Radius of Inner Cylinder given Torque exerted on Outer Cylinder Calculator

✖Torque on Outer Cylinder is torque on cylinder from the external shaft.ⓘ Torque on Outer Cylinder [T_o]			+10% -10%
✖The 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%
✖Angular Speed is defined as the rate of change of angular displacement.ⓘ Angular Speed [Ω]			+10% -10%
✖Clearance is the gap or space between two surfaces adjacent to each other.ⓘ Clearance [C]			+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 Outer Cylinder [r₁]

⎘ Copy

👎

Formula

✖

Radius of Inner Cylinder given Torque exerted on Outer Cylinder

Formula

`"r"_{"1"} = ("T"_{"o"}/("μ"_{"viscosity"}*pi*pi*"Ω"/(60*"C")))^(1/4)`

Example

`"11.97796m"=("7000kN*m"/("10.2P"*pi*pi*"5rev/s"/(60*"15.5mm")))^(1/4)`

Calculator

LaTeX

Reset

👍

Download Laminar Flow Formula PDF PDF Image

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_viscosity*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) - Radius of Inner Cylinder is the distance from center to inner cylinder's surface, crucial for viscosity measurement.
Torque on Outer Cylinder - (Measured in Newton Meter) - Torque on Outer Cylinder is torque on cylinder from the external shaft.
Dynamic Viscosity - (Measured in Pascal Second) - The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.
Angular Speed - (Measured in Radian per Second) - Angular Speed is defined as the rate of change of angular displacement.
Clearance - (Measured in Meter) - Clearance is 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_viscosity*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 00.004 seconds)

You are here -

Home » Engineering » Civil » Hydraulics and Waterworks » Laminar Flow » Measurement of Viscosity Viscometers » Coaxial Cylinder Viscometers » Radius of Inner Cylinder given Torque exerted on Outer Cylinder

Credits

Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

Rithik Agrawal has created this Calculator and 1300+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Calculator and 2600+ more calculators!

< 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 Outer Cylinder Formula

Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4)
r₁ = (T_o/(μ_viscosity*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 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_viscosity), 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 is defined as the radius of smaller cylinder and is represented as r₁ = (T_o/(μ_viscosity*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). Torque on Outer Cylinder is torque on cylinder from the external shaft, The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Angular Speed is defined as the rate of change of angular displacement & Clearance is 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 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_viscosity), 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*Shear Stress))
Radius of Inner Cylinder = (30*Velocity Gradient*Radius of Outer Cylinder-pi*Radius of Outer Cylinder*Angular Speed)/(30*Velocity Gradient)

Home

FREE PDFs

🔍 Search