Change in volume of thin cylindrical shell Calculator

✖Diameter of Shell is the maximum width of cylinder in transverse direction.ⓘ Diameter of Shell [D]			+10% -10%
✖Length Of Cylindrical Shell is the measurement or extent of cylinder from end to end.ⓘ Length Of Cylindrical Shell [L_cylinder]			+10% -10%
✖The Change in Diameter is the difference between the initial and final diameter.ⓘ Change in Diameter [∆d]			+10% -10%
✖Change in Length is after the application of force, change in the dimensions of the object.ⓘ Change in Length [ΔL]			+10% -10%

✖The Change in volume is difference of initial and final volume.ⓘ Change in volume of thin cylindrical shell [∆V]

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Formula

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Change in volume of thin cylindrical shell

Formula

`"∆V" = (pi/4)*((2*"D"*"L"_{"cylinder"}*"∆d")+("ΔL"*("D"^2)))`

Example

`"4.705006m³"=(pi/4)*((2*"2200mm"*"3000mm"*"50.5mm")+("1100mm"*(("2200mm")^2)))`

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Change in volume of thin cylindrical shell Solution

STEP 0: Pre-Calculation Summary

Formula Used

Change in Volume = (pi/4)*((2*Diameter of Shell*Length Of Cylindrical Shell*Change in Diameter)+(Change in Length*(Diameter of Shell^2)))
∆V = (pi/4)*((2*D*L_cylinder*∆d)+(ΔL*(D^2)))
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Change in Volume - (Measured in Cubic Meter) - The Change in volume is difference of initial and final volume.
Diameter of Shell - (Measured in Meter) - Diameter of Shell is the maximum width of cylinder in transverse direction.
Length Of Cylindrical Shell - (Measured in Meter) - Length Of Cylindrical Shell is the measurement or extent of cylinder from end to end.
Change in Diameter - (Measured in Meter) - The Change in Diameter is the difference between the initial and final diameter.
Change in Length - (Measured in Meter) - Change in Length is after the application of force, change in the dimensions of the object.

STEP 1: Convert Input(s) to Base Unit

Diameter of Shell: 2200 Millimeter --> 2.2 Meter (Check conversion here)
Length Of Cylindrical Shell: 3000 Millimeter --> 3 Meter (Check conversion here)
Change in Diameter: 50.5 Millimeter --> 0.0505 Meter (Check conversion here)
Change in Length: 1100 Millimeter --> 1.1 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∆V = (pi/4)*((2*D*L_cylinder*∆d)+(ΔL*(D^2))) --> (pi/4)*((2*2.2*3*0.0505)+(1.1*(2.2^2)))

Evaluating ... ...

∆V = 4.70500623764875

STEP 3: Convert Result to Output's Unit

4.70500623764875 Cubic Meter --> No Conversion Required

FINAL ANSWER

4.70500623764875 ≈ 4.705006 Cubic Meter <-- Change in Volume

(Calculation completed in 00.008 seconds)

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Home » Physics » Strength of Materials » Thin Cylinders And Spheres » Effect of Internal Pressure on Dimension of Thin Cylindrical Shell » Change in Dimensions » Change in volume of thin cylindrical shell

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National Institute Of Technology (NIT), Hamirpur

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< 12 Change in Dimensions Calculators

Change in length of thin cylindrical shell given internal fluid pressure

Go Change in Length = ((Internal Pressure in thin shell*Diameter of Shell*Length Of Cylindrical Shell)/(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))*((1/2)-Poisson's Ratio)

Change in diameter of vessel given internal fluid pressure

Go Change in Diameter = ((Internal Pressure in thin shell*(Inner Diameter of Cylinder^2))/(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))*(1-(Poisson's Ratio/2))

Change in diameter of cylindrical shell given change in volume of cylindrical shell

Go Change in Diameter = ((Change in Volume/(pi/4))-(Change in Length*(Diameter of Shell^2)))/(2*Diameter of Shell*Length Of Cylindrical Shell)

Change in length of cylindrical shell given change in volume of cylindrical shell

Go Change in Length = ((Change in Volume/(pi/4))-(2*Diameter of Shell*Length Of Cylindrical Shell*Change in Diameter))/((Diameter of Shell^2))

Change in volume of thin cylindrical shell

Go Change in Volume = (pi/4)*((2*Diameter of Shell*Length Of Cylindrical Shell*Change in Diameter)+(Change in Length*(Diameter of Shell^2)))

