Thickness of Cylinder Calculator

✖Specific resistance is also known as resisitivity. The resistivity of a material is the resistance of a wire of that material of unit length and unit area of cross-section.ⓘ Specific Resistance [ρ]			+10% -10%
✖Relative permeability is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum.ⓘ Relative Permeability [μ_r]			+10% -10%
✖Frequency of induction furnace is the operating frequency of coreless induction furnace.ⓘ Frequency of Induction Furnace [f_furnace]			+10% -10%

✖Thickness Of Cylinder is the length of the cylinder used.ⓘ Thickness of Cylinder [t_c]

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Formula

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Thickness of Cylinder

Formula

`"t"_{"c"} = 1/(2*pi)*sqrt(("ρ"*10^9)/("μ"_{"r"}*"f"_{"furnace"}))`

Example

`"10.60986cm"=1/(2*pi)*sqrt(("113.59μΩ*cm"*10^9)/("0.9"*"2.84kHz"))`

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Thickness of Cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

Thickness of Cylinder = 1/(2*pi)*sqrt((Specific Resistance*10^9)/(Relative Permeability*Frequency of Induction Furnace))
t_c = 1/(2*pi)*sqrt((ρ*10^9)/(μ_r*f_furnace))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

Thickness of Cylinder - (Measured in Meter) - Thickness Of Cylinder is the length of the cylinder used.
Specific Resistance - (Measured in Ohm Meter) - Specific resistance is also known as resisitivity. The resistivity of a material is the resistance of a wire of that material of unit length and unit area of cross-section.
Relative Permeability - Relative permeability is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum.
Frequency of Induction Furnace - (Measured in Hertz) - Frequency of induction furnace is the operating frequency of coreless induction furnace.

STEP 1: Convert Input(s) to Base Unit

Specific Resistance: 113.59 Microhm Centimeter --> 1.1359E-06 Ohm Meter (Check conversion here)
Relative Permeability: 0.9 --> No Conversion Required
Frequency of Induction Furnace: 2.84 Kilohertz --> 2840 Hertz (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_c = 1/(2*pi)*sqrt((ρ*10^9)/(μ_r*f_furnace)) --> 1/(2*pi)*sqrt((1.1359E-06*10^9)/(0.9*2840))

Evaluating ... ...

t_c = 0.106098625252409

STEP 3: Convert Result to Output's Unit

0.106098625252409 Meter -->10.6098625252409 Centimeter (Check conversion here)

FINAL ANSWER

10.6098625252409 ≈ 10.60986 Centimeter <-- Thickness of Cylinder

(Calculation completed in 00.004 seconds)

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< 8 Furnace Heating Calculators

Heat Conduction

Go Heat Conduction = (Thermal Conductivity*Area of Furnace*Total Time*(Temperature of Wall 1-Temperature of Wall 2))/Thickness of Wall

Energy Required by Furnace to Melt Steel

Go Energy = (Mass*Specific Heat*(Temperature of Wall 2-Temperature of Wall 1))+(Mass*Latent Heat)

Thickness of Cylinder

Go Thickness of Cylinder = 1/(2*pi)*sqrt((Specific Resistance*10^9)/(Relative Permeability*Frequency of Induction Furnace))

Equivalent Inductance of Furnace

Go Inductance = (pi*4*pi*10^-7*Number of Coil Turns^2*Diameter of Melt^2)/(4*Height of Melt)

Heat Radiation

Go Heat Radiation = 5.72*Emissivity*Radiating Efficiency*((Temperature of Wall 1/100)^4-(Temperature of Wall 2/100)^4)

Operating Frequency

Go Frequency of Induction Furnace = (Specific Resistance*10^9)/(4*pi^2*Thickness of Cylinder^2*Relative Permeability)

Specific Resistance using Operating Frequency

Go Specific Resistance = (Frequency of Induction Furnace*4*pi^2*Thickness of Cylinder^2*Relative Permeability)/10^9

Energy Efficiency

Go Energy Efficiency = Theoretical Energy/Actual Energy

Thickness of Cylinder Formula

Thickness of Cylinder = 1/(2*pi)*sqrt((Specific Resistance*10^9)/(Relative Permeability*Frequency of Induction Furnace))
t_c = 1/(2*pi)*sqrt((ρ*10^9)/(μ_r*f_furnace))

What is permeability?

Permeability is the measure of magnetization that a material obtains in response to an applied magnetic field.

How to Calculate Thickness of Cylinder?

Thickness of Cylinder calculator uses Thickness of Cylinder = 1/(2*pi)*sqrt((Specific Resistance*10^9)/(Relative Permeability*Frequency of Induction Furnace)) to calculate the Thickness of Cylinder, The Thickness of cylinder formula is defined as the thickness of the cylindrical layer used in the middle of the crucible. Thickness of Cylinder is denoted by t_c symbol.

How to calculate Thickness of Cylinder using this online calculator? To use this online calculator for Thickness of Cylinder, enter Specific Resistance (ρ), Relative Permeability (μ_r) & Frequency of Induction Furnace (f_furnace) and hit the calculate button. Here is how the Thickness of Cylinder calculation can be explained with given input values -> 1060.986 = 1/(2*pi)*sqrt((1.1359E-06*10^9)/(0.9*2840)).

FAQ

What is Thickness of Cylinder?

The Thickness of cylinder formula is defined as the thickness of the cylindrical layer used in the middle of the crucible and is represented as t_c = 1/(2*pi)*sqrt((ρ*10^9)/(μ_r*f_furnace)) or Thickness of Cylinder = 1/(2*pi)*sqrt((Specific Resistance*10^9)/(Relative Permeability*Frequency of Induction Furnace)). Specific resistance is also known as resisitivity. The resistivity of a material is the resistance of a wire of that material of unit length and unit area of cross-section, Relative permeability is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum & Frequency of induction furnace is the operating frequency of coreless induction furnace.

How to calculate Thickness of Cylinder?

The Thickness of cylinder formula is defined as the thickness of the cylindrical layer used in the middle of the crucible is calculated using Thickness of Cylinder = 1/(2*pi)*sqrt((Specific Resistance*10^9)/(Relative Permeability*Frequency of Induction Furnace)). To calculate Thickness of Cylinder, you need Specific Resistance (ρ), Relative Permeability (μ_r) & Frequency of Induction Furnace (f_furnace). With our tool, you need to enter the respective value for Specific Resistance, Relative Permeability & Frequency of Induction Furnace 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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