Angular Speed of Outer Cylinder in Rotating Cylinder Method Calculator

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✖The Outer Radius of Cylinder is a straight line from the center to the Cylinder's base to outer surface of the Cylinder.ⓘ Outer Radius of Cylinder [r₂]			+10% -10%
✖The Inner Radius of Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder.ⓘ Inner Radius of Cylinder [r₁]			+10% -10%
✖Clearance or gap is the distance between two surfaces adjacent to each other.ⓘ Clearance [C]			+10% -10%
✖Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.ⓘ Torque Exerted on Wheel [τ]			+10% -10%
✖The Viscosity of fluid is a measure of its resistance to deformation at a given rate.ⓘ Viscosity of Fluid [μ]			+10% -10%
✖The Initial height of liquid is a variable from the tank emptying through an orifice at its bottom.ⓘ Initial Height of Liquid [H_i]			+10% -10%

✖Mean Speed in RPM is an average of individual vehicle speeds.ⓘ Angular Speed of Outer Cylinder in Rotating Cylinder Method [N]

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Angular Speed of Outer Cylinder in Rotating Cylinder Method

Formula

`"N" = (2*("r"_{"2"}-"r"_{"1"})*"C"*"τ")/(pi*"r"_{"1"}^2*"μ"*(4*"H"_{"i"}*"C"*"r"_{"2"}+"r"_{"1"}^2*("r"_{"2"}-"r"_{"1"})))`

Example

`"1.069076rev/min"=(2*("12.51m"-"1.52m")*"0.95m"*"50N*m")/(pi*("1.52m")^2*"8.23N*s/m²"*(4*"20.1m"*"0.95m"*"12.51m"+("1.52m")^2*("12.51m"-"1.52m")))`

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Angular Speed of Outer Cylinder in Rotating Cylinder Method Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean Speed in RPM = (2*(Outer Radius of Cylinder-Inner Radius of Cylinder)*Clearance*Torque Exerted on Wheel)/(pi*Inner Radius of Cylinder^2*Viscosity of Fluid*(4*Initial Height of Liquid*Clearance*Outer Radius of Cylinder+Inner Radius of Cylinder^2*(Outer Radius of Cylinder-Inner Radius of Cylinder)))
N = (2*(r₂-r₁)*C*τ)/(pi*r₁^2*μ*(4*H_i*C*r₂+r₁^2*(r₂-r₁)))
This formula uses 1 Constants, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Mean Speed in RPM - (Measured in Hertz) - Mean Speed in RPM is an average of individual vehicle speeds.
Outer Radius of Cylinder - (Measured in Meter) - The Outer Radius of Cylinder is a straight line from the center to the Cylinder's base to outer surface of the Cylinder.
Inner Radius of Cylinder - (Measured in Meter) - The Inner Radius of Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder.
Clearance - (Measured in Meter) - Clearance or gap is the distance between two surfaces adjacent to each other.
Torque Exerted on Wheel - (Measured in Newton Meter) - Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.
Viscosity of Fluid - (Measured in Pascal Second) - The Viscosity of fluid is a measure of its resistance to deformation at a given rate.
Initial Height of Liquid - (Measured in Meter) - The Initial height of liquid is a variable from the tank emptying through an orifice at its bottom.

STEP 1: Convert Input(s) to Base Unit

Outer Radius of Cylinder: 12.51 Meter --> 12.51 Meter No Conversion Required
Inner Radius of Cylinder: 1.52 Meter --> 1.52 Meter No Conversion Required
Clearance: 0.95 Meter --> 0.95 Meter No Conversion Required
Torque Exerted on Wheel: 50 Newton Meter --> 50 Newton Meter No Conversion Required
Viscosity of Fluid: 8.23 Newton Second per Square Meter --> 8.23 Pascal Second (Check conversion here)
Initial Height of Liquid: 20.1 Meter --> 20.1 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N = (2*(r₂-r₁)*C*τ)/(pi*r₁^2*μ*(4*H_i*C*r₂+r₁^2*(r₂-r₁))) --> (2*(12.51-1.52)*0.95*50)/(pi*1.52^2*8.23*(4*20.1*0.95*12.51+1.52^2*(12.51-1.52)))

Evaluating ... ...

N = 0.0178179371677733

STEP 3: Convert Result to Output's Unit

0.0178179371677733 Hertz -->1.0690762300664 Revolution per Minute (Check conversion here)

FINAL ANSWER

1.0690762300664 ≈ 1.069076 Revolution per Minute <-- Mean Speed in RPM

(Calculation completed in 00.008 seconds)

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Created by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

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Amrita School of Engineering (ASE), Vallikavu

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< 21 Fluid Flow and Resistance Calculators

Total Torque Measured by Strain in Rotating Cylinder Method

Go Torque Exerted on Wheel = (Viscosity of Fluid*pi*Inner Radius of Cylinder^2*Mean Speed in RPM*(4*Initial Height of Liquid*Clearance*Outer Radius of Cylinder+(Inner Radius of Cylinder^2)*(Outer Radius of Cylinder-Inner Radius of Cylinder)))/(2*(Outer Radius of Cylinder-Inner Radius of Cylinder)*Clearance)