Change in diameter in thin cylindrical strain given volumetric strain

Go Change in Diameter = (Volumetric Strain-(Change in Length/Length Of Cylindrical Shell))*Diameter of Shell/2

Change in length in thin cylindrical strain given volumetric strain

Go Change in Length = (Volumetric Strain-(2*Change in Diameter/Diameter of Shell))*Length Of Cylindrical Shell

Change in volume given circumferential strain and longitudinal strain

Go Change in Volume = Volume of Thin Cylindrical Shell*((2*Circumferential strain Thin Shell)+Longitudinal Strain)

Change in circumference of vessel due to pressure given circumferential strain

Go Change in circumference = Original Circumference*Circumferential strain Thin Shell

Change in diameter of thin cylindrical vessel (Circumferential strain)

Go Change in Diameter = Circumferential strain Thin Shell*Original Diameter

Change in length of thin cylindrical vessel given longitudinal strain

Go Change in Length = Longitudinal Strain*Initial Length

Change in volume of cylindrical shell given volumetric strain

Go Change in Volume = Volumetric Strain*Original Volume

Change in volume of thin cylindrical shell Formula

Change in Volume = (pi/4)*((2*Diameter of Shell*Length Of Cylindrical Shell*Change in Diameter)+(Change in Length*(Diameter of Shell^2)))
∆V = (pi/4)*((2*D*L_cylinder*∆d)+(ΔL*(D^2)))

What is the relation between lateral strain and longitudinal strain?

Lateral strain is defined as the ratio of decrease in the length of the bar in the perpendicular direction of applied load to that of the original length (gauge length). Poisson's ratio: The ratio of lateral strain to that of the longitudinal strain is termed as Poisson's ratio and it is represented by ϻ or 1/m.

How to Calculate Change in volume of thin cylindrical shell?

Change in volume of thin cylindrical shell calculator uses Change in Volume = (pi/4)*((2*Diameter of Shell*Length Of Cylindrical Shell*Change in Diameter)+(Change in Length*(Diameter of Shell^2))) to calculate the Change in Volume, The Change in volume of thin cylindrical shell formula is caused by a force exerted uniformly over the entire exposed surface of the solid. Change in Volume is denoted by ∆V symbol.

How to calculate Change in volume of thin cylindrical shell using this online calculator? To use this online calculator for Change in volume of thin cylindrical shell, enter Diameter of Shell (D), Length Of Cylindrical Shell (L_cylinder), Change in Diameter (∆d) & Change in Length (ΔL) and hit the calculate button. Here is how the Change in volume of thin cylindrical shell calculation can be explained with given input values -> 4.705006 = (pi/4)*((2*2.2*3*0.0505)+(1.1*(2.2^2))).

FAQ

What is Change in volume of thin cylindrical shell?

The Change in volume of thin cylindrical shell formula is caused by a force exerted uniformly over the entire exposed surface of the solid and is represented as ∆V = (pi/4)*((2*D*L_cylinder*∆d)+(ΔL*(D^2))) or Change in Volume = (pi/4)*((2*Diameter of Shell*Length Of Cylindrical Shell*Change in Diameter)+(Change in Length*(Diameter of Shell^2))). Diameter of Shell is the maximum width of cylinder in transverse direction, Length Of Cylindrical Shell is the measurement or extent of cylinder from end to end, The Change in Diameter is the difference between the initial and final diameter & Change in Length is after the application of force, change in the dimensions of the object.

How to calculate Change in volume of thin cylindrical shell?

The Change in volume of thin cylindrical shell formula is caused by a force exerted uniformly over the entire exposed surface of the solid is calculated using Change in Volume = (pi/4)*((2*Diameter of Shell*Length Of Cylindrical Shell*Change in Diameter)+(Change in Length*(Diameter of Shell^2))). To calculate Change in volume of thin cylindrical shell, you need Diameter of Shell (D), Length Of Cylindrical Shell (L_cylinder), Change in Diameter (∆d) & Change in Length (ΔL). With our tool, you need to enter the respective value for Diameter of Shell, Length Of Cylindrical Shell, Change in Diameter & Change in Length and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Change in Volume?

In this formula, Change in Volume uses Diameter of Shell, Length Of Cylindrical Shell, Change in Diameter & Change in Length. We can use 2 other way(s) to calculate the same, which is/are as follows -

Change in Volume = Volume of Thin Cylindrical Shell*((2*Circumferential strain Thin Shell)+Longitudinal Strain)
Change in Volume = Volumetric Strain*Original Volume

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