Radius of Inner Cylinder given Torque exerted on Inner Cylinder Calculator

✖Torque on Inner Cylinder is torque on cylinder from the external shaft.ⓘ Torque on Inner Cylinder [T]			+10% -10%
✖Height is the distance between the lowest and highest points of a person/ shape/ object standing upright.ⓘ Height [h]			+10% -10%
✖Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress [𝜏]			+10% -10%

✖Radius of Inner Cylinder is the distance from center to inner cylinder's surface, crucial for viscosity measurement.ⓘ Radius of Inner Cylinder given Torque exerted on Inner Cylinder [r₁]

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Radius of Inner Cylinder given Torque exerted on Inner Cylinder

Formula

`"r"_{"1"} = sqrt("T"/(2*pi*"h"*"𝜏"))`

Example

`"8.475137m"=sqrt("500kN*m"/(2*pi*"11.9m"*"93.1Pa"))`

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Radius of Inner Cylinder given Torque exerted on Inner Cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Inner Cylinder = sqrt(Torque on Inner Cylinder/(2*pi*Height*Shear Stress))
r₁ = sqrt(T/(2*pi*h*𝜏))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Radius of Inner Cylinder - (Measured in Meter) - Radius of Inner Cylinder is the distance from center to inner cylinder's surface, crucial for viscosity measurement.
Torque on Inner Cylinder - (Measured in Newton Meter) - Torque on Inner Cylinder is torque on cylinder from the external shaft.
Height - (Measured in Meter) - Height is the distance between the lowest and highest points of a person/ shape/ object standing upright.
Shear Stress - (Measured in Pascal) - Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

STEP 1: Convert Input(s) to Base Unit

Torque on Inner Cylinder: 500 Kilonewton Meter --> 500000 Newton Meter (Check conversion here)
Height: 11.9 Meter --> 11.9 Meter No Conversion Required
Shear Stress: 93.1 Pascal --> 93.1 Pascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r₁ = sqrt(T/(2*pi*h*𝜏)) --> sqrt(500000/(2*pi*11.9*93.1))

Evaluating ... ...

r₁ = 8.47513738112387

STEP 3: Convert Result to Output's Unit

8.47513738112387 Meter --> No Conversion Required

FINAL ANSWER

8.47513738112387 ≈ 8.475137 Meter <-- Radius of Inner Cylinder

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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National Institute of Technology (NIT), Warangal

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< 20 Coaxial Cylinder Viscometers Calculators

Torque exerted on Inner Cylinder given Dynamic Viscosity of Fluid

Go Torque on Inner Cylinder = Dynamic Viscosity/((15*(Radius of Outer Cylinder-Radius of Inner Cylinder))/(pi*pi*Radius of Inner Cylinder*Radius of Inner Cylinder*Radius of Outer Cylinder*Height*Angular Speed))

Speed of Outer Cylinder given Dynamic Viscosity of Fluid

Go Angular Speed = (15*Torque on Inner Cylinder*(Radius of Outer Cylinder-Radius of Inner Cylinder))/(pi*pi*Radius of Inner Cylinder*Radius of Inner Cylinder*Radius of Outer Cylinder*Height*Dynamic Viscosity)

Height of Cylinder given Dynamic Viscosity of Fluid

Go Height = (15*Torque on Inner Cylinder*(Radius of Outer Cylinder-Radius of Inner Cylinder))/(pi*pi*Radius of Inner Cylinder*Radius of Inner Cylinder*Radius of Outer Cylinder*Dynamic Viscosity*Angular Speed)

Dynamic Viscosity of Fluid Flow given Torque

Go Dynamic Viscosity = (15*Torque on Inner Cylinder*(Radius of Outer Cylinder-Radius of Inner Cylinder))/(pi*pi*Radius of Inner Cylinder*Radius of Inner Cylinder*Radius of Outer Cylinder*Height*Angular Speed)

Radius of Inner Cylinder given Velocity Gradient

Go Radius of Inner Cylinder = (30*Velocity Gradient*Radius of Outer Cylinder-pi*Radius of Outer Cylinder*Angular Speed)/(30*Velocity Gradient)

Radius of Inner Cylinder given Torque exerted on Outer Cylinder

Go Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4)

Speed of Outer Cylinder given Torque exerted on Outer Cylinder

Go Angular Speed = Torque on Outer Cylinder/(pi*pi*Dynamic Viscosity*(Radius of Inner Cylinder^4)/(60*Clearance))

Dynamic Viscosity given Torque exerted on Outer Cylinder

Go Dynamic Viscosity = Torque on Outer Cylinder/(pi*pi*Angular Speed*(Radius of Inner Cylinder^4)/(60*Clearance))

Clearance given Torque exerted on Outer Cylinder

Go Clearance = Dynamic Viscosity*pi*pi*Angular Speed*(Radius of Inner Cylinder^4)/(60*Torque on Outer Cylinder)

