Thickness of Bottom Head subjected to Pressure Calculator

✖Crown Radius for Jacketed Reaction Vessel is the horizontal distance, as seen in plan view, from the trunk of a tree to the edge of the crown.ⓘ Crown Radius for Jacketed Reaction Vessel [R_c]			+10% -10%
✖Poisson ratio is defined as the deformation of a material in directions perpendicular to the direction of loading.ⓘ Poisson Ratio [u]			+10% -10%
✖Internal Pressure in Vessel is a measure of how the internal energy of a system changes when it expands or contracts at constant temperature.ⓘ Internal Pressure in Vessel [p]			+10% -10%
✖Modulus of Elasticity Jacketed Reaction Vessel refers to the measure of the vessel's ability to deform elastically under an applied load.ⓘ Modulus of Elasticity Jacketed Reaction Vessel [E]			+10% -10%

✖Head Thickness is the distance through an object, as distinct from width or height.ⓘ Thickness of Bottom Head subjected to Pressure [t_h]

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Formula

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Thickness of Bottom Head subjected to Pressure

Formula

`"t"_{"h"} = 4.4*"R"_{"c"}*(3*(1-("u")^(2)))^(1/4)*sqrt("p"/(2*"E"))`

Example

`"9.799269mm"=4.4*"1401mm"*(3*(1-("0.3")^(2)))^(1/4)*sqrt("0.52N/mm²"/(2*"170000N/mm²"))`

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Thickness of Bottom Head subjected to Pressure Solution

STEP 0: Pre-Calculation Summary

Formula Used

Head Thickness = 4.4*Crown Radius for Jacketed Reaction Vessel*(3*(1-(Poisson Ratio)^(2)))^(1/4)*sqrt(Internal Pressure in Vessel/(2*Modulus of Elasticity Jacketed Reaction Vessel))
t_h = 4.4*R_c*(3*(1-(u)^(2)))^(1/4)*sqrt(p/(2*E))
This formula uses 1 Functions, 5 Variables

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

Head Thickness - (Measured in Millimeter) - Head Thickness is the distance through an object, as distinct from width or height.
Crown Radius for Jacketed Reaction Vessel - (Measured in Millimeter) - Crown Radius for Jacketed Reaction Vessel is the horizontal distance, as seen in plan view, from the trunk of a tree to the edge of the crown.
Poisson Ratio - Poisson ratio is defined as the deformation of a material in directions perpendicular to the direction of loading.
Internal Pressure in Vessel - (Measured in Newton per Square Millimeter) - Internal Pressure in Vessel is a measure of how the internal energy of a system changes when it expands or contracts at constant temperature.
Modulus of Elasticity Jacketed Reaction Vessel - (Measured in Newton per Square Millimeter) - Modulus of Elasticity Jacketed Reaction Vessel refers to the measure of the vessel's ability to deform elastically under an applied load.

STEP 1: Convert Input(s) to Base Unit

Crown Radius for Jacketed Reaction Vessel: 1401 Millimeter --> 1401 Millimeter No Conversion Required
Poisson Ratio: 0.3 --> No Conversion Required
Internal Pressure in Vessel: 0.52 Newton per Square Millimeter --> 0.52 Newton per Square Millimeter No Conversion Required
Modulus of Elasticity Jacketed Reaction Vessel: 170000 Newton per Square Millimeter --> 170000 Newton per Square Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_h = 4.4*R_c*(3*(1-(u)^(2)))^(1/4)*sqrt(p/(2*E)) --> 4.4*1401*(3*(1-(0.3)^(2)))^(1/4)*sqrt(0.52/(2*170000))

Evaluating ... ...

t_h = 9.79926916171982

STEP 3: Convert Result to Output's Unit

0.00979926916171982 Meter -->9.79926916171982 Millimeter (Check conversion here)

FINAL ANSWER

9.79926916171982 ≈ 9.799269 Millimeter <-- Head Thickness

(Calculation completed in 00.021 seconds)

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< 21 Jacketed Reaction Vessel Calculators

Total Axial Stress in Vessel Shell

Go Total Axial Stress = ((Internal Pressure in Vessel*Internal Diameter of Shell)/(4*Shell Thickness*Joint Efficiency for Shell))+((Design Jacket Pressure*Internal Diameter of Half Coil)/(2*Shell Thickness*Joint Efficiency for Shell))+(2*Maximum difference between Coil and Shell Pressure*(Outer Diameter of Half Coil)^(2))/(3*Shell Thickness^(2))

