Radius of Inner Cylinder given Velocity Gradient Calculator

✖The Velocity Gradient refers to the difference in velocity between the adjacent layers of the fluid.ⓘ Velocity Gradient [V_G]			+10% -10%
✖The Radius of Outer Cylinder refers to the spacing for measuring fluid viscosity based on inner cylinder rotation.ⓘ Radius of Outer Cylinder [r₂]			+10% -10%
✖The Angular Speed refers to the rate of change of angular displacement.ⓘ Angular Speed [Ω]			+10% -10%

✖The Radius of Inner Cylinder refers to the distance from center to inner cylinder's surface, crucial for viscosity measurement.ⓘ Radius of Inner Cylinder given Velocity Gradient [r₁]

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Radius of Inner Cylinder given Velocity Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Radius of Inner Cylinder - (Measured in Meter) - The Radius of Inner Cylinder refers to the distance from center to inner cylinder's surface, crucial for viscosity measurement.
Velocity Gradient - (Measured in Meter per Second) - The Velocity Gradient refers to the difference in velocity between the adjacent layers of the fluid.
Radius of Outer Cylinder - (Measured in Meter) - The Radius of Outer Cylinder refers to the spacing for measuring fluid viscosity based on inner cylinder rotation.
Angular Speed - (Measured in Radian per Second) - The Angular Speed refers to 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 Outer Cylinder: 13 Meter --> 13 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

r₁ = (30*V_G*r₂-pi*r₂*Ω)/(30*V_G) --> (30*76.6*13-pi*13*31.4159265342981)/(30*76.6)

Evaluating ... ...

r₁ = 12.4416672880434

STEP 3: Convert Result to Output's Unit

12.4416672880434 Meter --> No Conversion Required

FINAL ANSWER

12.4416672880434 ≈ 12.44167 Meter <-- Radius of Inner Cylinder

(Calculation completed in 00.020 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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National Institute of Technology (NIT), Warangal

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< Coaxial Cylinder Viscometers Calculators

Radius of Inner Cylinder given Torque exerted on Inner Cylinder

LaTeX Go Radius of Inner Cylinder = sqrt(Torque on Inner Cylinder/(2*pi*Height of Cylinder*Shear Stress))

Shear Stress on Cylinder given Torque exerted on Inner Cylinder

LaTeX Go Shear Stress = Torque on Inner Cylinder/(2*pi*((Radius of Inner Cylinder)^2)*Height of Cylinder)

Height of Cylinder given Torque exerted on Inner Cylinder

LaTeX Go Height of Cylinder = Torque on Inner Cylinder/(2*pi*((Radius of Inner Cylinder)^2)*Shear Stress)

Torque exerted on Inner Cylinder

LaTeX Go Total Torque = 2*((Radius of Inner Cylinder)^2)*Height of Cylinder*Shear Stress

Radius of Inner Cylinder given Velocity Gradient Formula

LaTeX Go

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

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 Inner Cylinder given Velocity Gradient?

Radius of Inner Cylinder given Velocity Gradient calculator uses Radius of Inner Cylinder = (30*Velocity Gradient*Radius of Outer Cylinder-pi*Radius of Outer Cylinder*Angular Speed)/(30*Velocity Gradient) to calculate 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 calculate Radius of Inner Cylinder given Velocity Gradient using this online calculator? To use this online calculator 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. Here is how the Radius of Inner Cylinder given Velocity Gradient calculation can be explained with given input values -> 12.44167 = (30*76.6*13-pi*13*31.4159265342981)/(30*76.6).

FAQ

What is Radius of Inner Cylinder given Velocity Gradient?

The Radius of Inner Cylinder given Velocity Gradient formula is defined as the smaller radius of coaxial placed cylinder and is represented as r₁ = (30*V_G*r₂-pi*r₂*Ω)/(30*V_G) or Radius of Inner Cylinder = (30*Velocity Gradient*Radius of Outer Cylinder-pi*Radius of Outer Cylinder*Angular Speed)/(30*Velocity Gradient). The Velocity Gradient refers to the difference in velocity between the adjacent layers of the fluid, The Radius of Outer Cylinder refers to the spacing for measuring fluid viscosity based on inner cylinder rotation & The Angular Speed refers to the rate of change of angular displacement.

How to calculate Radius of Inner Cylinder given Velocity Gradient?

The Radius of Inner Cylinder given Velocity Gradient formula is defined as the smaller radius of coaxial placed cylinder is calculated using Radius of Inner Cylinder = (30*Velocity Gradient*Radius of Outer Cylinder-pi*Radius of Outer Cylinder*Angular Speed)/(30*Velocity Gradient). To calculate Radius of Inner Cylinder given Velocity Gradient, you need Velocity Gradient (V_G), Radius of Outer Cylinder (r₂) & Angular Speed (Ω). With our tool, you need to enter the respective value for Velocity Gradient, Radius of Outer Cylinder & Angular Speed 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 Velocity Gradient, Radius of Outer Cylinder & Angular Speed. 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 of Cylinder*Shear Stress))
Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4)

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