Depth of Torisperical Head 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%
✖Vessel Shell Outer Diameter refers to the outermost dimension of the cylindrical shell of a vessel, such as a tank or pressure vessel.ⓘ Vessel Shell Outer Diameter [D_o]			+10% -10%
✖Knuckle Radius refers to the radius of curvature between the bottom of the vessel's cylindrical shell and the vessel's bottom head or dished end.ⓘ Knuckle Radius [R_k]			+10% -10%

✖Depth of Head refers to the vertical distance between the top of the vessel and the liquid level in the vessel when it is filled to its maximum operating capacity.ⓘ Depth of Torisperical Head [h_o]

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Formula

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Depth of Torisperical Head

Formula

`"h"_{"o"} = "R"_{"c"}-sqrt(("R"_{"c"}-"D"_{"o"}/2)*("R"_{"c"}+"D"_{"o"}/2-2*"R"_{"k"}))`

Example

`"73.10091mm"="1401mm"-sqrt(("1401mm"-"550mm"/2)*("1401mm"+"550mm"/2-2*"55mm"))`

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Depth of Torisperical Head Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
h_o = R_c-sqrt((R_c-D_o/2)*(R_c+D_o/2-2*R_k))
This formula uses 1 Functions, 4 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

Depth of Head - (Measured in Millimeter) - Depth of Head refers to the vertical distance between the top of the vessel and the liquid level in the vessel when it is filled to its maximum operating capacity.
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.
Vessel Shell Outer Diameter - (Measured in Millimeter) - Vessel Shell Outer Diameter refers to the outermost dimension of the cylindrical shell of a vessel, such as a tank or pressure vessel.
Knuckle Radius - (Measured in Millimeter) - Knuckle Radius refers to the radius of curvature between the bottom of the vessel's cylindrical shell and the vessel's bottom head or dished end.

STEP 1: Convert Input(s) to Base Unit

Crown Radius for Jacketed Reaction Vessel: 1401 Millimeter --> 1401 Millimeter No Conversion Required
Vessel Shell Outer Diameter: 550 Millimeter --> 550 Millimeter No Conversion Required
Knuckle Radius: 55 Millimeter --> 55 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_o = R_c-sqrt((R_c-D_o/2)*(R_c+D_o/2-2*R_k)) --> 1401-sqrt((1401-550/2)*(1401+550/2-2*55))

Evaluating ... ...

h_o = 73.1009074481601

STEP 3: Convert Result to Output's Unit

0.0731009074481601 Meter -->73.1009074481601 Millimeter (Check conversion here)

FINAL ANSWER

73.1009074481601 ≈ 73.10091 Millimeter <-- Depth of Head

(Calculation completed in 00.004 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

Depth of Torisperical Head Formula

What is Jacketed Reaction Vessel?

A jacketed reaction vessel is a type of vessel used in the process of chemical reactions or mixing substances together under certain conditions. The vessel is typically made of a durable material such as stainless steel or glass and is designed to withstand high temperatures and pressures. The jacket surrounding the vessel is filled with a heating or cooling medium, such as water or oil, to control the temperature of the contents inside the vessel. The jacketed design allows for precise temperature control and uniform heating or cooling of the contents inside the vessel during the reaction process. These vessels are commonly used in chemical, pharmaceutical, and food processing industries.

What is Head?

In the context of a vessel or tank, a head refers to the end closure of the vessel. It is typically a circular plate or dome-shaped structure that is attached to the cylindrical body of the vessel. The head is used to provide access to the interior of the vessel for inspection, maintenance, and cleaning. There are different types of heads used in vessel design, such as flat, dished, hemispherical, elliptical, torispherical, and conical heads. The choice of head type depends on factors such as the pressure rating, volume, and application of the vessel.

How to Calculate Depth of Torisperical Head?

Depth of Torisperical Head calculator uses 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)) to calculate the Depth of Head, Depth of Torisperical Head refers to the vertical distance between the top of the vessel and the liquid level in the vessel when it is filled to its maximum operating capacity. Depth of Head is denoted by h_o symbol.

How to calculate Depth of Torisperical Head using this online calculator? To use this online calculator for Depth of Torisperical Head, enter Crown Radius for Jacketed Reaction Vessel (R_c), Vessel Shell Outer Diameter (D_o) & Knuckle Radius (R_k) and hit the calculate button. Here is how the Depth of Torisperical Head calculation can be explained with given input values -> 73100.91 = 1.401-sqrt((1.401-0.55/2)*(1.401+0.55/2-2*0.055)).

FAQ

What is Depth of Torisperical Head?

Depth of Torisperical Head refers to the vertical distance between the top of the vessel and the liquid level in the vessel when it is filled to its maximum operating capacity and is represented as h_o = R_c-sqrt((R_c-D_o/2)*(R_c+D_o/2-2*R_k)) or 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)). 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, Vessel Shell Outer Diameter refers to the outermost dimension of the cylindrical shell of a vessel, such as a tank or pressure vessel & Knuckle Radius refers to the radius of curvature between the bottom of the vessel's cylindrical shell and the vessel's bottom head or dished end.

How to calculate Depth of Torisperical Head?

Depth of Torisperical Head refers to the vertical distance between the top of the vessel and the liquid level in the vessel when it is filled to its maximum operating capacity is calculated using 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)). To calculate Depth of Torisperical Head, you need Crown Radius for Jacketed Reaction Vessel (R_c), Vessel Shell Outer Diameter (D_o) & Knuckle Radius (R_k). With our tool, you need to enter the respective value for Crown Radius for Jacketed Reaction Vessel, Vessel Shell Outer Diameter & Knuckle Radius 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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