Speed of Outer Cylinder given Dynamic Viscosity of Fluid Calculator

✖The Torque on Inner Cylinder refers to the measure of how much a force acting on a cylinder causing it to rotate.ⓘ Torque on Inner Cylinder [T]			+10% -10%
✖The Radius of Outer Cylinder refers to the spacing for measuring fluid viscosity based on inner cylinder rotation.ⓘ Radius of Outer Cylinder [r₂]			+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 Height of Cylinder refers to the distance between the lowest and highest points of a person/ shape/ object standing upright.ⓘ Height of Cylinder [h]			+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.ⓘ Speed of Outer Cylinder given Dynamic Viscosity of Fluid [Ω]

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Speed of Outer Cylinder given Dynamic Viscosity of Fluid Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
Ω = (15*T*(r₂-r₁))/(pi*pi*r₁*r₁*r₂*h*μ)
This formula uses 1 Constants, 6 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 Inner Cylinder - (Measured in Newton Meter) - The Torque on Inner Cylinder refers to the measure of how much a force acting on a cylinder causing it to rotate.
Radius of Outer Cylinder - (Measured in Meter) - The Radius of Outer Cylinder refers to the spacing for measuring fluid viscosity based on inner cylinder rotation.
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.
Height of Cylinder - (Measured in Meter) - The Height of Cylinder refers to the distance between the lowest and highest points of a person/ shape/ object standing upright.
Dynamic Viscosity - (Measured in Pascal Second) - The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.

STEP 1: Convert Input(s) to Base Unit

Torque on Inner Cylinder: 500 Kilonewton Meter --> 500000 Newton Meter (Check conversion here)
Radius of Outer Cylinder: 13 Meter --> 13 Meter No Conversion Required
Radius of Inner Cylinder: 12 Meter --> 12 Meter No Conversion Required
Height of Cylinder: 11.9 Meter --> 11.9 Meter No Conversion Required
Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Ω = (15*T*(r₂-r₁))/(pi*pi*r₁*r₁*r₂*h*μ) --> (15*500000*(13-12))/(pi*pi*12*12*13*11.9*1.02)

Evaluating ... ...

Ω = 33.4432550120522

STEP 3: Convert Result to Output's Unit

33.4432550120522 Radian per Second -->5.32265934852195 Revolution per Second (Check conversion here)

FINAL ANSWER

5.32265934852195 ≈ 5.322659 Revolution per Second <-- Angular Speed

(Calculation completed in 00.007 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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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 Dynamic Viscosity of Fluid Formula

LaTeX Go

What is Dynamic Viscosity?

The dynamic viscosity η (η = "eta") is a measure of the viscosity of a fluid (fluid: liquid, flowing substance). The higher the viscosity, the thicker (less liquid) the fluid; the lower the viscosity, the thinner (more liquid) it is.

How to Calculate Speed of Outer Cylinder given Dynamic Viscosity of Fluid?

Speed of Outer Cylinder given Dynamic Viscosity of Fluid calculator uses 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) to calculate the Angular Speed, The Speed of Outer Cylinder given Dynamic Viscosity of Fluid formula is defined as speed in revolutions per minutes for cylinder. Angular Speed is denoted by Ω symbol.

How to calculate Speed of Outer Cylinder given Dynamic Viscosity of Fluid using this online calculator? To use this online calculator for Speed of Outer Cylinder given Dynamic Viscosity of Fluid, enter Torque on Inner Cylinder (T), Radius of Outer Cylinder (r₂), Radius of Inner Cylinder (r₁), Height of Cylinder (h) & Dynamic Viscosity (μ) and hit the calculate button. Here is how the Speed of Outer Cylinder given Dynamic Viscosity of Fluid calculation can be explained with given input values -> 0.847128 = (15*500000*(13-12))/(pi*pi*12*12*13*11.9*1.02).

FAQ

What is Speed of Outer Cylinder given Dynamic Viscosity of Fluid?

The Speed of Outer Cylinder given Dynamic Viscosity of Fluid formula is defined as speed in revolutions per minutes for cylinder and is represented as Ω = (15*T*(r₂-r₁))/(pi*pi*r₁*r₁*r₂*h*μ) or 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). The Torque on Inner Cylinder refers to the measure of how much a force acting on a cylinder causing it to rotate, The Radius of Outer Cylinder refers to the spacing for measuring fluid viscosity based on inner cylinder rotation, The Radius of Inner Cylinder refers to the distance from center to inner cylinder's surface, crucial for viscosity measurement, The Height of Cylinder refers to the distance between the lowest and highest points of a person/ shape/ object standing upright & The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.

How to calculate Speed of Outer Cylinder given Dynamic Viscosity of Fluid?

The Speed of Outer Cylinder given Dynamic Viscosity of Fluid formula is defined as speed in revolutions per minutes for cylinder is calculated using 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). To calculate Speed of Outer Cylinder given Dynamic Viscosity of Fluid, you need Torque on Inner Cylinder (T), Radius of Outer Cylinder (r₂), Radius of Inner Cylinder (r₁), Height of Cylinder (h) & Dynamic Viscosity (μ). With our tool, you need to enter the respective value for Torque on Inner Cylinder, Radius of Outer Cylinder, Radius of Inner Cylinder, Height of Cylinder & Dynamic Viscosity 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 Inner Cylinder, Radius of Outer Cylinder, Radius of Inner Cylinder, Height of Cylinder & Dynamic Viscosity. 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 = Torque on Outer Cylinder/(pi*pi*Dynamic Viscosity*(Radius of Inner Cylinder^4)/(60*Clearance))
Angular Speed = Total Torque/(Viscometer Constant*Dynamic Viscosity)

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