Velocity Gradients Calculator

✖Radius of Outer Cylinder is the spacing for measuring fluid viscosity based on inner cylinder rotation.ⓘ Radius of Outer Cylinder [r₂]			+10% -10%
✖Angular Speed is defined as the rate of change of angular displacement.ⓘ Angular Speed [Ω]			+10% -10%
✖Radius of Inner Cylinder is the distance from center to inner cylinder's surface, crucial for viscosity measurement.ⓘ Radius of Inner Cylinder [r₁]			+10% -10%

✖Velocity Gradient is the difference in velocity between the adjacent layers of the fluid.ⓘ Velocity Gradients [VG]

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Velocity Gradients

Formula

`"VG" = pi*"r"_{"2"}*"Ω"/(30*("r"_{"2"}-"r"_{"1"}))`

Example

`"42.76829m/s"=pi*"13m"*"5rev/s"/(30*("13m"-"12m"))`

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Velocity Gradients Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

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)
Radius of Inner Cylinder: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

VG = pi*r₂*Ω/(30*(r₂-r₁)) --> pi*13*31.4159265342981/(30*(13-12))

Evaluating ... ...

VG = 42.7682857358759

STEP 3: Convert Result to Output's Unit

42.7682857358759 Meter per Second --> No Conversion Required

FINAL ANSWER

42.7682857358759 ≈ 42.76829 Meter per Second <-- Velocity Gradient

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Laminar Flow » Measurement of Viscosity Viscometers » Coaxial Cylinder Viscometers » Velocity Gradients

Credits

Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

Rithik Agrawal has created this Calculator and 1300+ more calculators!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Calculator and 1700+ more calculators!

< 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

Velocity Gradients Formula

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

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 Velocity Gradients?

Velocity Gradients calculator uses Velocity Gradient = pi*Radius of Outer Cylinder*Angular Speed/(30*(Radius of Outer Cylinder-Radius of Inner Cylinder)) to calculate the Velocity Gradient, The Velocity Gradients is defined as the change in velocity with respect to change in distance along the measured direction. Velocity Gradient is denoted by VG symbol.

How to calculate Velocity Gradients using this online calculator? To use this online calculator for Velocity Gradients, enter Radius of Outer Cylinder (r₂), Angular Speed (Ω) & Radius of Inner Cylinder (r₁) and hit the calculate button. Here is how the Velocity Gradients calculation can be explained with given input values -> 42.76829 = pi*13*31.4159265342981/(30*(13-12)).

FAQ

What is Velocity Gradients?

The Velocity Gradients is defined as the change in velocity with respect to change in distance along the measured direction and is represented as VG = pi*r₂*Ω/(30*(r₂-r₁)) or Velocity Gradient = pi*Radius of Outer Cylinder*Angular Speed/(30*(Radius of Outer Cylinder-Radius of Inner Cylinder)). 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 & Radius of Inner Cylinder is the distance from center to inner cylinder's surface, crucial for viscosity measurement.

How to calculate Velocity Gradients?

The Velocity Gradients is defined as the change in velocity with respect to change in distance along the measured direction is calculated using Velocity Gradient = pi*Radius of Outer Cylinder*Angular Speed/(30*(Radius of Outer Cylinder-Radius of Inner Cylinder)). To calculate Velocity Gradients, you need Radius of Outer Cylinder (r₂), Angular Speed (Ω) & Radius of Inner Cylinder (r₁). With our tool, you need to enter the respective value for Radius of Outer Cylinder, Angular Speed & Radius of Inner Cylinder 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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