Speed of Outer 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 Radius of Inner Cylinder refers to the distance from center to inner cylinder's surface, crucial for viscosity measurement.ⓘ Radius of Inner Cylinder [r₁]			+10% -10%
✖The Clearance refers to the gap or space between two surfaces adjacent to each other.ⓘ Clearance [C]			+10% -10%

✖The Angular Speed refers to the rate of change of angular displacement.ⓘ Speed of Outer Cylinder given Torque exerted on Outer Cylinder [Ω]

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Speed of Outer Cylinder given Torque exerted on Outer Cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Angular Speed - (Measured in Radian per Second) - The Angular Speed refers to the rate of change of angular displacement.
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.
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.
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)
Radius of Inner Cylinder: 12 Meter --> 12 Meter No Conversion Required
Clearance: 15.5 Millimeter --> 0.0155 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Ω = T_o/(pi*pi*μ*(r₁^4)/(60*C)) --> 7000000/(pi*pi*1.02*(12^4)/(60*0.0155))

Evaluating ... ...

Ω = 31.185742400808

STEP 3: Convert Result to Output's Unit

31.185742400808 Radian per Second -->4.96336505733186 Revolution per Second (Check conversion here)

FINAL ANSWER

4.96336505733186 ≈ 4.963365 Revolution per Second <-- Angular Speed

(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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< 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

Speed of Outer Cylinder given Torque exerted on Outer Cylinder Formula

LaTeX Go

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

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 Speed of Outer Cylinder given Torque exerted on Outer Cylinder?

Speed of Outer Cylinder given Torque exerted on Outer Cylinder calculator uses Angular Speed = Torque on Outer Cylinder/(pi*pi*Dynamic Viscosity*(Radius of Inner Cylinder^4)/(60*Clearance)) to calculate the Angular Speed, The Speed of Outer Cylinder given Torque exerted on Outer Cylinder formula is defined as the torque applied to it, following the relationship between torque, rotational inertia, and angular acceleration. Angular Speed is denoted by Ω symbol.

How to calculate Speed of Outer Cylinder given Torque exerted on Outer Cylinder using this online calculator? To use this online calculator for Speed of Outer Cylinder given Torque exerted on Outer Cylinder, enter Torque on Outer Cylinder (T_o), Dynamic Viscosity (μ), Radius of Inner Cylinder (r₁) & Clearance (C) and hit the calculate button. Here is how the Speed of Outer Cylinder given Torque exerted on Outer Cylinder calculation can be explained with given input values -> 0.789944 = 7000000/(pi*pi*1.02*(12^4)/(60*0.0155)).

FAQ

What is Speed of Outer Cylinder given Torque exerted on Outer Cylinder?

The Speed of Outer Cylinder given Torque exerted on Outer Cylinder formula is defined as the torque applied to it, following the relationship between torque, rotational inertia, and angular acceleration and is represented as Ω = T_o/(pi*pi*μ*(r₁^4)/(60*C)) or Angular Speed = Torque on Outer Cylinder/(pi*pi*Dynamic Viscosity*(Radius of Inner Cylinder^4)/(60*Clearance)). 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 Radius of Inner Cylinder refers to the distance from center to inner cylinder's surface, crucial for viscosity measurement & The Clearance refers to the gap or space between two surfaces adjacent to each other.

How to calculate Speed of Outer Cylinder given Torque exerted on Outer Cylinder?

The Speed of Outer Cylinder given Torque exerted on Outer Cylinder formula is defined as the torque applied to it, following the relationship between torque, rotational inertia, and angular acceleration is calculated using Angular Speed = Torque on Outer Cylinder/(pi*pi*Dynamic Viscosity*(Radius of Inner Cylinder^4)/(60*Clearance)). To calculate Speed of Outer Cylinder given Torque exerted on Outer Cylinder, you need Torque on Outer Cylinder (T_o), Dynamic Viscosity (μ), Radius of Inner Cylinder (r₁) & Clearance (C). With our tool, you need to enter the respective value for Torque on Outer Cylinder, Dynamic Viscosity, Radius of Inner Cylinder & 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 Angular Speed?

In this formula, Angular Speed uses Torque on Outer Cylinder, Dynamic Viscosity, Radius of Inner Cylinder & Clearance. We can use 3 other way(s) to calculate the same, which is/are as follows -

Angular Speed = Velocity Gradient/((pi*Radius of Outer Cylinder)/(30*(Radius of Outer Cylinder-Radius of Inner Cylinder)))
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 of Cylinder*Dynamic Viscosity)
Angular Speed = Total Torque/(Viscometer Constant*Dynamic Viscosity)

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