Maximum Equivalent Stress at Junction with Shell

Go Maximum Equivalent Stress at Junction with Shell = (sqrt((Total Axial Stress)^(2)+(Total Hoop Stress)^(2)+(Maximum Hoop Stress in Coil at Junction with Shell)^(2)-((Total Axial Stress*Total Hoop Stress)+(Total Axial Stress*Maximum Hoop Stress in Coil at Junction with Shell)+(Maximum Hoop Stress in Coil at Junction with Shell*Total Hoop Stress))))

Total Hoop Stress in Shell

Go Total Hoop Stress = (Design Pressure Shell*Internal Diameter of Shell)/(2*Shell Thickness*Joint Efficiency for Shell)+(Design Jacket Pressure*Internal Diameter of Half Coil)/((4*Thickness of Half Coil Jacket*Weld Joint Efficiency Factor for Coil)+(2.5*Shell Thickness*Joint Efficiency for Shell))

Combined Moment of Inertia of Shell and Stiffener per Unit Length

Go Combined Moment of Inertia of Shell and Stiffener = (Vessel Shell Outer Diameter^(2)*Effective Length Between Stiffeners*(Shell Thickness for Jackted Reaction Vessel+Cross Sectional Area of Stiffening Ring/Effective Length Between Stiffeners)*Allowable Stress for Jacket Material)/(12*Modulus of Elasticity Jacketed Reaction Vessel)

Shell Thickness for Critical External Pressure

Go Critical External Pressure = (2.42*Modulus of Elasticity Jacketed Reaction Vessel)/(1-(Poisson Ratio)^(2))^(3/4)*((Vessel Thickness/Vessel Shell Outer Diameter)^(5/2)/((Length of Shell/Vessel Shell Outer Diameter)-0.45*(Vessel Thickness/Vessel Shell Outer Diameter)^(1/2)))

Depth of Torisperical Head

Go Depth of Head = Crown Radius for Jacketed Reaction Vessel-sqrt((Crown Radius for Jacketed Reaction Vessel-Vessel Shell Outer Diameter/2)*(Crown Radius for Jacketed Reaction Vessel+Vessel Shell Outer Diameter/2-2*Knuckle Radius))

Design of Shell Thickness Subjected to Internal Pressure

Go Shell Thickness for Jackted Reaction Vessel = (Internal Pressure in Vessel*Internal Diameter of Shell)/((2*Allowable Stress for Jacket Material*Joint Efficiency for Shell)-(Internal Pressure in Vessel))+Corrosion Allowance

Maximum Axial Stress in Coil at Junction with Shell

Go Maximum Axial Stress in Coil at Junction = (Design Jacket Pressure*Internal Diameter of Half Coil)/((4*Thickness of Half Coil Jacket*Weld Joint Efficiency Factor for Coil)+(2.5*Shell Thickness*Joint Efficiency for Shell))

Dished Head Thickness

Go Dished Head Thickness = ((Internal Pressure in Vessel*Crown Radius for Jacketed Reaction Vessel*Stress Intensification Factor)/(2*Allowable Stress for Jacket Material*Joint Efficiency for Shell))+Corrosion Allowance

Thickness of Bottom Head subjected to Pressure

Go Head Thickness = 4.4*Crown Radius for Jacketed Reaction Vessel*(3*(1-(Poisson Ratio)^(2)))^(1/4)*sqrt(Internal Pressure in Vessel/(2*Modulus of Elasticity Jacketed Reaction Vessel))

Thickness of Half Coil Jacket

Go Thickness of Half Coil Jacket = (Design Jacket Pressure*Internal Diameter of Half Coil)/((2*Allowable Stress for Jacket Material*Joint Efficiency for Shell))+Corrosion Allowance

Thickness of Jacket Shell for Internal Pressure

Go Required Thickness of Jacket = (Design Jacket Pressure*Internal Diameter of Shell)/((2*Allowable Stress for Jacket Material*Joint Efficiency for Shell)-Design Jacket Pressure)

Channel Jacket Thickness

Go Channel Wall Thickness = Design Length of Channel Section*(sqrt((0.12*Design Jacket Pressure)/(Allowable Stress for Jacket Material)))+Corrosion Allowance

Maximum Hoop Stress in Coil at Junction with Shell

Go Maximum Hoop Stress in Coil at Junction with Shell = (Design Jacket Pressure*Internal Diameter of Half Coil)/(2*Thickness of Half Coil Jacket*Weld Joint Efficiency Factor for Coil)

Vessel Wall Thickness for Channel Type Jacket

Go Vessel Thickness = Design Length of Channel Section*sqrt((0.167*Design Jacket Pressure)/(Allowable Stress for Jacket Material))+Corrosion Allowance

Required Plate Thickness for Dimple Jacket

Go Required Thickness of Dimple Jacket = Maximum Pitch between Steam Weld Centre Lines*sqrt(Design Jacket Pressure/(3*Allowable Stress for Jacket Material))

