Archimedes Number Calculator

✖A characteristic length is usually the volume of a system divided by its surface.ⓘ Characteristic Length [L_c]			+10% -10%
✖Density of Fluid is defined as the mass of fluid per unit volume of the said fluid.ⓘ Density of Fluid [ρ_Fluid]			+10% -10%
✖Density of Body is the physical quantity that expresses the relationship between its mass and its volume.ⓘ Density of Body [ρ_B]			+10% -10%
✖Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.ⓘ Dynamic Viscosity [μ_viscosity]			+10% -10%

✖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 [Ar]

⎘ Copy

👎

Formula

✖

Archimedes Number

Formula

`"Ar" = ("[g]"*"L"_{"c"}^(3)*"ρ"_{"Fluid"}*("ρ"_{"B"}-"ρ"_{"Fluid"}))/("μ"_{"viscosity"})^(2)`

Example

`"154331.2"=("[g]"*("9.9m")^(3)*"1.225kg/m³"*("15kg/m³"-"1.225kg/m³"))/("1.02Pa*s")^(2)`

Calculator

LaTeX

Reset

👍

Download Chemical Engineering Formula PDF PDF Image

Archimedes Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Archimedes Number = ([g]*Characteristic Length^(3)*Density of Fluid*(Density of Body-Density of Fluid))/(Dynamic Viscosity)^(2)
Ar = ([g]*L_c^(3)*ρ_Fluid*(ρ_B-ρ_Fluid))/(μ_viscosity)^(2)
This formula uses 1 Constants, 5 Variables

Constants Used

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

Variables Used

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.
Characteristic Length - (Measured in Meter) - A characteristic length is usually the volume of a system divided by its surface.
Density of Fluid - (Measured in Kilogram per Cubic Meter) - Density of Fluid is defined as the mass of fluid per unit volume of the said fluid.
Density of Body - (Measured in Kilogram per Cubic Meter) - Density of Body is the physical quantity that expresses the relationship between its mass and its volume.
Dynamic Viscosity - (Measured in Pascal Second) - Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.

STEP 1: Convert Input(s) to Base Unit

Characteristic Length: 9.9 Meter --> 9.9 Meter No Conversion Required
Density of Fluid: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required
Density of Body: 15 Kilogram per Cubic Meter --> 15 Kilogram per Cubic Meter No Conversion Required
Dynamic Viscosity: 1.02 Pascal Second --> 1.02 Pascal Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Ar = ([g]*L_c^(3)*ρ_Fluid*(ρ_B-ρ_Fluid))/(μ_viscosity)^(2) --> ([g]*9.9^(3)*1.225*(15-1.225))/(1.02)^(2)

Evaluating ... ...

Ar = 154331.157008579

STEP 3: Convert Result to Output's Unit

154331.157008579 --> No Conversion Required

FINAL ANSWER

154331.157008579 ≈ 154331.2 <-- Archimedes Number

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Chemical Engineering » Fluid Dynamics » Dimensionless Numbers » Archimedes Number

Credits

Created by Heet

Thadomal Shahani Engineering College (Tsec), Mumbai

Heet has created this Calculator and 200+ more calculators!

Verified by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

Prerana Bakli has verified this Calculator and 1600+ more calculators!

< 11 Dimensionless Numbers Calculators

Archimedes Number

Go Archimedes Number = ([g]*Characteristic Length^(3)*Density of Fluid*(Density of Body-Density of Fluid))/(Dynamic Viscosity)^(2)

Sommerfeld Number

Go Sommerfeld Number = ((Radius of Shaft/Radial Clearance)^(2))*(Absolute Viscosity*Speed of Rotating Shaft)/(Load per Unit of Area)

Reynolds Number

Go Reynolds Number = (Density of Liquid*Fluid Velocity*Pipe Diameter)/Dynamic Viscosity

Euler Number using Fluid Velocity

Go Euler Number = Fluid Velocity/(sqrt(Change in Pressure/Density of Fluid))

Weber Number

Go Weber Number = ((Density*(Velocity of Fluid^2)*Length)/Surface Tension)

Eckert Number

Go Eckert Number = (Flow Velocity)^2/(Specific Heat Capacity*Temperature Difference)

Grashof Number

Go Grashof Number = (Buoyant Force)/(Viscous Force)

Rayleigh Number

Go Rayleigh Number = Grashof Number*Prandtl Number

Mach Number

Go Mach Number = Speed of Object/Speed of Sound

Froude Number

Go Froude Number = Inertia Force/Gravity Force

Euler Number

Go Euler Number = Pressure Force/Inertia Force

Archimedes Number Formula

Archimedes Number = ([g]*Characteristic Length^(3)*Density of Fluid*(Density of Body-Density of Fluid))/(Dynamic Viscosity)^(2)
Ar = ([g]*L_c^(3)*ρ_Fluid*(ρ_B-ρ_Fluid))/(μ_viscosity)^(2)

What is Dimensionless Number?

Dimensionless numbers in many fields of engineering are collections of variables that provide order-of-magnitude estimates about the behavior of a system

How to Calculate Archimedes Number?

Archimedes Number calculator uses Archimedes Number = ([g]*Characteristic Length^(3)*Density of Fluid*(Density of Body-Density of Fluid))/(Dynamic Viscosity)^(2) to calculate 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 calculate Archimedes Number using this online calculator? To use this online calculator 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. Here is how the Archimedes Number calculation can be explained with given input values -> 154331.2 = ([g]*9.9^(3)*1.225*(15-1.225))/(1.02)^(2).

FAQ

What is 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 and is represented as Ar = ([g]*L_c^(3)*ρ_Fluid*(ρ_B-ρ_Fluid))/(μ_viscosity)^(2) or Archimedes Number = ([g]*Characteristic Length^(3)*Density of Fluid*(Density of Body-Density of Fluid))/(Dynamic Viscosity)^(2). A characteristic length is usually the volume of a system divided by its surface, Density of Fluid is defined as the mass of fluid per unit volume of the said fluid, Density of Body is the physical quantity that expresses the relationship between its mass and its volume & Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.

How to calculate 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 is calculated using Archimedes Number = ([g]*Characteristic Length^(3)*Density of Fluid*(Density of Body-Density of Fluid))/(Dynamic Viscosity)^(2). To calculate Archimedes Number, you need Characteristic Length (L_c), Density of Fluid (ρ_Fluid), Density of Body (ρ_B) & Dynamic Viscosity (μ_viscosity). With our tool, you need to enter the respective value for Characteristic Length, Density of Fluid, Density of Body & Dynamic Viscosity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search