Height of Container given Radius and Angular Velocity of Container Calculator

✖Height of Free Surface of Liquid without Rotation is defined as the normal height of liquid when the container is not rotating about its axis.ⓘ Height of Free Surface of Liquid without Rotation [h_o]			+10% -10%
✖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%
✖Radius of Cylindrical Container is defined as the radius of the container in which the liquid is kept and will show rotational motion.ⓘ Radius of Cylindrical Container [R]			+10% -10%

✖Height of Container is defined as the height of the cylindrical container in which the liquid is kept.ⓘ Height of Container given Radius and Angular Velocity of Container [H]

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Formula

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Height of Container given Radius and Angular Velocity of Container

Formula

`"H" = "h"_{"o"}+(("ω"^2*"R"^2)/(4*"[g]"))`

Example

`"2.318967m"="2.24m"+((("2.2rad/s")^2*("0.8m")^2)/(4*"[g]"))`

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Height of Container given Radius and Angular Velocity of Container Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Container = Height of Free Surface of Liquid without Rotation+((Angular Velocity^2*Radius of Cylindrical Container^2)/(4*[g]))
H = h_o+((ω^2*R^2)/(4*[g]))
This formula uses 1 Constants, 4 Variables

Constants Used

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

Variables Used

Height of Container - (Measured in Meter) - Height of Container is defined as the height of the cylindrical container in which the liquid is kept.
Height of Free Surface of Liquid without Rotation - (Measured in Meter) - Height of Free Surface of Liquid without Rotation is defined as the normal height of liquid when the container is not rotating about its axis.
Angular Velocity - (Measured in Radian per Second) - 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.
Radius of Cylindrical Container - (Measured in Meter) - Radius of Cylindrical Container is defined as the radius of the container in which the liquid is kept and will show rotational motion.

STEP 1: Convert Input(s) to Base Unit

Height of Free Surface of Liquid without Rotation: 2.24 Meter --> 2.24 Meter No Conversion Required
Angular Velocity: 2.2 Radian per Second --> 2.2 Radian per Second No Conversion Required
Radius of Cylindrical Container: 0.8 Meter --> 0.8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H = h_o+((ω^2*R^2)/(4*[g])) --> 2.24+((2.2^2*0.8^2)/(4*[g]))

Evaluating ... ...

H = 2.31896682353301

STEP 3: Convert Result to Output's Unit

2.31896682353301 Meter --> No Conversion Required

FINAL ANSWER

2.31896682353301 ≈ 2.318967 Meter <-- Height of Container

(Calculation completed in 00.020 seconds)

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University School of Chemical Technology-USCT (GGSIPU), New Delhi

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< 12 Fluids in Rigid Body Motion Calculators

Pressure at Point in Rigid Body Motion of Liquid in Linearly Accelerating Tank

Go Pressure at any Point in Fluid = Initial Pressure-(Density of Fluid*Acceleration in X Direction*Location of Point from Origin in X Direction)-(Density of Fluid*([g]+Acceleration in Z Direction)*Location of Point from Origin in Z Direction)

Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure

Go Distance of Free Surface from Bottom of Container = Height of Free Surface of Liquid without Rotation-((Angular Velocity of Rotating Liquid^2/(4*[g]))*(Radius of Cylindrical Container^2-(2*Radius at any given Point^2)))

Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction

Go Change in Z Coordinate of Liquid's Free Surface = -(Acceleration in X Direction/([g]+Acceleration in Z Direction))*(Location of Point 2 from Origin in X Direction-Location of Point 1 from Origin in X Direction)

Angular Velocity of Liquid in Rotating Cylinder at Constant Pressure when r is Equal to R

Go Angular Velocity of Rotating Liquid = sqrt((4*[g]*(Distance of Free Surface from Bottom of Container-Height of Free Surface of Liquid without Rotation))/(Radius of Cylindrical Container^2))

Angular Velocity of Liquid in Rotating Cylinder just before Liquid Starts Spilling

Go Angular Velocity of Rotating Liquid = sqrt((4*[g]*(Height of Container-Height of Free Surface of Liquid without Rotation))/(Radius of Cylindrical Container^2))

Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure when r is Equal to R

Go Distance of Free Surface from Bottom of Container = Height of Free Surface of Liquid without Rotation+(Angular Velocity of Rotating Liquid^2*Radius of Cylindrical Container^2/(4*[g]))

Free Surface Isobars in Incompressible Fluid with Constant Acceleration

Go Z Coordinate of Free Surface at Constant Pressure = -(Acceleration in X Direction/([g]+Acceleration in Z Direction))*Location of Point from Origin in X Direction

