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Inner diameter of Hollow Shaft using Polar Modulus Formula

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The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft. Check FAQs

d i = {(({d o}^{4}) - (\frac{Z p \cdot 16 \cdot d o}{π}))}^{\frac{1}{4}}

d_i - Inner Dia of Shaft?d_o - Outer Diameter of Shaft?Z_p - Polar Modulus?π - Archimedes' constant?

Inner diameter of Hollow Shaft using Polar Modulus Example

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Here is how the Inner diameter of Hollow Shaft using Polar Modulus equation looks like with Values.

Here is how the Inner diameter of Hollow Shaft using Polar Modulus equation looks like with Units.

Here is how the Inner diameter of Hollow Shaft using Polar Modulus equation looks like.

0.688 = {((700^{4}) - (\frac{0.0045 \cdot 16 \cdot 700}{3.1416}))}^{\frac{1}{4}}

0.688m = {(({700mm}^{4}) - (\frac{0.0045m³ \cdot 16 \cdot 700mm}{3.1416}))}^{\frac{1}{4}}

0.688 = {((700^{4}) - (\frac{0.0045 \cdot 16 \cdot 700}{3.1416}))}^{\frac{1}{4}}

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Inner diameter of Hollow Shaft using Polar Modulus Solution

Follow our step by step solution on how to calculate Inner diameter of Hollow Shaft using Polar Modulus?

FIRST Step Consider the formula

d i = {(({d o}^{4}) - (\frac{Z p \cdot 16 \cdot d o}{π}))}^{\frac{1}{4}}

Next Step Substitute values of Variables

∴

d i = {(({700mm}^{4}) - (\frac{0.0045m³ \cdot 16 \cdot 700mm}{π}))}^{\frac{1}{4}}

Next Step Substitute values of Constants

∴

d i = {(({700mm}^{4}) - (\frac{0.0045m³ \cdot 16 \cdot 700mm}{3.1416}))}^{\frac{1}{4}}

Next Step Convert Units

∴

d i = {(({0.7m}^{4}) - (\frac{0.0045m³ \cdot 16 \cdot 0.7m}{3.1416}))}^{\frac{1}{4}}

Next Step Prepare to Evaluate

∴

d i = {(({0.7}^{4}) - (\frac{0.0045 \cdot 16 \cdot 0.7}{3.1416}))}^{\frac{1}{4}}

Next Step Evaluate

∴

d i = 0.688002026180089m

LAST Step Rounding Answer

∴

d i = 0.688m

Inner diameter of Hollow Shaft using Polar Modulus Formula Elements

Variables

Constants

Inner Dia of Shaft

The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft.

Symbol: d_i

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Inner Dia of Shaft

Outer Diameter of Shaft

Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft.

Symbol: d_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Diameter of Shaft

Polar Modulus

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.

Symbol: Z_p

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Polar Modulus

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

Other formulas in Polar Modulus category

Go Diameter of Solid Shaft with known Polar Modulus

d = {(\frac{16 \cdot Z p}{π})}^{\frac{1}{3}}

Go Polar Modulus

Z p = \frac{J}{R}

Go Polar Modulus of Hollow Shaft

Z p = \frac{π \cdot (({d o}^{4}) - ({d i}^{4}))}{16 \cdot d o}

Go Polar Modulus of Solid Shaft

Z p = \frac{π \cdot d^{3}}{16}

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

Inner diameter of Hollow Shaft using Polar Modulus evaluator uses Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4) to evaluate 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 evaluate Inner diameter of Hollow Shaft using Polar Modulus using this online evaluator? To use this online evaluator 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.

FAQs on Inner diameter of Hollow Shaft using Polar Modulus

What is the formula to find Inner diameter of Hollow Shaft using Polar Modulus?

The formula of Inner diameter of Hollow Shaft using Polar Modulus is expressed as Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4). Here is an example- 0.688002 = ((0.7^4)-((0.0045*16*0.7)/pi))^(1/4).

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

With Outer Diameter of Shaft (d_o) & Polar Modulus (Z_p) we can find Inner diameter of Hollow Shaft using Polar Modulus using the formula - Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4). This formula also uses Archimedes' constant .

Can the Inner diameter of Hollow Shaft using Polar Modulus be negative?

Yes, the Inner diameter of Hollow Shaft using Polar Modulus, measured in Length can be negative.

Which unit is used to measure Inner diameter of Hollow Shaft using Polar Modulus?

Inner diameter of Hollow Shaft using Polar Modulus is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Inner diameter of Hollow Shaft using Polar Modulus can be measured.

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