Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder Calculator

✖Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.ⓘ Dynamic Viscosity [μ_viscosity]			+10% -10%
✖The Radius of Inner Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder.ⓘ Radius of Inner Cylinder [R]			+10% -10%
✖Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.ⓘ Angular Velocity [ω]			+10% -10%
✖Length of cylinder is the vertical height of the cylinder.ⓘ Length of Cylinder [L_Cylinder]			+10% -10%
✖Thickness of Fluid Layer is defined as the thickness of the layer of fluid of which viscosity needs to be calculated.ⓘ Thickness of Fluid Layer [ℓ_fluid]			+10% -10%

✖Torque is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.ⓘ Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder [T]

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Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

Torque = (Dynamic Viscosity*2*pi*(Radius of Inner Cylinder^3)*Angular Velocity*Length of Cylinder)/(Thickness of Fluid Layer)
T = (μ_viscosity*2*pi*(R^3)*ω*L_Cylinder)/(ℓ_fluid)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Torque - (Measured in Newton Meter) - Torque is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.
Dynamic Viscosity - (Measured in Pascal Second) - Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.
Radius of Inner Cylinder - (Measured in Meter) - The Radius of Inner Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder.
Angular Velocity - (Measured in Radian per Second) - Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
Length of Cylinder - (Measured in Meter) - Length of cylinder is the vertical height of the cylinder.
Thickness of Fluid Layer - (Measured in Meter) - Thickness of Fluid Layer is defined as the thickness of the layer of fluid of which viscosity needs to be calculated.

STEP 1: Convert Input(s) to Base Unit

Dynamic Viscosity: 1.02 Pascal Second --> 1.02 Pascal Second No Conversion Required
Radius of Inner Cylinder: 0.06 Meter --> 0.06 Meter No Conversion Required
Angular Velocity: 33.3 Radian per Second --> 33.3 Radian per Second No Conversion Required
Length of Cylinder: 0.4 Meter --> 0.4 Meter No Conversion Required
Thickness of Fluid Layer: 0.0015 Meter --> 0.0015 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = (μ_viscosity*2*pi*(R^3)*ω*L_Cylinder)/(ℓ_fluid) --> (1.02*2*pi*(0.06^3)*33.3*0.4)/(0.0015)

Evaluating ... ...

T = 12.2926851154749

STEP 3: Convert Result to Output's Unit

12.2926851154749 Newton Meter --> No Conversion Required

FINAL ANSWER

12.2926851154749 ≈ 12.29269 Newton Meter <-- Torque

(Calculation completed in 00.020 seconds)

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Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder Formula

LaTeX Go

Torque = (Dynamic Viscosity*2*pi*(Radius of Inner Cylinder^3)*Angular Velocity*Length of Cylinder)/(Thickness of Fluid Layer)
T = (μ_viscosity*2*pi*(R^3)*ω*L_Cylinder)/(ℓ_fluid)

What is Fluid Mechanics?

Fluid dynamics is “the branch of applied science that is concerned with the movement of liquids and gases”. It involves a wide range of applications such as calculating force & moments, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space, and modelling fission weapon detonation.

What is Viscosity?

Viscosity is a measure of a fluid’s resistance to flow. The SI unit of viscosity is poiseiulle (PI). Its other units are newton-second per square metre (N s m-2) or pascal-second (Pa s.). The viscosity of liquids decreases rapidly with an increase in temperature, and the viscosity of gases increases with an increase in temperature. Thus, upon heating, liquids flow more easily, whereas gases flow more slowly. Also, viscosity does not change as the amount of matter changes, therefore it is an intensive property.

How to Calculate Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder?

Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder calculator uses Torque = (Dynamic Viscosity*2*pi*(Radius of Inner Cylinder^3)*Angular Velocity*Length of Cylinder)/(Thickness of Fluid Layer) to calculate the Torque, The Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder formula is defined as the function of dynamic viscosity, radius of inner cylinder, angular velocity, length of cylinder and thickness of fluid layer. In one-dimensional shear flow of Newtonian fluids, shear stress can be expressed by the linear relationship where the constant of proportionality 𝜇 is called the coefficient of viscosity or the dynamic (or absolute) viscosity of the fluid. The rate of deformation (velocity gradient) of a Newtonian fluid is proportional to shear stress, and the constant of proportionality is the viscosity. Torque is denoted by T symbol.

How to calculate Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder using this online calculator? To use this online calculator for Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder, enter Dynamic Viscosity (μ_viscosity), Radius of Inner Cylinder (R), Angular Velocity (ω), Length of Cylinder (L_Cylinder) & Thickness of Fluid Layer (ℓ_fluid) and hit the calculate button. Here is how the Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder calculation can be explained with given input values -> 12.29269 = (1.02*2*pi*(0.06^3)*33.3*0.4)/(0.0015).

FAQ

What is Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder?

The Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder formula is defined as the function of dynamic viscosity, radius of inner cylinder, angular velocity, length of cylinder and thickness of fluid layer. In one-dimensional shear flow of Newtonian fluids, shear stress can be expressed by the linear relationship where the constant of proportionality 𝜇 is called the coefficient of viscosity or the dynamic (or absolute) viscosity of the fluid. The rate of deformation (velocity gradient) of a Newtonian fluid is proportional to shear stress, and the constant of proportionality is the viscosity and is represented as T = (μ_viscosity*2*pi*(R^3)*ω*L_Cylinder)/(ℓ_fluid) or Torque = (Dynamic Viscosity*2*pi*(Radius of Inner Cylinder^3)*Angular Velocity*Length of Cylinder)/(Thickness of Fluid Layer). Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, The Radius of Inner Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder, Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time, Length of cylinder is the vertical height of the cylinder & Thickness of Fluid Layer is defined as the thickness of the layer of fluid of which viscosity needs to be calculated.

How to calculate Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder?

The Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder formula is defined as the function of dynamic viscosity, radius of inner cylinder, angular velocity, length of cylinder and thickness of fluid layer. In one-dimensional shear flow of Newtonian fluids, shear stress can be expressed by the linear relationship where the constant of proportionality 𝜇 is called the coefficient of viscosity or the dynamic (or absolute) viscosity of the fluid. The rate of deformation (velocity gradient) of a Newtonian fluid is proportional to shear stress, and the constant of proportionality is the viscosity is calculated using Torque = (Dynamic Viscosity*2*pi*(Radius of Inner Cylinder^3)*Angular Velocity*Length of Cylinder)/(Thickness of Fluid Layer). To calculate Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder, you need Dynamic Viscosity (μ_viscosity), Radius of Inner Cylinder (R), Angular Velocity (ω), Length of Cylinder (L_Cylinder) & Thickness of Fluid Layer (ℓ_fluid). With our tool, you need to enter the respective value for Dynamic Viscosity, Radius of Inner Cylinder, Angular Velocity, Length of Cylinder & Thickness of Fluid Layer 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 Torque?

In this formula, Torque uses Dynamic Viscosity, Radius of Inner Cylinder, Angular Velocity, Length of Cylinder & Thickness of Fluid Layer. We can use 1 other way(s) to calculate the same, which is/are as follows -

Torque = (Dynamic Viscosity*4*(pi^2)*(Radius of Inner Cylinder^3)*Revolutions per Second*Length of Cylinder)/(Thickness of Fluid Layer)

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