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Radius of Inner Cylinder given Torque exerted on Outer Cylinder Formula

GoRadius of Inner Cylinder given Torque exerted on Inner Cylinder Formula

GoRadius of Inner Cylinder given Velocity Gradient Formula

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The Radius of Inner Cylinder refers to the distance from center to inner cylinder's surface, crucial for viscosity measurement. Check FAQs

r 1 = {(\frac{T o}{μ \cdot π \cdot π \cdot \frac{Ω}{60 \cdot C}})}^{\frac{1}{4}}

r₁ - Radius of Inner Cylinder?T_o - Torque on Outer Cylinder?μ - Dynamic Viscosity?Ω - Angular Speed?C - Clearance?π - Archimedes' constant?

Radius of Inner Cylinder given Torque exerted on Outer Cylinder Example

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Here is how the Radius of Inner Cylinder given Torque exerted on Outer Cylinder equation looks like with Values.

Here is how the Radius of Inner Cylinder given Torque exerted on Outer Cylinder equation looks like with Units.

Here is how the Radius of Inner Cylinder given Torque exerted on Outer Cylinder equation looks like.

11.978 = {(\frac{7000}{10.2 \cdot 3.1416 \cdot 3.1416 \cdot \frac{5}{60 \cdot 15.5}})}^{\frac{1}{4}}

11.978m = {(\frac{7000kN*m}{10.2P \cdot 3.1416 \cdot 3.1416 \cdot \frac{5rev/s}{60 \cdot 15.5mm}})}^{\frac{1}{4}}

11.978 = {(\frac{7000}{10.2 \cdot 3.1416 \cdot 3.1416 \cdot \frac{5}{60 \cdot 15.5}})}^{\frac{1}{4}}

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Radius of Inner Cylinder given Torque exerted on Outer Cylinder Solution

Follow our step by step solution on how to calculate Radius of Inner Cylinder given Torque exerted on Outer Cylinder?

FIRST Step Consider the formula

r 1 = {(\frac{T o}{μ \cdot π \cdot π \cdot \frac{Ω}{60 \cdot C}})}^{\frac{1}{4}}

Next Step Substitute values of Variables

∴

r 1 = {(\frac{7000kN*m}{10.2P \cdot π \cdot π \cdot \frac{5rev/s}{60 \cdot 15.5mm}})}^{\frac{1}{4}}

Next Step Substitute values of Constants

∴

r 1 = {(\frac{7000kN*m}{10.2P \cdot 3.1416 \cdot 3.1416 \cdot \frac{5rev/s}{60 \cdot 15.5mm}})}^{\frac{1}{4}}

Next Step Convert Units

∴

r 1 = {(\frac{7E+6N*m}{1.02Pa*s \cdot 3.1416 \cdot 3.1416 \cdot \frac{31.4159rad/s}{60 \cdot 0.0155m}})}^{\frac{1}{4}}

Next Step Prepare to Evaluate

∴

r 1 = {(\frac{7E+6}{1.02 \cdot 3.1416 \cdot 3.1416 \cdot \frac{31.4159}{60 \cdot 0.0155}})}^{\frac{1}{4}}

Next Step Evaluate

∴

r 1 = 11.9779583796012m

LAST Step Rounding Answer

∴

r 1 = 11.978m

Radius of Inner Cylinder given Torque exerted on Outer Cylinder Formula Elements

Variables

Constants

Radius of Inner Cylinder

The Radius of Inner Cylinder refers to the distance from center to inner cylinder's surface, crucial for viscosity measurement.

Symbol: r₁

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Inner Cylinder

Torque on Outer Cylinder

The Torque on Outer Cylinder refers to the measure of how much a force acting on a cylinder causing it to rotate.

Symbol: T_o

Measurement: TorqueUnit: kN*m

Note: Value should be greater than 0.

Formulas to find Torque on Outer Cylinder

Dynamic Viscosity

The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.

Symbol: μ

Measurement: Dynamic ViscosityUnit: P

Note: Value should be greater than 0.

