Inner diameter of Hollow Shaft using Polar Modulus Calculator

✖Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Shaft [d_o]			+10% -10%
✖The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp.ⓘ Polar Modulus [Z_p]			+10% -10%

✖The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft.ⓘ Inner diameter of Hollow Shaft using Polar Modulus [d_i]

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Inner diameter of Hollow Shaft using Polar Modulus Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4)
d_i = ((d_o^4)-((Z_p*16*d_o)/pi))^(1/4)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Inner Dia of Shaft - (Measured in Meter) - The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft.
Outer Diameter of Shaft - (Measured in Meter) - Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft.
Polar Modulus - (Measured in Cubic Meter) - The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp.

STEP 1: Convert Input(s) to Base Unit

Outer Diameter of Shaft: 700 Millimeter --> 0.7 Meter (Check conversion here)
Polar Modulus: 0.0045 Cubic Meter --> 0.0045 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_i = ((d_o^4)-((Z_p*16*d_o)/pi))^(1/4) --> ((0.7^4)-((0.0045*16*0.7)/pi))^(1/4)

Evaluating ... ...

d_i = 0.688002026180089

STEP 3: Convert Result to Output's Unit

0.688002026180089 Meter --> No Conversion Required

FINAL ANSWER

0.688002026180089 ≈ 0.688002 Meter <-- Inner Dia of Shaft

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Mechanical » Polar Modulus » Inner diameter of Hollow Shaft using Polar Modulus

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National Institute Of Technology (NIT), Hamirpur

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< Polar Modulus Calculators

Polar Moment of Inertia using Polar Modulus

LaTeX Go Polar Moment of Inertia = Radius of Shaft*Polar Modulus

Radius of Shaft using Polar Modulus

LaTeX Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus

Polar Modulus

LaTeX Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft

Polar Moment of Inertia of Solid Shaft

LaTeX Go Polar Moment of Inertia = (pi*Dia of Shaft^4)/32

< Polar Modulus Calculators

Inner diameter of Hollow Shaft using Polar Modulus

LaTeX Go Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4)

Polar Modulus of Hollow Shaft

LaTeX Go Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)

Polar Modulus

LaTeX Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft

Diameter of Solid Shaft with known Polar Modulus

LaTeX Go Dia of Shaft = ((16*Polar Modulus)/pi)^(1/3)

Inner diameter of Hollow Shaft using Polar Modulus Formula

LaTeX Go

Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4)
d_i = ((d_o^4)-((Z_p*16*d_o)/pi))^(1/4)

What is difference between Moment of Inertia and Polar Moment of Inertia?

The main difference between the moment of inertia and the polar moment of inertia is that the moment of inertia measures how an object resists angular acceleration, whereas the polar moment of inertia measures how an object resists torsion.

How to Calculate Inner diameter of Hollow Shaft using Polar Modulus?

Inner diameter of Hollow Shaft using Polar Modulus calculator uses Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4) to calculate the Inner Dia of Shaft, The Inner diameter of Hollow Shaft using Polar Modulus formula is defined as a chord that runs through the center point of the circle. Inner Dia of Shaft is denoted by d_i symbol.

How to calculate Inner diameter of Hollow Shaft using Polar Modulus using this online calculator? To use this online calculator for Inner diameter of Hollow Shaft using Polar Modulus, enter Outer Diameter of Shaft (d_o) & Polar Modulus (Z_p) and hit the calculate button. Here is how the Inner diameter of Hollow Shaft using Polar Modulus calculation can be explained with given input values -> 0.688002 = ((0.7^4)-((0.0045*16*0.7)/pi))^(1/4).

FAQ

What is Inner diameter of Hollow Shaft using Polar Modulus?

The Inner diameter of Hollow Shaft using Polar Modulus formula is defined as a chord that runs through the center point of the circle and is represented as d_i = ((d_o^4)-((Z_p*16*d_o)/pi))^(1/4) or Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4). Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft & The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp.

How to calculate Inner diameter of Hollow Shaft using Polar Modulus?

The Inner diameter of Hollow Shaft using Polar Modulus formula is defined as a chord that runs through the center point of the circle is calculated using Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4). To calculate Inner diameter of Hollow Shaft using Polar Modulus, you need Outer Diameter of Shaft (d_o) & Polar Modulus (Z_p). With our tool, you need to enter the respective value for Outer Diameter of Shaft & Polar Modulus 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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