Radius of Inner Cylinder given Torque exerted on Outer Cylinder Calculator

✖The Torque on Outer Cylinder refers to the measure of how much a force acting on a cylinder causing it to rotate.ⓘ Torque on Outer Cylinder [T_o]			+10% -10%
✖The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.ⓘ Dynamic Viscosity [μ]			+10% -10%
✖The Angular Speed refers to the rate of change of angular displacement.ⓘ Angular Speed [Ω]			+10% -10%
✖The Clearance refers to the gap or space between two surfaces adjacent to each other.ⓘ Clearance [C]			+10% -10%

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

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Radius of Inner Cylinder given Torque exerted on Outer Cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4)
r₁ = (T_o/(μ*pi*pi*Ω/(60*C)))^(1/4)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Radius of Inner Cylinder - (Measured in Meter) - The Radius of Inner Cylinder refers to the distance from center to inner cylinder's surface, crucial for viscosity measurement.
Torque on Outer Cylinder - (Measured in Newton Meter) - The Torque on Outer Cylinder refers to the measure of how much a force acting on a cylinder causing it to rotate.
Dynamic Viscosity - (Measured in Pascal Second) - The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.
Angular Speed - (Measured in Radian per Second) - The Angular Speed refers to the rate of change of angular displacement.
Clearance - (Measured in Meter) - The Clearance refers to the gap or space between two surfaces adjacent to each other.

STEP 1: Convert Input(s) to Base Unit

Torque on Outer Cylinder: 7000 Kilonewton Meter --> 7000000 Newton Meter (Check conversion here)
Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Angular Speed: 5 Revolution per Second --> 31.4159265342981 Radian per Second (Check conversion here)
Clearance: 15.5 Millimeter --> 0.0155 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r₁ = (T_o/(μ*pi*pi*Ω/(60*C)))^(1/4) --> (7000000/(1.02*pi*pi*31.4159265342981/(60*0.0155)))^(1/4)

Evaluating ... ...

r₁ = 11.9779583796012

STEP 3: Convert Result to Output's Unit

11.9779583796012 Meter --> No Conversion Required

FINAL ANSWER

11.9779583796012 ≈ 11.97796 Meter <-- Radius of Inner Cylinder

(Calculation completed in 00.020 seconds)

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< Coaxial Cylinder Viscometers Calculators

Radius of Inner Cylinder given Torque exerted on Inner Cylinder

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

Shear Stress on Cylinder given Torque exerted on Inner Cylinder

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

Height of Cylinder given Torque exerted on Inner Cylinder

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

Torque exerted on Inner Cylinder

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

Radius of Inner Cylinder given Torque exerted on Outer Cylinder Formula

LaTeX Go

Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4)
r₁ = (T_o/(μ*pi*pi*Ω/(60*C)))^(1/4)

What is Clearance?

The gap or lack of it between the hole and shaft is called the clearance. Clearance is determined by the size difference between the parts. Fits and tolerances are used to specify the size range of parts.

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

Radius of Inner Cylinder given Torque exerted on Outer Cylinder calculator uses Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4) to calculate the Radius of Inner Cylinder, The Radius of Inner Cylinder given Torque exerted on Outer Cylinder formula is defined as the radius of smaller cylinder. Radius of Inner Cylinder is denoted by r₁ symbol.

How to calculate Radius of Inner Cylinder given Torque exerted on Outer Cylinder using this online calculator? To use this online calculator for Radius of Inner Cylinder given Torque exerted on Outer Cylinder, enter Torque on Outer Cylinder (T_o), Dynamic Viscosity (μ), Angular Speed (Ω) & Clearance (C) and hit the calculate button. Here is how the Radius of Inner Cylinder given Torque exerted on Outer Cylinder calculation can be explained with given input values -> 11.97796 = (7000000/(1.02*pi*pi*31.4159265342981/(60*0.0155)))^(1/4).

FAQ

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

The Radius of Inner Cylinder given Torque exerted on Outer Cylinder formula is defined as the radius of smaller cylinder and is represented as r₁ = (T_o/(μ*pi*pi*Ω/(60*C)))^(1/4) or Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4). The Torque on Outer Cylinder refers to the measure of how much a force acting on a cylinder causing it to rotate, The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied, The Angular Speed refers to the rate of change of angular displacement & The Clearance refers to the gap or space between two surfaces adjacent to each other.

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

The Radius of Inner Cylinder given Torque exerted on Outer Cylinder formula is defined as the radius of smaller cylinder is calculated using Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4). To calculate Radius of Inner Cylinder given Torque exerted on Outer Cylinder, you need Torque on Outer Cylinder (T_o), Dynamic Viscosity (μ), Angular Speed (Ω) & Clearance (C). With our tool, you need to enter the respective value for Torque on Outer Cylinder, Dynamic Viscosity, Angular Speed & Clearance 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 Outer Cylinder, Dynamic Viscosity, Angular Speed & Clearance. We can use 2 other way(s) to calculate the same, which is/are as follows -

Radius of Inner Cylinder = sqrt(Torque on Inner Cylinder/(2*pi*Height of Cylinder*Shear Stress))
Radius of Inner Cylinder = (30*Velocity Gradient*Radius of Outer Cylinder-pi*Radius of Outer Cylinder*Angular Speed)/(30*Velocity Gradient)

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