Formulas to find Dynamic Viscosity

Angular Speed

The Angular Speed refers to the rate of change of angular displacement.

Symbol: Ω

Measurement: Angular VelocityUnit: rev/s

Note: Value should be greater than 0.

Formulas to find Angular Speed

Clearance

The Clearance refers to the gap or space between two surfaces adjacent to each other.

Symbol: C

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Clearance

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Radius of Inner Cylinder

Go Radius of Inner Cylinder given Torque exerted on Inner Cylinder

r 1 = \sqrt{\frac{T}{2 \cdot π \cdot h \cdot 𝜏}}

Go Radius of Inner Cylinder given Velocity Gradient

r 1 = \frac{30 \cdot V G \cdot r 2 - π \cdot r 2 \cdot Ω}{30 \cdot V G}

Other formulas in Coaxial Cylinder Viscometers category

Go Torque exerted on Inner Cylinder

Τ Torque = 2 \cdot ({(r 1)}^{2}) \cdot h \cdot 𝜏

Go Height of Cylinder given Torque exerted on Inner Cylinder

h = \frac{T}{2 \cdot π \cdot ({(r 1)}^{2}) \cdot 𝜏}

Go Shear Stress on Cylinder given Torque exerted on Inner Cylinder

𝜏 = \frac{T}{2 \cdot π \cdot ({(r 1)}^{2}) \cdot h}

Go Velocity Gradients

V G = π \cdot r 2 \cdot \frac{Ω}{30 \cdot (r 2 - r 1)}

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

Radius of Inner Cylinder given Torque exerted on Outer Cylinder evaluator uses Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4) to evaluate 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 evaluate Radius of Inner Cylinder given Torque exerted on Outer Cylinder using this online evaluator? To use this online evaluator 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.

FAQs on Radius of Inner Cylinder given Torque exerted on Outer Cylinder

What is the formula to find Radius of Inner Cylinder given Torque exerted on Outer Cylinder?

The formula of Radius of Inner Cylinder given Torque exerted on Outer Cylinder is expressed as Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4). Here is an example- 11.97796 = (7000000/(1.02*pi*pi*31.4159265342981/(60*0.0155)))^(1/4).

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

With Torque on Outer Cylinder (T_o), Dynamic Viscosity (μ), Angular Speed (Ω) & Clearance (C) we can find Radius of Inner Cylinder given Torque exerted on Outer Cylinder using the formula - Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4). This formula also uses Archimedes' constant .

What are the other ways to Calculate Radius of Inner Cylinder?

Here are the different ways to Calculate Radius of Inner Cylinder-

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)

Can the Radius of Inner Cylinder given Torque exerted on Outer Cylinder be negative?

No, the Radius of Inner Cylinder given Torque exerted on Outer Cylinder, measured in Length cannot be negative.

Which unit is used to measure Radius of Inner Cylinder given Torque exerted on Outer Cylinder?

Radius of Inner Cylinder given Torque exerted on Outer Cylinder is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Radius of Inner Cylinder given Torque exerted on Outer Cylinder can be measured.

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Radius of Inner Cylinder given Torque exerted on Outer Cylinder Formula

​GoRadius of Inner Cylinder given Torque exerted on Inner Cylinder Formula

​GoRadius of Inner Cylinder given Velocity Gradient Formula

Radius of Inner Cylinder given Torque exerted on Outer Cylinder Example

Radius of Inner Cylinder given Torque exerted on Outer Cylinder Solution

Radius of Inner Cylinder given Torque exerted on Outer Cylinder Formula Elements

Other Formulas to find Radius of Inner Cylinder

Other formulas in Coaxial Cylinder Viscometers category

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

FAQs on Radius of Inner Cylinder given Torque exerted on Outer Cylinder

Variable Name

GoRadius of Inner Cylinder given Torque exerted on Inner Cylinder Formula

GoRadius of Inner Cylinder given Velocity Gradient Formula