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*VG*r2-pi*r2*Ω)/(30*VG)
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) - Radius of Inner Cylinder is the distance from center to inner cylinder's surface, crucial for viscosity measurement.
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.
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 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*VG*r2-pi*r2*Ω)/(30*VG) --> (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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National Institute of Technology Karnataka (NITK), Surathkal
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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 Inner Cylinder given Velocity Gradient Formula

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

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 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 (VG), 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 is defined as the smaller radius of coaxial placed cylinder and is represented as r1 = (30*VG*r2-pi*r2*Ω)/(30*VG) or Radius of Inner Cylinder = (30*Velocity Gradient*Radius of Outer Cylinder-pi*Radius of Outer Cylinder*Angular Speed)/(30*Velocity Gradient). 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 & Angular Speed is defined as 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 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 (VG), 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*Shear Stress))
  • Radius of Inner Cylinder = (Torque on Outer Cylinder/(Dynamic Viscosity*pi*pi*Angular Speed/(60*Clearance)))^(1/4)
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