Dynamic Viscosity of Fluid Flow given Torque Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
μviscosity = (15*T*(r2-r1))/(pi*pi*r1*r1*r2*h*Ω)
This formula uses 1 Constants, 6 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Dynamic Viscosity - (Measured in Pascal Second) - The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.
Torque on Inner Cylinder - (Measured in Newton Meter) - Torque on Inner Cylinder is torque on cylinder from the external shaft.
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.
Height - (Measured in Meter) - Height is the distance between the lowest and highest points of a person/ shape/ object standing upright.
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
Torque on Inner Cylinder: 500 Kilonewton Meter --> 500000 Newton Meter (Check conversion here)
Radius of Outer Cylinder: 13 Meter --> 13 Meter No Conversion Required
Radius of Inner Cylinder: 12 Meter --> 12 Meter No Conversion Required
Height: 11.9 Meter --> 11.9 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
μviscosity = (15*T*(r2-r1))/(pi*pi*r1*r1*r2*h*Ω) --> (15*500000*(13-12))/(pi*pi*12*12*13*11.9*31.4159265342981)
Evaluating ... ...
μviscosity = 1.08582250709848
STEP 3: Convert Result to Output's Unit
1.08582250709848 Pascal Second -->10.8582250709848 Poise (Check conversion here)
FINAL ANSWER
10.8582250709848 10.85823 Poise <-- Dynamic Viscosity
(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

Dynamic Viscosity of Fluid Flow given Torque Formula

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)
μviscosity = (15*T*(r2-r1))/(pi*pi*r1*r1*r2*h*Ω)

What is Dynamic Viscosity?

The dynamic viscosity η (η = "eta") is a measure of the viscosity of a fluid (fluid: liquid, flowing substance). The higher the viscosity, the thicker (less liquid) the fluid; the lower the viscosity, the thinner (more liquid) it is.

How to Calculate Dynamic Viscosity of Fluid Flow given Torque?

Dynamic Viscosity of Fluid Flow given Torque calculator uses 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) to calculate the Dynamic Viscosity, The Dynamic Viscosity of Fluid Flow given torque is defined as the resistance offered by fluid on flow due to viscous nature of fluid. Dynamic Viscosity is denoted by μviscosity symbol.

How to calculate Dynamic Viscosity of Fluid Flow given Torque using this online calculator? To use this online calculator for Dynamic Viscosity of Fluid Flow given Torque, enter Torque on Inner Cylinder (T), Radius of Outer Cylinder (r2), Radius of Inner Cylinder (r1), Height (h) & Angular Speed (Ω) and hit the calculate button. Here is how the Dynamic Viscosity of Fluid Flow given Torque calculation can be explained with given input values -> 108.5823 = (15*500000*(13-12))/(pi*pi*12*12*13*11.9*31.4159265342981).

FAQ

What is Dynamic Viscosity of Fluid Flow given Torque?
The Dynamic Viscosity of Fluid Flow given torque is defined as the resistance offered by fluid on flow due to viscous nature of fluid and is represented as μviscosity = (15*T*(r2-r1))/(pi*pi*r1*r1*r2*h*Ω) or 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). Torque on Inner Cylinder is torque on cylinder from the external shaft, 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, Height is the distance between the lowest and highest points of a person/ shape/ object standing upright & Angular Speed is defined as the rate of change of angular displacement.
How to calculate Dynamic Viscosity of Fluid Flow given Torque?
The Dynamic Viscosity of Fluid Flow given torque is defined as the resistance offered by fluid on flow due to viscous nature of fluid is calculated using 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). To calculate Dynamic Viscosity of Fluid Flow given Torque, you need Torque on Inner Cylinder (T), Radius of Outer Cylinder (r2), Radius of Inner Cylinder (r1), Height (h) & Angular Speed (Ω). With our tool, you need to enter the respective value for Torque on Inner Cylinder, Radius of Outer Cylinder, Radius of Inner Cylinder, Height & 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 Dynamic Viscosity?
In this formula, Dynamic Viscosity uses Torque on Inner Cylinder, Radius of Outer Cylinder, Radius of Inner Cylinder, Height & Angular Speed. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Dynamic Viscosity = Torque on Outer Cylinder/(pi*pi*Angular Speed*(Radius of Inner Cylinder^4)/(60*Clearance))
  • Dynamic Viscosity = Total Torque/(Viscometer Constant*Angular Speed)
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