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

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Speed of Outer Cylinder given Velocity Gradient

Formula

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

Example

`"8.955234rev/s"="76.6m/s"/((pi*"13m")/(30*("13m"-"12m")))`

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Speed of Outer Cylinder given Velocity Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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

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 Outer Cylinder: 13 Meter --> 13 Meter No Conversion Required
Radius of Inner Cylinder: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Ω = VG/((pi*r₂)/(30*(r₂-r₁))) --> 76.6/((pi*13)/(30*(13-12)))

Evaluating ... ...

Ω = 56.2673937269501

STEP 3: Convert Result to Output's Unit

56.2673937269501 Radian per Second -->8.95523384699803 Revolution per Second (Check conversion here)

FINAL ANSWER

8.95523384699803 ≈ 8.955234 Revolution per Second <-- Angular Speed

(Calculation completed in 00.004 seconds)

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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

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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

Speed of Outer Cylinder given Velocity Gradient Formula

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

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 Speed of Outer Cylinder given Velocity Gradient?

Speed of Outer Cylinder given Velocity Gradient calculator uses Angular Speed = Velocity Gradient/((pi*Radius of Outer Cylinder)/(30*(Radius of Outer Cylinder-Radius of Inner Cylinder))) to calculate the Angular Speed, The Speed of Outer Cylinder given Velocity Gradient is defined as the speed at which cylinder is rotating in revolution per minutes. Angular Speed is denoted by Ω symbol.

How to calculate Speed of Outer Cylinder given Velocity Gradient using this online calculator? To use this online calculator for Speed of Outer Cylinder given Velocity Gradient, enter Velocity Gradient (VG), Radius of Outer Cylinder (r₂) & Radius of Inner Cylinder (r₁) and hit the calculate button. Here is how the Speed of Outer Cylinder given Velocity Gradient calculation can be explained with given input values -> 1.42527 = 76.6/((pi*13)/(30*(13-12))).

FAQ

What is Speed of Outer Cylinder given Velocity Gradient?

The Speed of Outer Cylinder given Velocity Gradient is defined as the speed at which cylinder is rotating in revolution per minutes and is represented as Ω = VG/((pi*r₂)/(30*(r₂-r₁))) or Angular Speed = Velocity Gradient/((pi*Radius of Outer Cylinder)/(30*(Radius of Outer Cylinder-Radius of Inner Cylinder))). Velocity Gradient is the difference in velocity between the adjacent layers of the fluid, Radius of Outer Cylinder is the spacing for measuring fluid viscosity based on inner cylinder rotation & Radius of Inner Cylinder is the distance from center to inner cylinder's surface, crucial for viscosity measurement.

How to calculate Speed of Outer Cylinder given Velocity Gradient?

The Speed of Outer Cylinder given Velocity Gradient is defined as the speed at which cylinder is rotating in revolution per minutes is calculated using Angular Speed = Velocity Gradient/((pi*Radius of Outer Cylinder)/(30*(Radius of Outer Cylinder-Radius of Inner Cylinder))). To calculate Speed of Outer Cylinder given Velocity Gradient, you need Velocity Gradient (VG), Radius of Outer Cylinder (r₂) & Radius of Inner Cylinder (r₁). With our tool, you need to enter the respective value for Velocity Gradient, Radius of Outer Cylinder & Radius of Inner Cylinder 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 Velocity Gradient, Radius of Outer Cylinder & Radius of Inner Cylinder. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)
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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