Torque exerted on Outer Cylinder

Go Torque on Outer Cylinder = Dynamic Viscosity*pi*pi*Angular Speed*(Radius of Inner Cylinder^4)/(60*Clearance)

Speed of Outer Cylinder given Velocity Gradient

Go Angular Speed = Velocity Gradient/((pi*Radius of Outer Cylinder)/(30*(Radius of Outer Cylinder-Radius of Inner Cylinder)))

Velocity Gradients

Go Velocity Gradient = pi*Radius of Outer Cylinder*Angular Speed/(30*(Radius of Outer Cylinder-Radius of Inner Cylinder))

Radius of Outer Cylinder given Velocity Gradient

Go Radius of Outer Cylinder = (30*Velocity Gradient*Radius of Inner Cylinder)/(30*Velocity Gradient-pi*Angular Speed)

Radius of Inner Cylinder given Torque exerted on Inner Cylinder

Go Radius of Inner Cylinder = sqrt(Torque on Inner Cylinder/(2*pi*Height*Shear Stress))

Shear Stress on Cylinder given Torque exerted on Inner Cylinder

Go Shear Stress = Torque on Inner Cylinder/(2*pi*((Radius of Inner Cylinder)^2)*Height)

Height of Cylinder given Torque exerted on Inner Cylinder

Go Height = Torque on Inner Cylinder/(2*pi*((Radius of Inner Cylinder)^2)*Shear Stress)

Speed of Outer Cylinder given Total Torque

Go Angular Speed = Total Torque/(Viscometer Constant*Dynamic Viscosity)

Dynamic Viscosity given Total Torque

Go Dynamic Viscosity = Total Torque/(Viscometer Constant*Angular Speed)

Torque exerted on Inner Cylinder

Go Total Torque = 2*((Radius of Inner Cylinder)^2)*Height*Shear Stress

Total Torque

Go Total Torque = Viscometer Constant*Dynamic Viscosity*Angular Speed

Radius of Inner Cylinder given Torque exerted on Inner Cylinder Formula

Radius of Inner Cylinder = sqrt(Torque on Inner Cylinder/(2*pi*Height*Shear Stress))
r₁ = sqrt(T/(2*pi*h*𝜏))

What is Torque?

Torque is the rotational equivalent of linear force. It is also referred to as the moment, moment of force, rotational force or turning effect, depending on the field of study. The concept originated with the studies by Archimedes of the usage of levers.

How to Calculate Radius of Inner Cylinder given Torque exerted on Inner Cylinder?

Radius of Inner Cylinder given Torque exerted on Inner Cylinder calculator uses Radius of Inner Cylinder = sqrt(Torque on Inner Cylinder/(2*pi*Height*Shear Stress)) to calculate the Radius of Inner Cylinder, The Radius of Inner Cylinder given Torque exerted on Inner Cylinder is defined as the width of rotating arm or section. Radius of Inner Cylinder is denoted by r₁ symbol.

How to calculate Radius of Inner Cylinder given Torque exerted on Inner Cylinder using this online calculator? To use this online calculator for Radius of Inner Cylinder given Torque exerted on Inner Cylinder, enter Torque on Inner Cylinder (T), Height (h) & Shear Stress (𝜏) and hit the calculate button. Here is how the Radius of Inner Cylinder given Torque exerted on Inner Cylinder calculation can be explained with given input values -> 8.475137 = sqrt(500000/(2*pi*11.9*93.1)).

FAQ

What is Radius of Inner Cylinder given Torque exerted on Inner Cylinder?

The Radius of Inner Cylinder given Torque exerted on Inner Cylinder is defined as the width of rotating arm or section and is represented as r₁ = sqrt(T/(2*pi*h*𝜏)) or Radius of Inner Cylinder = sqrt(Torque on Inner Cylinder/(2*pi*Height*Shear Stress)). Torque on Inner Cylinder is torque on cylinder from the external shaft, Height is the distance between the lowest and highest points of a person/ shape/ object standing upright & Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

How to calculate Radius of Inner Cylinder given Torque exerted on Inner Cylinder?

The Radius of Inner Cylinder given Torque exerted on Inner Cylinder is defined as the width of rotating arm or section is calculated using Radius of Inner Cylinder = sqrt(Torque on Inner Cylinder/(2*pi*Height*Shear Stress)). To calculate Radius of Inner Cylinder given Torque exerted on Inner Cylinder, you need Torque on Inner Cylinder (T), Height (h) & Shear Stress (𝜏). With our tool, you need to enter the respective value for Torque on Inner Cylinder, Height & Shear Stress 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 Radius of Inner Cylinder?

In this formula, Radius of Inner Cylinder uses Torque on Inner Cylinder, Height & Shear Stress. We can use 2 other way(s) to calculate the same, which is/are as follows -

Radius of Inner Cylinder = (30*Velocity Gradient*Radius of Outer Cylinder-pi*Radius of Outer Cylinder*Angular Speed)/(30*Velocity Gradient)
Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4)

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