Constant Angular Velocity given Equation of Free Surface of Liquid Solution

STEP 0: Pre-Calculation Summary
Formula Used
Angular Velocity = sqrt(Height of Crack*(2*[g])/(Distance from Center to Point^2))
ω = sqrt(h*(2*[g])/(d'^2))
This formula uses 1 Constants, 1 Functions, 3 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Angular Velocity - (Measured in Radian per Second) - The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
Height of Crack - (Measured in Meter) - Height of Crack is the size of a flaw or crack in a material that can lead to catastrophic failure under a given stress.
Distance from Center to Point - (Measured in Meter) - Distance from center to point is the length of line segment measured from the center of a body to a particular point.
STEP 1: Convert Input(s) to Base Unit
Height of Crack: 12000 Millimeter --> 12 Meter (Check conversion here)
Distance from Center to Point: 10000 Millimeter --> 10 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ω = sqrt(h*(2*[g])/(d'^2)) --> sqrt(12*(2*[g])/(10^2))
Evaluating ... ...
ω = 1.53414340920267
STEP 3: Convert Result to Output's Unit
1.53414340920267 Radian per Second --> No Conversion Required
FINAL ANSWER
1.53414340920267 1.534143 Radian per Second <-- Angular Velocity
(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal
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9 Cylindrical Vessel Containing Liquid Rotating with its Axis Vertical Calculators

Radial Distance for Pressure at Any Point with Origin at Free Surface
Go Radial Distance from Central Axis = sqrt((2*[g]/Specific Weight of Liquid*(Angular Velocity^2))*(Absolute Pressure-Atmospheric Pressure+Specific Weight of Liquid*Height of Crack))
Atmospheric Pressure given Pressure at any Point with Origin at Free Surface
Go Atmospheric Pressure = Absolute Pressure-((Specific Weight of Liquid/[g])*(0.5*(Angular Velocity*Radial Distance from Central Axis)^2)+Angular Velocity*Height of Crack)
Vertical Depth given Pressure at any point with Origin at Free Surface
Go Height of Crack = (Atmospheric Pressure-Absolute Pressure+(Specific Weight of Liquid/[g])*(0.5*(Angular Velocity*Radial Distance from Central Axis)^2))/Angular Velocity
Pressure at any Point with Origin at Free Surface
Go Absolute Pressure = Atmospheric Pressure+(Specific Weight of Liquid/[g])*(0.5*(Angular Velocity*Radial Distance from Central Axis)^2)-Angular Velocity*Height of Crack
Constant Angular Velocity given Equation of Free Surface of Liquid
Go Angular Velocity = sqrt(Height of Crack*(2*[g])/(Distance from Center to Point^2))
Constant Angular Velocity given Centripetal acceleration at radial distance r from axis
Go Angular Velocity = sqrt(Centripetal acceleration/Radial Distance from Central Axis)
Equation of Free Surface of liquid
Go Height of Crack = ((Angular Velocity*Distance from Center to Point)^2)/(2*[g])
Centripetal Acceleration Exerted on Liquid Mass at Radial Distance from Axis
Go Centripetal acceleration = (Angular Velocity^2)*Radial Distance from Central Axis
Radial Distance given Centripetal Acceleration from Axis
Go Radial Distance from Central Axis = Centripetal acceleration/(Angular Velocity^2)

Constant Angular Velocity given Equation of Free Surface of Liquid Formula

Angular Velocity = sqrt(Height of Crack*(2*[g])/(Distance from Center to Point^2))
ω = sqrt(h*(2*[g])/(d'^2))

What is Free Surface?

A Free surface is the surface of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids, for example liquid water and the air in the Earth's atmosphere.

How to Calculate Constant Angular Velocity given Equation of Free Surface of Liquid?

Constant Angular Velocity given Equation of Free Surface of Liquid calculator uses Angular Velocity = sqrt(Height of Crack*(2*[g])/(Distance from Center to Point^2)) to calculate the Angular Velocity, The Constant Angular Velocity given Equation of Free Surface of Liquid formula is defined as velocity with which fluid is rotating. Angular Velocity is denoted by ω symbol.

How to calculate Constant Angular Velocity given Equation of Free Surface of Liquid using this online calculator? To use this online calculator for Constant Angular Velocity given Equation of Free Surface of Liquid, enter Height of Crack (h) & Distance from Center to Point (d') and hit the calculate button. Here is how the Constant Angular Velocity given Equation of Free Surface of Liquid calculation can be explained with given input values -> 1.534783 = sqrt(12*(2*[g])/(10^2)).

FAQ

What is Constant Angular Velocity given Equation of Free Surface of Liquid?
The Constant Angular Velocity given Equation of Free Surface of Liquid formula is defined as velocity with which fluid is rotating and is represented as ω = sqrt(h*(2*[g])/(d'^2)) or Angular Velocity = sqrt(Height of Crack*(2*[g])/(Distance from Center to Point^2)). Height of Crack is the size of a flaw or crack in a material that can lead to catastrophic failure under a given stress & Distance from center to point is the length of line segment measured from the center of a body to a particular point.
How to calculate Constant Angular Velocity given Equation of Free Surface of Liquid?
The Constant Angular Velocity given Equation of Free Surface of Liquid formula is defined as velocity with which fluid is rotating is calculated using Angular Velocity = sqrt(Height of Crack*(2*[g])/(Distance from Center to Point^2)). To calculate Constant Angular Velocity given Equation of Free Surface of Liquid, you need Height of Crack (h) & Distance from Center to Point (d'). With our tool, you need to enter the respective value for Height of Crack & Distance from Center to Point 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 Angular Velocity?
In this formula, Angular Velocity uses Height of Crack & Distance from Center to Point. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Angular Velocity = sqrt(Centripetal acceleration/Radial Distance from Central Axis)
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