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Thickness of Base Metal for Desired Cooling Rate Formula

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Thickness refers to the measurement of the distance through an object or material from one surface to its opposite surface. It indicates how thick the object or material is. Check FAQs

z = H net \cdot \sqrt{\frac{R}{2 \cdot π \cdot k \cdot ρ \cdot Q c \cdot ({(T c - t a)}^{3})}}

z - Thickness?H_net - Net Heat Supplied Per Unit Length?R - Cooling Rate of Thick Plate?k - Thermal Conductivity?ρ - Density of Electrode?Q_c - Specific Heat Capacity?T_c - Temperature for Cooling Rate?t_a - Ambient Temperature?π - Archimedes' constant?

Thickness of Base Metal for Desired Cooling Rate Example

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Here is how the Thickness of Base Metal for Desired Cooling Rate equation looks like with Values.

Here is how the Thickness of Base Metal for Desired Cooling Rate equation looks like with Units.

Here is how the Thickness of Base Metal for Desired Cooling Rate equation looks like.

22.7544 = 1000 \cdot \sqrt{\frac{13.7116}{2 \cdot 3.1416 \cdot 10.18 \cdot 997 \cdot 4.184 \cdot ({(500 - 37)}^{3})}}

22.7544mm = 1000J/mm \cdot \sqrt{\frac{13.7116°C/s}{2 \cdot 3.1416 \cdot 10.18W/(m*K) \cdot 997kg/m³ \cdot 4.184kJ/kg*K \cdot ({(500°C - 37°C)}^{3})}}

22.7544 = 1000 \cdot \sqrt{\frac{13.7116}{2 \cdot 3.1416 \cdot 10.18 \cdot 997 \cdot 4.184 \cdot ({(500 - 37)}^{3})}}

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Thickness of Base Metal for Desired Cooling Rate Solution

Follow our step by step solution on how to calculate Thickness of Base Metal for Desired Cooling Rate?

FIRST Step Consider the formula

z = H net \cdot \sqrt{\frac{R}{2 \cdot π \cdot k \cdot ρ \cdot Q c \cdot ({(T c - t a)}^{3})}}

Next Step Substitute values of Variables

∴

z = 1000J/mm \cdot \sqrt{\frac{13.7116°C/s}{2 \cdot π \cdot 10.18W/(m*K) \cdot 997kg/m³ \cdot 4.184kJ/kg*K \cdot ({(500°C - 37°C)}^{3})}}

Next Step Substitute values of Constants

∴

z = 1000J/mm \cdot \sqrt{\frac{13.7116°C/s}{2 \cdot 3.1416 \cdot 10.18W/(m*K) \cdot 997kg/m³ \cdot 4.184kJ/kg*K \cdot ({(500°C - 37°C)}^{3})}}

Next Step Convert Units

∴

z = 1E+6J/m \cdot \sqrt{\frac{13.7116K/s}{2 \cdot 3.1416 \cdot 10.18W/(m*K) \cdot 997kg/m³ \cdot 4184J/(kg*K) \cdot ({(773.15K - 310.15K)}^{3})}}

Next Step Prepare to Evaluate

∴

z = 1E+6 \cdot \sqrt{\frac{13.7116}{2 \cdot 3.1416 \cdot 10.18 \cdot 997 \cdot 4184 \cdot ({(773.15 - 310.15)}^{3})}}

Next Step Evaluate

∴

z = 0.022754439004016m

Next Step Convert to Output's Unit

∴

z = 22.754439004016mm

LAST Step Rounding Answer

∴

z = 22.7544mm

Thickness of Base Metal for Desired Cooling Rate Formula Elements

Variables

Constants

Functions

Thickness

Thickness refers to the measurement of the distance through an object or material from one surface to its opposite surface. It indicates how thick the object or material is.

Symbol: z

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness

Net Heat Supplied Per Unit Length

Net Heat Supplied Per Unit Length refers to the amount of heat energy transferred per unit length along a material or medium.

Symbol: H_net

Measurement: Energy per Unit LengthUnit: J/mm

Note: Value should be greater than 0.

Formulas to find Net Heat Supplied Per Unit Length

Cooling Rate of Thick Plate

Cooling Rate of Thick Plate is the rate of decrease of temperature of a particular thick sheet of material.

Symbol: R

Measurement: Rate of Temperature ChangeUnit: °C/s

Note: Value can be positive or negative.

Formulas to find Cooling Rate of Thick Plate

Thermal Conductivity

Thermal Conductivity is the rate at which heat passes through a material, defined as heat flow per unit time per unit area with a temperature gradient of one degree per unit distance.