Angular Speed of Outer Cylinder in Rotating Cylinder Method

Go Mean Speed in RPM = (2*(Outer Radius of Cylinder-Inner Radius of Cylinder)*Clearance*Torque Exerted on Wheel)/(pi*Inner Radius of Cylinder^2*Viscosity of Fluid*(4*Initial Height of Liquid*Clearance*Outer Radius of Cylinder+Inner Radius of Cylinder^2*(Outer Radius of Cylinder-Inner Radius of Cylinder)))

Discharge in Capillary Tube Method

Go Discharge in Capillary Tube = (4*pi*Density of Liquid*[g]*Difference in Pressure Head*Radius of Pipe^4)/(128*Viscosity of Fluid*Length of Pipe)

Rotational Speed for Torque Required in Collar Bearing

Go Mean Speed in RPM = (Torque Exerted on Wheel*Thickness of Oil Film)/(Viscosity of Fluid*pi^2*(Outer Radius of Collar^4-Inner Radius of Collar^4))

Torque Required to Overcome Viscous Resistance in Collar Bearing

Go Torque Exerted on Wheel = (Viscosity of Fluid*pi^2*Mean Speed in RPM*(Outer Radius of Collar^4-Inner Radius of Collar^4))/Thickness of Oil Film

Velocity of Piston or Body for Movement of Piston in Dash-Pot

Go Velocity of Fluid = (4*Weight of Body*Clearance^3)/(3*pi*Length of Pipe*Piston Diameter^3*Viscosity of Fluid)

Shear Force or Viscous Resistance in Journal Bearing

Go Shear Force = (pi^2*Viscosity of Fluid*Mean Speed in RPM*Length of Pipe*Shaft Diameter^2)/(Thickness of Oil Film)

Speed of Rotation for Shear Force in Journal Bearing

Go Mean Speed in RPM = (Shear Force*Thickness of Oil Film)/(Viscosity of Fluid*pi^2*Shaft Diameter^2*Length of Pipe)

Shear Stress in Fluid or Oil of Journal Bearing

Go Shear Stress = (pi*Viscosity of Fluid*Shaft Diameter*Mean Speed in RPM)/(60*Thickness of Oil Film)

Rotational Speed for Torque Required in Foot-Step Bearing

Go Mean Speed in RPM = (Torque Exerted on Wheel*Thickness of Oil Film)/(Viscosity of Fluid*pi^2*(Shaft Diameter/2)^4)

Torque Required to Overcome Viscous Resistance in Foot-Step Bearing

Go Torque Exerted on Wheel = (Viscosity of Fluid*pi^2*Mean Speed in RPM*(Shaft Diameter/2)^4)/Thickness of Oil Film

Velocity of Sphere in Falling Sphere Resistance Method

Go Velocity of Sphere = Drag Force/(3*pi*Viscosity of Fluid*Diameter of Sphere)

Drag Force in Falling Sphere Resistance Method

Go Drag Force = 3*pi*Viscosity of Fluid*Velocity of Sphere*Diameter of Sphere

Density of Fluid in Falling Sphere Resistance Method

Go Density of Liquid = Buoyant Force/(pi/6*Diameter of Sphere^3*[g])

Buoyant Force in Falling Sphere Resistance Method

Go Buoyant Force = pi/6*Density of Liquid*[g]*Diameter of Sphere^3

Velocity at Any Radius given Radius of Pipe, and Maximum Velocity

Go Velocity of Fluid = Maximum Velocity*(1-(Radius of Pipe/(Pipe Diameter/2))^2)

Maximum Velocity at any Radius using Velocity

Go Maximum Velocity = Velocity of Fluid/(1-(Radius of Pipe/(Pipe Diameter/2))^2)

Rotational Speed considering Power Absorbed and Torque in Journal Bearing

Go Mean Speed in RPM = Power Absorbed/(2*pi*Torque Exerted on Wheel)

Torque Required Considering Power Absorbed in Journal Bearing

Go Torque Exerted on Wheel = Power Absorbed/(2*pi*Mean Speed in RPM)

Shear Force for Torque and Diameter of Shaft in Journal Bearing

Go Shear Force = Torque Exerted on Wheel/(Shaft Diameter/2)

Torque Required to Overcome Shear Force in Journal Bearing

Go Torque Exerted on Wheel = Shear Force*Shaft Diameter/2

Angular Speed of Outer Cylinder in Rotating Cylinder Method Formula

What is rotating cylinder method?

A method of measuring the viscosity of a fluid in which the fluid fills the space between two concentric cylinders and the torque on the stationary inner cylinder is measured when the outer cylinder is rotated at a constant speed.

What causes viscosity in fluids?

Viscosity is caused by friction within a fluid. It is the result of intermolecular forces between particles within a fluid.

