Shear Stress on Cylinder given Torque exerted on Inner Cylinder Solution

STEP 0: Pre-Calculation Summary
Formula Used
Shear Stress = Torque on Inner Cylinder/(2*pi*((Radius of Inner Cylinder)^2)*Height)
๐œ = T/(2*pi*((r1)^2)*h)
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Shear Stress - (Measured in Pascal) - Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
Torque on Inner Cylinder - (Measured in Newton Meter) - Torque on Inner Cylinder is torque on cylinder from the external shaft.
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.
STEP 1: Convert Input(s) to Base Unit
Torque on Inner Cylinder: 500 Kilonewton Meter --> 500000 Newton Meter (Check conversion here)
Radius of Inner Cylinder: 12 Meter --> 12 Meter No Conversion Required
Height: 11.9 Meter --> 11.9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
๐œ = T/(2*pi*((r1)^2)*h) --> 500000/(2*pi*((12)^2)*11.9)
Evaluating ... ...
๐œ = 46.438767242033
STEP 3: Convert Result to Output's Unit
46.438767242033 Pascal --> No Conversion Required
FINAL ANSWER
46.438767242033 โ‰ˆ 46.43877 Pascal <-- Shear Stress
(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

Shear Stress on Cylinder given Torque exerted on Inner Cylinder Formula

Shear Stress = Torque on Inner Cylinder/(2*pi*((Radius of Inner Cylinder)^2)*Height)
๐œ = T/(2*pi*((r1)^2)*h)

What is Shear Stress?

Shear stress, often denoted by ฯ„, is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section.

How to Calculate Shear Stress on Cylinder given Torque exerted on Inner Cylinder?

Shear Stress on Cylinder given Torque exerted on Inner Cylinder calculator uses Shear Stress = Torque on Inner Cylinder/(2*pi*((Radius of Inner Cylinder)^2)*Height) to calculate the Shear Stress, The Shear Stress on Cylinder given Torque exerted on Inner Cylinder is defined as the stress developed due to frictional resistance between the gap. Shear Stress is denoted by ๐œ symbol.

How to calculate Shear Stress on Cylinder given Torque exerted on Inner Cylinder using this online calculator? To use this online calculator for Shear Stress on Cylinder given Torque exerted on Inner Cylinder, enter Torque on Inner Cylinder (T), Radius of Inner Cylinder (r1) & Height (h) and hit the calculate button. Here is how the Shear Stress on Cylinder given Torque exerted on Inner Cylinder calculation can be explained with given input values -> 46.43877 = 500000/(2*pi*((12)^2)*11.9).

FAQ

What is Shear Stress on Cylinder given Torque exerted on Inner Cylinder?
The Shear Stress on Cylinder given Torque exerted on Inner Cylinder is defined as the stress developed due to frictional resistance between the gap and is represented as ๐œ = T/(2*pi*((r1)^2)*h) or Shear Stress = Torque on Inner Cylinder/(2*pi*((Radius of Inner Cylinder)^2)*Height). Torque on Inner Cylinder is torque on cylinder from the external shaft, 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.
How to calculate Shear Stress on Cylinder given Torque exerted on Inner Cylinder?
The Shear Stress on Cylinder given Torque exerted on Inner Cylinder is defined as the stress developed due to frictional resistance between the gap is calculated using Shear Stress = Torque on Inner Cylinder/(2*pi*((Radius of Inner Cylinder)^2)*Height). To calculate Shear Stress on Cylinder given Torque exerted on Inner Cylinder, you need Torque on Inner Cylinder (T), Radius of Inner Cylinder (r1) & Height (h). With our tool, you need to enter the respective value for Torque on Inner Cylinder, Radius of Inner Cylinder & Height 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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