Required Thickness for Jacket Closer Member with Jacket Width

Go Required Thickness for Jacket Closer Member = 0.886*Jacket Width*sqrt(Design Jacket Pressure/Allowable Stress for Jacket Material)

Length of Shell under Combined Moment of Inertia

Go Length of Shell = 1.1*sqrt(Vessel Shell Outer Diameter*Vessel Thickness)

Cross Sectional Area of Stiffening Ring

Go Cross Sectional Area of Stiffening Ring = Width of Stiffener*Thickness of Stiffener

Length of Shell for Jacket

Go Length of Shell for Jacket = Length of Straight Side Jacket+1/3*Depth of Head

Jacket Width

Go Jacket Width = (Inside Diameter of Jacket-Outer Diameter of Vessel)/2

Thickness of Bottom Head subjected to Pressure Formula

What is Design Thickness?

Design thickness is a term used in structural engineering to refer to the thickness of a structural element (such as a beam, column, or plate) that has been calculated or specified based on the design requirements of the structure. The design thickness is the thickness that has been calculated or specified based on the structural requirements of the beam and the strength and deformability of the soil or foundation on which the beam will be supported. The design thickness of a bottom plate is typically determined by a structural engineer or using structural engineering software, and is used to ensure that the bottom plate is able to safely carry the loads that will be applied to it during the life of the structure.

How to Calculate Thickness of Bottom Head subjected to Pressure?

Thickness of Bottom Head subjected to Pressure calculator uses Head Thickness = 4.4*Crown Radius for Jacketed Reaction Vessel*(3*(1-(Poisson Ratio)^(2)))^(1/4)*sqrt(Internal Pressure in Vessel/(2*Modulus of Elasticity Jacketed Reaction Vessel)) to calculate the Head Thickness, Thickness of Bottom Head subjected to Pressure vessel refers to the minimum required thickness of the material used to construct the bottom head to withstand the internal pressure exerted by the contents of the vessel. Head Thickness is denoted by t_h symbol.

How to calculate Thickness of Bottom Head subjected to Pressure using this online calculator? To use this online calculator for Thickness of Bottom Head subjected to Pressure, enter Crown Radius for Jacketed Reaction Vessel (R_c), Poisson Ratio (u), Internal Pressure in Vessel (p) & Modulus of Elasticity Jacketed Reaction Vessel (E) and hit the calculate button. Here is how the Thickness of Bottom Head subjected to Pressure calculation can be explained with given input values -> 9799.269 = 4.4*1.401*(3*(1-(0.3)^(2)))^(1/4)*sqrt(520000/(2*170000000000)).

FAQ

What is Thickness of Bottom Head subjected to Pressure?

Thickness of Bottom Head subjected to Pressure vessel refers to the minimum required thickness of the material used to construct the bottom head to withstand the internal pressure exerted by the contents of the vessel and is represented as t_h = 4.4*R_c*(3*(1-(u)^(2)))^(1/4)*sqrt(p/(2*E)) or Head Thickness = 4.4*Crown Radius for Jacketed Reaction Vessel*(3*(1-(Poisson Ratio)^(2)))^(1/4)*sqrt(Internal Pressure in Vessel/(2*Modulus of Elasticity Jacketed Reaction Vessel)). Crown Radius for Jacketed Reaction Vessel is the horizontal distance, as seen in plan view, from the trunk of a tree to the edge of the crown, Poisson ratio is defined as the deformation of a material in directions perpendicular to the direction of loading, Internal Pressure in Vessel is a measure of how the internal energy of a system changes when it expands or contracts at constant temperature & Modulus of Elasticity Jacketed Reaction Vessel refers to the measure of the vessel's ability to deform elastically under an applied load.

How to calculate Thickness of Bottom Head subjected to Pressure?

Thickness of Bottom Head subjected to Pressure vessel refers to the minimum required thickness of the material used to construct the bottom head to withstand the internal pressure exerted by the contents of the vessel is calculated using Head Thickness = 4.4*Crown Radius for Jacketed Reaction Vessel*(3*(1-(Poisson Ratio)^(2)))^(1/4)*sqrt(Internal Pressure in Vessel/(2*Modulus of Elasticity Jacketed Reaction Vessel)). To calculate Thickness of Bottom Head subjected to Pressure, you need Crown Radius for Jacketed Reaction Vessel (R_c), Poisson Ratio (u), Internal Pressure in Vessel (p) & Modulus of Elasticity Jacketed Reaction Vessel (E). With our tool, you need to enter the respective value for Crown Radius for Jacketed Reaction Vessel, Poisson Ratio, Internal Pressure in Vessel & Modulus of Elasticity Jacketed Reaction Vessel 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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