How to Calculate Angular Speed of Outer Cylinder in Rotating Cylinder Method?

Angular Speed of Outer Cylinder in Rotating Cylinder Method calculator uses Mean Speed in RPM = (2*(Outer Radius of Cylinder-Inner Radius of Cylinder)*Clearance*Torque Exerted on Wheel)/(pi*Inner Radius of Cylinder^2*Viscosity of Fluid*(4*Initial Height of Liquid*Clearance*Outer Radius of Cylinder+Inner Radius of Cylinder^2*(Outer Radius of Cylinder-Inner Radius of Cylinder))) to calculate the Mean Speed in RPM, The Angular speed of outer cylinder in rotating cylinder method formula is known while considering the inner and outer radius of the cylinder, torque measured, the viscosity of fluid or oil, clearance, and the height of the liquid. Mean Speed in RPM is denoted by N symbol.

How to calculate Angular Speed of Outer Cylinder in Rotating Cylinder Method using this online calculator? To use this online calculator for Angular Speed of Outer Cylinder in Rotating Cylinder Method, enter Outer Radius of Cylinder (r₂), Inner Radius of Cylinder (r₁), Clearance (C), Torque Exerted on Wheel (τ), Viscosity of Fluid (μ) & Initial Height of Liquid (H_i) and hit the calculate button. Here is how the Angular Speed of Outer Cylinder in Rotating Cylinder Method calculation can be explained with given input values -> 66.02802 = (2*(12.51-1.52)*0.95*50)/(pi*1.52^2*8.23*(4*20.1*0.95*12.51+1.52^2*(12.51-1.52))).

FAQ

What is Angular Speed of Outer Cylinder in Rotating Cylinder Method?

The Angular speed of outer cylinder in rotating cylinder method formula is known while considering the inner and outer radius of the cylinder, torque measured, the viscosity of fluid or oil, clearance, and the height of the liquid and is represented as N = (2*(r₂-r₁)*C*τ)/(pi*r₁^2*μ*(4*H_i*C*r₂+r₁^2*(r₂-r₁))) or Mean Speed in RPM = (2*(Outer Radius of Cylinder-Inner Radius of Cylinder)*Clearance*Torque Exerted on Wheel)/(pi*Inner Radius of Cylinder^2*Viscosity of Fluid*(4*Initial Height of Liquid*Clearance*Outer Radius of Cylinder+Inner Radius of Cylinder^2*(Outer Radius of Cylinder-Inner Radius of Cylinder))). The Outer Radius of Cylinder is a straight line from the center to the Cylinder's base to outer surface of the Cylinder, The Inner Radius of Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder, Clearance or gap is the distance between two surfaces adjacent to each other, Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ, The Viscosity of fluid is a measure of its resistance to deformation at a given rate & The Initial height of liquid is a variable from the tank emptying through an orifice at its bottom.

How to calculate Angular Speed of Outer Cylinder in Rotating Cylinder Method?

The Angular speed of outer cylinder in rotating cylinder method formula is known while considering the inner and outer radius of the cylinder, torque measured, the viscosity of fluid or oil, clearance, and the height of the liquid is calculated using Mean Speed in RPM = (2*(Outer Radius of Cylinder-Inner Radius of Cylinder)*Clearance*Torque Exerted on Wheel)/(pi*Inner Radius of Cylinder^2*Viscosity of Fluid*(4*Initial Height of Liquid*Clearance*Outer Radius of Cylinder+Inner Radius of Cylinder^2*(Outer Radius of Cylinder-Inner Radius of Cylinder))). To calculate Angular Speed of Outer Cylinder in Rotating Cylinder Method, you need Outer Radius of Cylinder (r₂), Inner Radius of Cylinder (r₁), Clearance (C), Torque Exerted on Wheel (τ), Viscosity of Fluid (μ) & Initial Height of Liquid (H_i). With our tool, you need to enter the respective value for Outer Radius of Cylinder, Inner Radius of Cylinder, Clearance, Torque Exerted on Wheel, Viscosity of Fluid & Initial Height of Liquid 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 Mean Speed in RPM?

In this formula, Mean Speed in RPM uses Outer Radius of Cylinder, Inner Radius of Cylinder, Clearance, Torque Exerted on Wheel, Viscosity of Fluid & Initial Height of Liquid. We can use 4 other way(s) to calculate the same, which is/are as follows -

Mean Speed in RPM = (Shear Force*Thickness of Oil Film)/(Viscosity of Fluid*pi^2*Shaft Diameter^2*Length of Pipe)
Mean Speed in RPM = Power Absorbed/(2*pi*Torque Exerted on Wheel)
Mean Speed in RPM = (Torque Exerted on Wheel*Thickness of Oil Film)/(Viscosity of Fluid*pi^2*(Shaft Diameter/2)^4)
Mean Speed in RPM = (Torque Exerted on Wheel*Thickness of Oil Film)/(Viscosity of Fluid*pi^2*(Outer Radius of Collar^4-Inner Radius of Collar^4))

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