Sommerfeld Number Calculator

✖Radius of shaft is the distance between the center and the circumference of the shaft.ⓘ Radius of Shaft [R_shaft]			+10% -10%
✖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.ⓘ Radial Clearance [c_R]			+10% -10%
✖Absolute Viscosity is the measurement of the fluid's internal resistance to flow.ⓘ Absolute Viscosity [μ]			+10% -10%
✖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.ⓘ Speed of Rotating Shaft [N]			+10% -10%
✖Load per Unit of Area is the ratio of internal resistive force to the deformation per unit area and can be defined as Stress.ⓘ Load per Unit of Area [P]			+10% -10%

✖The Sommerfeld number is a dimensionless number that is used in designing a hydrodynamic bearing.ⓘ Sommerfeld Number [S]

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Sommerfeld Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sommerfeld Number = ((Radius of Shaft/Radial Clearance)^(2))*(Absolute Viscosity*Speed of Rotating Shaft)/(Load per Unit of Area)
S = ((R_shaft/c_R)^(2))*(μ*N)/(P)
This formula uses 6 Variables

Variables Used

Sommerfeld Number - The Sommerfeld number is a dimensionless number that is used in designing a hydrodynamic bearing.
Radius of Shaft - (Measured in Meter) - Radius of shaft is the distance between the center and the circumference of the shaft.
Radial Clearance - (Measured in Meter) - 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.
Absolute Viscosity - (Measured in Pascal Second) - Absolute Viscosity is the measurement of the fluid's internal resistance to flow.
Speed of Rotating Shaft - (Measured in Hertz) - 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.
Load per Unit of Area - (Measured in Pascal) - Load per Unit of Area is the ratio of internal resistive force to the deformation per unit area and can be defined as Stress.

STEP 1: Convert Input(s) to Base Unit

Radius of Shaft: 1.35 Meter --> 1.35 Meter No Conversion Required
Radial Clearance: 0.09 Meter --> 0.09 Meter No Conversion Required
Absolute Viscosity: 0.001 Pascal Second --> 0.001 Pascal Second No Conversion Required
Speed of Rotating Shaft: 17 Revolution per Second --> 17 Hertz (Check conversion here)
Load per Unit of Area: 99 Pascal --> 99 Pascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S = ((R_shaft/c_R)^(2))*(μ*N)/(P) --> ((1.35/0.09)^(2))*(0.001*17)/(99)

Evaluating ... ...

S = 0.0386363636363636

STEP 3: Convert Result to Output's Unit

0.0386363636363636 --> No Conversion Required

FINAL ANSWER

0.0386363636363636 ≈ 0.038636 <-- Sommerfeld Number

(Calculation completed in 00.004 seconds)

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Sommerfeld Number Formula

LaTeX Go

Sommerfeld Number = ((Radius of Shaft/Radial Clearance)^(2))*(Absolute Viscosity*Speed of Rotating Shaft)/(Load per Unit of Area)
S = ((R_shaft/c_R)^(2))*(μ*N)/(P)

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 Sommerfeld Number?

Sommerfeld Number calculator uses Sommerfeld Number = ((Radius of Shaft/Radial Clearance)^(2))*(Absolute Viscosity*Speed of Rotating Shaft)/(Load per Unit of Area) to calculate 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 calculate Sommerfeld Number using this online calculator? To use this online calculator 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. Here is how the Sommerfeld Number calculation can be explained with given input values -> 0.038636 = ((1.35/0.09)^(2))*(0.001*17)/(99).

FAQ

What is Sommerfeld Number?

Sommerfeld number (S) is a dimensionless quantity used extensively in hydrodynamic lubrication analysis and is represented as S = ((R_shaft/c_R)^(2))*(μ*N)/(P) or Sommerfeld Number = ((Radius of Shaft/Radial Clearance)^(2))*(Absolute Viscosity*Speed of Rotating Shaft)/(Load per Unit of Area). Radius of shaft is the distance between the center and the circumference of the shaft, 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, Absolute Viscosity is the measurement of the fluid's internal resistance to flow, 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 & Load per Unit of Area is the ratio of internal resistive force to the deformation per unit area and can be defined as Stress.

How to calculate Sommerfeld Number?

Sommerfeld number (S) is a dimensionless quantity used extensively in hydrodynamic lubrication analysis is calculated using Sommerfeld Number = ((Radius of Shaft/Radial Clearance)^(2))*(Absolute Viscosity*Speed of Rotating Shaft)/(Load per Unit of Area). To calculate Sommerfeld Number, you need Radius of Shaft (R_shaft), Radial Clearance (c_R), Absolute Viscosity (μ), Speed of Rotating Shaft (N) & Load per Unit of Area (P). With our tool, you need to enter the respective value for Radius of Shaft, Radial Clearance, Absolute Viscosity, Speed of Rotating Shaft & Load per Unit of Area and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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