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Sommerfeld Number Formula

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The Sommerfeld number is a dimensionless number that is used in designing a hydrodynamic bearing. Check FAQs

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

S - Sommerfeld Number?R_shaft - Radius of Shaft?c_R - Radial Clearance?μ - Absolute Viscosity?N - Speed of Rotating Shaft?P - Load per Unit of Area?

Sommerfeld Number Example

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With units

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

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

Here is how the Sommerfeld Number equation looks like.

0.0386 = ({(\frac{1.35}{0.09})}^{2}) \cdot \frac{0.001 \cdot 17}{99}

0.0386 = ({(\frac{1.35m}{0.09m})}^{2}) \cdot \frac{0.001Pa*s \cdot 17rev/s}{99Pa}

0.0386 = ({(\frac{1.35}{0.09})}^{2}) \cdot \frac{0.001 \cdot 17}{99}

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Sommerfeld Number Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

S = ({(\frac{1.35m}{0.09m})}^{2}) \cdot \frac{0.001Pa*s \cdot 17rev/s}{99Pa}

Next Step Convert Units

∴

S = ({(\frac{1.35m}{0.09m})}^{2}) \cdot \frac{0.001Pa*s \cdot 17Hz}{99Pa}

Next Step Prepare to Evaluate

∴

S = ({(\frac{1.35}{0.09})}^{2}) \cdot \frac{0.001 \cdot 17}{99}

Next Step Evaluate

∴

S = 0.0386363636363636

LAST Step Rounding Answer

∴

S = 0.0386

Sommerfeld Number Formula Elements

Variables

Sommerfeld Number

The Sommerfeld number is a dimensionless number that is used in designing a hydrodynamic bearing.

Symbol: S

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Sommerfeld Number

Radius of Shaft

Radius of shaft is the distance between the center and the circumference of the shaft.

Symbol: R_shaft

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radius of Shaft

Radial Clearance

Radial Clearance is a measured value of the total movement of one ring relative to the other in a plane perpendicular to the bearing axis.

Symbol: c_R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radial Clearance

Absolute Viscosity

Absolute Viscosity is the measurement of the fluid's internal resistance to flow.

Symbol: μ

Measurement: Dynamic ViscosityUnit: Pa*s

Note: Value can be positive or negative.

Formulas to find Absolute Viscosity

Speed of Rotating Shaft

Speed of Rotating Shaft is defined at which a rotating shaft will tend to vibrate violently in the transverse direction if the shaft rotates in the horizontal direction.

Symbol: N

Measurement: FrequencyUnit: rev/s

Note: Value should be greater than 0.

Formulas to find Speed of Rotating Shaft

Load per Unit of Area

Load per Unit of Area is the ratio of internal resistive force to the deformation per unit area and can be defined as Stress.

Symbol: P

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Load per Unit of Area

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 Archimedes Number

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

Go Weber Number

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

How to Evaluate Sommerfeld Number?

Sommerfeld Number evaluator uses Sommerfeld Number = ((Radius of Shaft/Radial Clearance)^(2))*(Absolute Viscosity*Speed of Rotating Shaft)/(Load per Unit of Area) to evaluate the Sommerfeld Number, Sommerfeld number (S) is a dimensionless quantity used extensively in hydrodynamic lubrication analysis. Sommerfeld Number is denoted by S symbol.

How to evaluate Sommerfeld Number using this online evaluator? To use this online evaluator for Sommerfeld Number, enter Radius of Shaft (R_shaft), Radial Clearance (c_R), Absolute Viscosity (μ), Speed of Rotating Shaft (N) & Load per Unit of Area (P) and hit the calculate button.

FAQs on Sommerfeld Number

What is the formula to find Sommerfeld Number?

The formula of Sommerfeld Number is expressed as Sommerfeld Number = ((Radius of Shaft/Radial Clearance)^(2))*(Absolute Viscosity*Speed of Rotating Shaft)/(Load per Unit of Area). Here is an example- 0.038636 = ((1.35/0.09)^(2))*(0.001*17)/(99).

How to calculate Sommerfeld Number?

With Radius of Shaft (R_shaft), Radial Clearance (c_R), Absolute Viscosity (μ), Speed of Rotating Shaft (N) & Load per Unit of Area (P) we can find Sommerfeld Number using the formula - Sommerfeld Number = ((Radius of Shaft/Radial Clearance)^(2))*(Absolute Viscosity*Speed of Rotating Shaft)/(Load per Unit of Area).

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Sommerfeld Number Formula

Sommerfeld Number Example

Sommerfeld Number Solution

Sommerfeld Number Formula Elements

Other formulas in Dimensionless Numbers category

How to Evaluate Sommerfeld Number?

FAQs on Sommerfeld Number

Variable Name