Radius of Outer Cylinder given Velocity Gradient Calculator

✖Velocity Gradient is the difference in velocity between the adjacent layers of the fluid.ⓘ Velocity Gradient [VG]			+10% -10%
✖Radius of Inner Cylinder is the distance from center to inner cylinder's surface, crucial for viscosity measurement.ⓘ Radius of Inner Cylinder [r₁]			+10% -10%
✖Angular Speed is defined as the rate of change of angular displacement.ⓘ Angular Speed [Ω]			+10% -10%

✖Radius of Outer Cylinder is the spacing for measuring fluid viscosity based on inner cylinder rotation.ⓘ Radius of Outer Cylinder given Velocity Gradient [r₂]

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Formula

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Radius of Outer Cylinder given Velocity Gradient

Formula

`"r"_{"2"} = (30*"VG"*"r"_{"1"})/(30*"VG"-pi*"Ω")`

Example

`"12.53851m"=(30*"76.6m/s"*"12m")/(30*"76.6m/s"-pi*"5rev/s")`

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Radius of Outer Cylinder given Velocity Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Outer Cylinder = (30*Velocity Gradient*Radius of Inner Cylinder)/(30*Velocity Gradient-pi*Angular Speed)
r₂ = (30*VG*r₁)/(30*VG-pi*Ω)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Radius of Outer Cylinder - (Measured in Meter) - Radius of Outer Cylinder is the spacing for measuring fluid viscosity based on inner cylinder rotation.
Velocity Gradient - (Measured in Meter per Second) - Velocity Gradient is the difference in velocity between the adjacent layers of the fluid.
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.
Angular Speed - (Measured in Radian per Second) - Angular Speed is defined as the rate of change of angular displacement.

STEP 1: Convert Input(s) to Base Unit

Velocity Gradient: 76.6 Meter per Second --> 76.6 Meter per Second No Conversion Required
Radius of Inner Cylinder: 12 Meter --> 12 Meter No Conversion Required
Angular Speed: 5 Revolution per Second --> 31.4159265342981 Radian per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r₂ = (30*VG*r₁)/(30*VG-pi*Ω) --> (30*76.6*12)/(30*76.6-pi*31.4159265342981)

Evaluating ... ...

r₂ = 12.5385124347376

STEP 3: Convert Result to Output's Unit

12.5385124347376 Meter --> No Conversion Required

FINAL ANSWER

12.5385124347376 ≈ 12.53851 Meter <-- Radius of Outer Cylinder

(Calculation completed in 00.008 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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< 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 Outer Cylinder given Velocity Gradient Formula

Radius of Outer Cylinder = (30*Velocity Gradient*Radius of Inner Cylinder)/(30*Velocity Gradient-pi*Angular Speed)
r₂ = (30*VG*r₁)/(30*VG-pi*Ω)

What is Velocity Gradient?

The difference in velocity between adjacent layers of the fluid is known as a velocity gradient and is given by v/x, where v is the velocity difference and x is the distance between the layers

How to Calculate Radius of Outer Cylinder given Velocity Gradient?

Radius of Outer Cylinder given Velocity Gradient calculator uses Radius of Outer Cylinder = (30*Velocity Gradient*Radius of Inner Cylinder)/(30*Velocity Gradient-pi*Angular Speed) to calculate the Radius of Outer Cylinder, The Radius of Outer Cylinder given Velocity Gradient formula is defined as the maximum or largest radius of coaxial cylinder. Radius of Outer Cylinder is denoted by r₂ symbol.

How to calculate Radius of Outer Cylinder given Velocity Gradient using this online calculator? To use this online calculator for Radius of Outer Cylinder given Velocity Gradient, enter Velocity Gradient (VG), Radius of Inner Cylinder (r₁) & Angular Speed (Ω) and hit the calculate button. Here is how the Radius of Outer Cylinder given Velocity Gradient calculation can be explained with given input values -> 12.53851 = (30*76.6*12)/(30*76.6-pi*31.4159265342981).

FAQ

What is Radius of Outer Cylinder given Velocity Gradient?

The Radius of Outer Cylinder given Velocity Gradient formula is defined as the maximum or largest radius of coaxial cylinder and is represented as r₂ = (30*VG*r₁)/(30*VG-pi*Ω) or Radius of Outer Cylinder = (30*Velocity Gradient*Radius of Inner Cylinder)/(30*Velocity Gradient-pi*Angular Speed). Velocity Gradient is the difference in velocity between the adjacent layers of the fluid, Radius of Inner Cylinder is the distance from center to inner cylinder's surface, crucial for viscosity measurement & Angular Speed is defined as the rate of change of angular displacement.

How to calculate Radius of Outer Cylinder given Velocity Gradient?

The Radius of Outer Cylinder given Velocity Gradient formula is defined as the maximum or largest radius of coaxial cylinder is calculated using Radius of Outer Cylinder = (30*Velocity Gradient*Radius of Inner Cylinder)/(30*Velocity Gradient-pi*Angular Speed). To calculate Radius of Outer Cylinder given Velocity Gradient, you need Velocity Gradient (VG), Radius of Inner Cylinder (r₁) & Angular Speed (Ω). With our tool, you need to enter the respective value for Velocity Gradient, Radius of Inner Cylinder & Angular Speed and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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