Symbol: k

Measurement: Thermal ConductivityUnit: W/(m*K)

Note: Value can be positive or negative.

Formulas to find Thermal Conductivity

Density of Electrode

The Density of Electrode in welding refers to the mass per unit volume of the electrode material, it is the filling material of the weld.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density of Electrode

Specific Heat Capacity

Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

Symbol: Q_c

Measurement: Specific Heat CapacityUnit: kJ/kg*K

Note: Value can be positive or negative.

Formulas to find Specific Heat Capacity

Temperature for Cooling Rate

Temperature for Cooling Rate is the temperature at which the cooling rate is calculated.

Symbol: T_c

Measurement: TemperatureUnit: °C

Note: Value can be positive or negative.

Formulas to find Temperature for Cooling Rate

Ambient Temperature

Ambient Temperature Ambient temperature refers to the air temperature of any object or environment where equipment is stored. In a more general sense, it is the temperature of the surrounding.

Symbol: t_a

Measurement: TemperatureUnit: °C

Note: Value should be greater than -273.15.

Formulas to find Ambient Temperature

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other formulas in Heat Flow in Welded Joints category

Go Peak Temperature Reached at any Point in Material

T p = t a + \frac{H net \cdot (T m - t a)}{(T m - t a) \cdot \sqrt{2 \cdot π \cdot e} \cdot ρ m \cdot t \cdot Q c \cdot y + H net}

Go Position of Peak Temperature from Fusion Boundary

y = \frac{(T m - T y) \cdot H net}{(T y - t a) \cdot (T m - t a) \cdot \sqrt{2 \cdot π \cdot e} \cdot ρ \cdot Q c \cdot t}

How to Evaluate Thickness of Base Metal for Desired Cooling Rate?

Thickness of Base Metal for Desired Cooling Rate evaluator uses Thickness = Net Heat Supplied Per Unit Length*sqrt(Cooling Rate of Thick Plate/(2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Temperature for Cooling Rate-Ambient Temperature)^3))) to evaluate the Thickness, The Thickness of Base Metal for Desired Cooling Rate formula is defined as the thickness of base metal as required for given cooling rate. Thickness is denoted by z symbol.

How to evaluate Thickness of Base Metal for Desired Cooling Rate using this online evaluator? To use this online evaluator for Thickness of Base Metal for Desired Cooling Rate, enter Net Heat Supplied Per Unit Length (H_net), Cooling Rate of Thick Plate (R), Thermal Conductivity (k), Density of Electrode (ρ), Specific Heat Capacity (Q_c), Temperature for Cooling Rate (T_c) & Ambient Temperature (t_a) and hit the calculate button.

FAQs on Thickness of Base Metal for Desired Cooling Rate

What is the formula to find Thickness of Base Metal for Desired Cooling Rate?

The formula of Thickness of Base Metal for Desired Cooling Rate is expressed as Thickness = Net Heat Supplied Per Unit Length*sqrt(Cooling Rate of Thick Plate/(2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Temperature for Cooling Rate-Ambient Temperature)^3))). Here is an example- 22753.07 = 1000000*sqrt(13.71165/(2*pi*10.18*997*4184*((773.15-310.15)^3))).

How to calculate Thickness of Base Metal for Desired Cooling Rate?

With Net Heat Supplied Per Unit Length (H_net), Cooling Rate of Thick Plate (R), Thermal Conductivity (k), Density of Electrode (ρ), Specific Heat Capacity (Q_c), Temperature for Cooling Rate (T_c) & Ambient Temperature (t_a) we can find Thickness of Base Metal for Desired Cooling Rate using the formula - Thickness = Net Heat Supplied Per Unit Length*sqrt(Cooling Rate of Thick Plate/(2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Temperature for Cooling Rate-Ambient Temperature)^3))). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Thickness of Base Metal for Desired Cooling Rate be negative?

No, the Thickness of Base Metal for Desired Cooling Rate, measured in Length cannot be negative.

Which unit is used to measure Thickness of Base Metal for Desired Cooling Rate?

Thickness of Base Metal for Desired Cooling Rate is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Thickness of Base Metal for Desired Cooling Rate can be measured.

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Thickness of Base Metal for Desired Cooling Rate Formula

Thickness of Base Metal for Desired Cooling Rate Example

Thickness of Base Metal for Desired Cooling Rate Solution

Thickness of Base Metal for Desired Cooling Rate Formula Elements

Other formulas in Heat Flow in Welded Joints category

How to Evaluate Thickness of Base Metal for Desired Cooling Rate?

FAQs on Thickness of Base Metal for Desired Cooling Rate

Variable Name