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Radius of Inner Cylinder given Velocity Gradient Formula

GoRadius of Inner Cylinder given Torque exerted on Inner Cylinder Formula

GoRadius of Inner Cylinder given Torque exerted on Outer Cylinder 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{30 \cdot V G \cdot r 2 - π \cdot r 2 \cdot Ω}{30 \cdot V G}

r₁ - Radius of Inner Cylinder?V_G - Velocity Gradient?r₂ - Radius of Outer Cylinder?Ω - Angular Speed?π - Archimedes' constant?

Radius of Inner Cylinder given Velocity Gradient Example

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Here is how the Radius of Inner Cylinder given Velocity Gradient equation looks like with Values.

Here is how the Radius of Inner Cylinder given Velocity Gradient equation looks like with Units.

Here is how the Radius of Inner Cylinder given Velocity Gradient equation looks like.

12.4417 = \frac{30 \cdot 76.6 \cdot 13 - 3.1416 \cdot 13 \cdot 5}{30 \cdot 76.6}

12.4417m = \frac{30 \cdot 76.6m/s \cdot 13m - 3.1416 \cdot 13m \cdot 5rev/s}{30 \cdot 76.6m/s}

12.4417 = \frac{30 \cdot 76.6 \cdot 13 - 3.1416 \cdot 13 \cdot 5}{30 \cdot 76.6}

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Radius of Inner Cylinder given Velocity Gradient Solution

Follow our step by step solution on how to calculate Radius of Inner Cylinder given Velocity Gradient?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r 1 = \frac{30 \cdot 76.6m/s \cdot 13m - π \cdot 13m \cdot 5rev/s}{30 \cdot 76.6m/s}

Next Step Substitute values of Constants

∴

r 1 = \frac{30 \cdot 76.6m/s \cdot 13m - 3.1416 \cdot 13m \cdot 5rev/s}{30 \cdot 76.6m/s}

Next Step Convert Units

∴

r 1 = \frac{30 \cdot 76.6m/s \cdot 13m - 3.1416 \cdot 13m \cdot 31.4159rad/s}{30 \cdot 76.6m/s}

Next Step Prepare to Evaluate

∴

r 1 = \frac{30 \cdot 76.6 \cdot 13 - 3.1416 \cdot 13 \cdot 31.4159}{30 \cdot 76.6}

Next Step Evaluate

∴

r 1 = 12.4416672880434m

LAST Step Rounding Answer

∴

r 1 = 12.4417m

Radius of Inner Cylinder given Velocity Gradient 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

Velocity Gradient

The Velocity Gradient refers to the difference in velocity between the adjacent layers of the fluid.

Symbol: V_G

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Velocity Gradient

Radius of Outer Cylinder

The Radius of Outer Cylinder refers to the spacing for measuring fluid viscosity based on inner cylinder rotation.

Symbol: r₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Outer Cylinder

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

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 Torque exerted on Outer Cylinder

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

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 Velocity Gradient?

Radius of Inner Cylinder given Velocity Gradient evaluator uses Radius of Inner Cylinder = (30*Velocity Gradient*Radius of Outer Cylinder-pi*Radius of Outer Cylinder*Angular Speed)/(30*Velocity Gradient) to evaluate the Radius of Inner Cylinder, The Radius of Inner Cylinder given Velocity Gradient formula is defined as the smaller radius of coaxial placed cylinder. Radius of Inner Cylinder is denoted by r₁ symbol.

How to evaluate Radius of Inner Cylinder given Velocity Gradient using this online evaluator? To use this online evaluator for Radius of Inner Cylinder given Velocity Gradient, enter Velocity Gradient (V_G), Radius of Outer Cylinder (r₂) & Angular Speed (Ω) and hit the calculate button.

FAQs on Radius of Inner Cylinder given Velocity Gradient

What is the formula to find Radius of Inner Cylinder given Velocity Gradient?

The formula of Radius of Inner Cylinder given Velocity Gradient is expressed as Radius of Inner Cylinder = (30*Velocity Gradient*Radius of Outer Cylinder-pi*Radius of Outer Cylinder*Angular Speed)/(30*Velocity Gradient). Here is an example- 12.44167 = (30*76.6*13-pi*13*31.4159265342981)/(30*76.6).

How to calculate Radius of Inner Cylinder given Velocity Gradient?

With Velocity Gradient (V_G), Radius of Outer Cylinder (r₂) & Angular Speed (Ω) we can find Radius of Inner Cylinder given Velocity Gradient using the formula - Radius of Inner Cylinder = (30*Velocity Gradient*Radius of Outer Cylinder-pi*Radius of Outer Cylinder*Angular Speed)/(30*Velocity Gradient). 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=(Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4)

Can the Radius of Inner Cylinder given Velocity Gradient be negative?

No, the Radius of Inner Cylinder given Velocity Gradient, measured in Length cannot be negative.

Which unit is used to measure Radius of Inner Cylinder given Velocity Gradient?

Radius of Inner Cylinder given Velocity Gradient 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 Velocity Gradient can be measured.

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Radius of Inner Cylinder given Velocity Gradient Formula

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

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

Radius of Inner Cylinder given Velocity Gradient Example

Radius of Inner Cylinder given Velocity Gradient Solution

Radius of Inner Cylinder given Velocity Gradient 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 Velocity Gradient?

FAQs on Radius of Inner Cylinder given Velocity Gradient

Variable Name

GoRadius of Inner Cylinder given Torque exerted on Inner Cylinder Formula

GoRadius of Inner Cylinder given Torque exerted on Outer Cylinder Formula