Equation of Free Surface of liquid Calculator

✖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.ⓘ Angular Velocity [ω]			+10% -10%
✖Distance from center to point is the length of line segment measured from the center of a body to a particular point.ⓘ Distance from Center to Point [d']			+10% -10%

✖Height of Crack is the size of a flaw or crack in a material that can lead to catastrophic failure under a given stress.ⓘ Equation of Free Surface of liquid [h]

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Formula

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Equation of Free Surface of liquid

Formula

`"h" = (("ω"*"d'")^2)/(2*"[g]")`

Example

`"20394.32mm"=(("2rad/s"*"10000mm")^2)/(2*"[g]")`

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Equation of Free Surface of liquid Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Crack = ((Angular Velocity*Distance from Center to Point)^2)/(2*[g])
h = ((ω*d')^2)/(2*[g])
This formula uses 1 Constants, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Variables Used

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.
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.
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

Angular Velocity: 2 Radian per Second --> 2 Radian per Second No Conversion Required
Distance from Center to Point: 10000 Millimeter --> 10 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = ((ω*d')^2)/(2*[g]) --> ((2*10)^2)/(2*[g])

Evaluating ... ...

h = 20.3943242595586

STEP 3: Convert Result to Output's Unit

20.3943242595586 Meter -->20394.3242595586 Millimeter (Check conversion here)

FINAL ANSWER

20394.3242595586 ≈ 20394.32 Millimeter <-- Height of Crack

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Liquids in Relative Equilibrium » Fluid Containers Subjected to Constant Rotation » Cylindrical Vessel Containing Liquid Rotating with its Axis Vertical » Equation of Free Surface of liquid

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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National Institute of Technology (NIT), Warangal

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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)

Equation of Free Surface of liquid Formula

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

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 Equation of Free Surface of liquid?

Equation of Free Surface of liquid calculator uses Height of Crack = ((Angular Velocity*Distance from Center to Point)^2)/(2*[g]) to calculate the Height of Crack, The Equation of Free Surface of liquid is defined as general equation of flow of fluid in rotation about vertical axis. Height of Crack is denoted by h symbol.

How to calculate Equation of Free Surface of liquid using this online calculator? To use this online calculator for Equation of Free Surface of liquid, enter Angular Velocity (ω) & Distance from Center to Point (d') and hit the calculate button. Here is how the Equation of Free Surface of liquid calculation can be explained with given input values -> 20.39432 = ((2*10)^2)/(2*[g]).

FAQ

What is Equation of Free Surface of liquid?

The Equation of Free Surface of liquid is defined as general equation of flow of fluid in rotation about vertical axis and is represented as h = ((ω*d')^2)/(2*[g]) or Height of Crack = ((Angular Velocity*Distance from Center to Point)^2)/(2*[g]). 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 & 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 Equation of Free Surface of liquid?

The Equation of Free Surface of liquid is defined as general equation of flow of fluid in rotation about vertical axis is calculated using Height of Crack = ((Angular Velocity*Distance from Center to Point)^2)/(2*[g]). To calculate Equation of Free Surface of liquid, you need Angular Velocity (ω) & Distance from Center to Point (d'). With our tool, you need to enter the respective value for Angular Velocity & 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 Height of Crack?

In this formula, Height of Crack uses Angular Velocity & Distance from Center to Point. We can use 1 other way(s) to calculate the same, which is/are as follows -

Height of Crack = (Atmospheric Pressure-Absolute Pressure+(Specific Weight of Liquid/[g])*(0.5*(Angular Velocity*Radial Distance from Central Axis)^2))/Angular Velocity

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