substitute values of Variables

∴

Ar = \frac{[g] \cdot {9.9m}^{3} \cdot 1.225kg/m³ \cdot (15kg/m³ - 1.225kg/m³)}{{(1.02Pa*s)}^{2}}

Next Step Substitute values of Constants

∴

Ar = \frac{9.8066m/s² \cdot {9.9m}^{3} \cdot 1.225kg/m³ \cdot (15kg/m³ - 1.225kg/m³)}{{(1.02Pa*s)}^{2}}

Next Step Prepare to Evaluate

∴

Ar = \frac{9.8066 \cdot {9.9}^{3} \cdot 1.225 \cdot (15 - 1.225)}{{(1.02)}^{2}}

Next Step Evaluate

∴

Ar = 154331.157008579

LAST Step Rounding Answer

∴

Ar = 154331.157

Archimedes Number Formula Elements

Variables

Constants

Archimedes Number

Archimedes Number (Ar), is a dimensionless number used to determine the motion of fluids due to density differences, named after the ancient Greek scientist and mathematician Archimedes.

Symbol: Ar

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Archimedes Number

Characteristic Length

A characteristic length is usually the volume of a system divided by its surface.

Symbol: L_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Characteristic Length

Density of Fluid

Density of Fluid is defined as the mass of fluid per unit volume of the said fluid.

Symbol: ρ_Fluid

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density of Fluid

Density of Body

Density of Body is the physical quantity that expresses the relationship between its mass and its volume.

Symbol: ρ_B

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density of Body

Dynamic Viscosity

Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.

Symbol: μ_viscosity

Measurement: Dynamic ViscosityUnit: Pa*s

Note: Value should be greater than 0.

Formulas to find Dynamic Viscosity

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

Other formulas in Dimensionless Numbers category

Go Reynolds Number

Re = \frac{ρ 1 \cdot v fd \cdot d p}{μ v}

Go Euler Number using Fluid Velocity

E u = \frac{v fluid}{\sqrt{\frac{dP}{ρ Fluid}}}

Go Weber Number

We = (\frac{ρ \cdot (V^{2}) \cdot L}{σ})

Go Sommerfeld Number

S = ({(\frac{R shaft}{c R})}^{2}) \cdot \frac{μ \cdot N}{P}

How to Evaluate Archimedes Number?

Archimedes Number evaluator uses Archimedes Number = ([g]*Characteristic Length^(3)*Density of Fluid*(Density of Body-Density of Fluid))/(Dynamic Viscosity)^(2) to evaluate the Archimedes Number, Archimedes Number (Ar), is a dimensionless number used to determine the motion of fluids due to density differences, named after the ancient Greek scientist and mathematician Archimedes. Archimedes Number is denoted by Ar symbol.

How to evaluate Archimedes Number using this online evaluator? To use this online evaluator for Archimedes Number, enter Characteristic Length (L_c), Density of Fluid (ρ_Fluid), Density of Body (ρ_B) & Dynamic Viscosity (μ_viscosity) and hit the calculate button.

FAQs on Archimedes Number

What is the formula to find Archimedes Number?

The formula of Archimedes Number is expressed as Archimedes Number = ([g]*Characteristic Length^(3)*Density of Fluid*(Density of Body-Density of Fluid))/(Dynamic Viscosity)^(2). Here is an example- 154331.2 = ([g]*9.9^(3)*1.225*(15-1.225))/(1.02)^(2).

How to calculate Archimedes Number?

With Characteristic Length (L_c), Density of Fluid (ρ_Fluid), Density of Body (ρ_B) & Dynamic Viscosity (μ_viscosity) we can find Archimedes Number using the formula - Archimedes Number = ([g]*Characteristic Length^(3)*Density of Fluid*(Density of Body-Density of Fluid))/(Dynamic Viscosity)^(2). This formula also uses Gravitational acceleration on Earth constant(s).

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Archimedes Number Formula

Archimedes Number Example

Archimedes Number Solution

Archimedes Number Formula Elements

Other formulas in Dimensionless Numbers category

How to Evaluate Archimedes Number?

FAQs on Archimedes Number

Variable Name