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)
di = ((do^4)-((Zp*16*do)/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
di = ((do^4)-((Zp*16*do)/pi))^(1/4) --> ((0.7^4)-((0.0045*16*0.7)/pi))^(1/4)
Evaluating ... ...
di = 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 00.004 seconds)

Credits

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National Institute Of Technology (NIT), Hamirpur
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9 Polar Modulus Calculators

Inner diameter of Hollow Shaft using Polar Modulus
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
Go Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)
Polar Moment of Inertia of Hollow Shaft
Go Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)
Polar Moment of Inertia using Polar Modulus
Go Polar Moment of Inertia = Radius of Shaft*Polar Modulus
Radius of Shaft using Polar Modulus
Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus
Polar Modulus
Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft
Polar Moment of Inertia of Solid Shaft
Go Polar Moment of Inertia = (pi*Dia of Shaft^4)/32
Diameter of Solid Shaft with known Polar Modulus
Go Dia of Shaft = ((16*Polar Modulus)/pi)^(1/3)
Polar Modulus of Solid Shaft
Go Polar Modulus = (pi*Dia of Shaft^3)/16

9 Polar Modulus Calculators

Inner diameter of Hollow Shaft using Polar Modulus
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
Go Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)
Polar Moment of Inertia given Torsional Section Modulus
Go Polar Moment of Inertia = Polar Modulus*Radius of Shaft
Polar Moment of Inertia using Polar Modulus
Go Polar Moment of Inertia = Radius of Shaft*Polar Modulus
Polar Modulus
Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft
Polar Moment of Inertia of Solid Shaft
Go Polar Moment of Inertia = (pi*Dia of Shaft^4)/32
Diameter of Solid Shaft with known Polar Modulus
Go Dia of Shaft = ((16*Polar Modulus)/pi)^(1/3)
Polar Modulus using Maximum Twisting Moment
Go Polar Modulus = (Torque/Maximum Shear Stress)
Polar Modulus of Solid Shaft
Go Polar Modulus = (pi*Dia of Shaft^3)/16

Inner diameter of Hollow Shaft using Polar Modulus Formula

Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4)
di = ((do^4)-((Zp*16*do)/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 di 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 (do) & Polar Modulus (Zp) 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 di = ((do^4)-((Zp*16*do)/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 (do) & Polar Modulus (Zp). 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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