Height of Container given Radius and Angular Velocity of Container

Go Height of Container = Height of Free Surface of Liquid without Rotation+((Angular Velocity^2*Radius of Cylindrical Container^2)/(4*[g]))

Vertical Rise of Free Surface

Go Change in Z Coordinate of Liquid's Free Surface = Z Coordinate of Liquid Free Surface at Point 2-Z Coordinate of Liquid Free Surface at Point 1

Slope of Isobar

Go Slope of Isobar = -(Acceleration in X Direction/([g]+Acceleration in Z Direction))

Centripetal Acceleration of Fluid Particle Rotating with Constant Angular Velocity

Go Centripetal Acceleration of Fluid Particle = Distance of Fluid Particle*(Angular Velocity^2)

Slope of Isobar given Inclination Angle of Free Surface

Go Slope of Isobar = -tan(Inclination Angle of Free Surface)

Height of Container given Radius and Angular Velocity of Container Formula

Height of Container = Height of Free Surface of Liquid without Rotation+((Angular Velocity^2*Radius of Cylindrical Container^2)/(4*[g]))
H = h_o+((ω^2*R^2)/(4*[g]))

What is Fluid Mechanics?

Fluid dynamics is “the branch of applied science that is concerned with the movement of liquids and gases”. It involves a wide range of applications such as calculating force & moments, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space, and modelling fission weapon detonation.

What is Hydrostatic Pressure?

Hydrostatic pressure is defined as “The pressure exerted by a fluid at equilibrium at any point of time due to the force of gravity”. Hydrostatic pressure is proportional to the depth measured from the surface as the weight of the fluid increases when a downward force is applied. The fluid pressure can be caused by gravity, acceleration or forces when in a closed container. Consider a layer of water from the top of the bottle. There is the pressure exerted by the layer of water acting on the sides of the bottle. As we move down from the top of the bottle to the bottom, the pressure exerted by the top layer on the bottom adds up. This phenomenon is responsible for more pressure at the bottom of the container.

How to Calculate Height of Container given Radius and Angular Velocity of Container?

Height of Container given Radius and Angular Velocity of Container calculator uses Height of Container = Height of Free Surface of Liquid without Rotation+((Angular Velocity^2*Radius of Cylindrical Container^2)/(4*[g])) to calculate the Height of Container, The Height of Container given Radius and Angular Velocity of Container formula is defined as the function height of free surface of liquid, radius of container, angular velocity of container and gravitational acceleration. During rigid-body motion of a liquid in a rotating cylinder, the surfaces of constant pressure are paraboloids of revolution. Pressure is a fundamental property, and it is hard to imagine a significant fluid flow problem that does not involve pressure. Height of Container is denoted by H symbol.

How to calculate Height of Container given Radius and Angular Velocity of Container using this online calculator? To use this online calculator for Height of Container given Radius and Angular Velocity of Container, enter Height of Free Surface of Liquid without Rotation (h_o), Angular Velocity (ω) & Radius of Cylindrical Container (R) and hit the calculate button. Here is how the Height of Container given Radius and Angular Velocity of Container calculation can be explained with given input values -> 2.318967 = 2.24+((2.2^2*0.8^2)/(4*[g])).

FAQ

What is Height of Container given Radius and Angular Velocity of Container?

The Height of Container given Radius and Angular Velocity of Container formula is defined as the function height of free surface of liquid, radius of container, angular velocity of container and gravitational acceleration. During rigid-body motion of a liquid in a rotating cylinder, the surfaces of constant pressure are paraboloids of revolution. Pressure is a fundamental property, and it is hard to imagine a significant fluid flow problem that does not involve pressure and is represented as H = h_o+((ω^2*R^2)/(4*[g])) or Height of Container = Height of Free Surface of Liquid without Rotation+((Angular Velocity^2*Radius of Cylindrical Container^2)/(4*[g])). Height of Free Surface of Liquid without Rotation is defined as the normal height of liquid when the container is not rotating about its axis, 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 & Radius of Cylindrical Container is defined as the radius of the container in which the liquid is kept and will show rotational motion.

How to calculate Height of Container given Radius and Angular Velocity of Container?

The Height of Container given Radius and Angular Velocity of Container formula is defined as the function height of free surface of liquid, radius of container, angular velocity of container and gravitational acceleration. During rigid-body motion of a liquid in a rotating cylinder, the surfaces of constant pressure are paraboloids of revolution. Pressure is a fundamental property, and it is hard to imagine a significant fluid flow problem that does not involve pressure is calculated using Height of Container = Height of Free Surface of Liquid without Rotation+((Angular Velocity^2*Radius of Cylindrical Container^2)/(4*[g])). To calculate Height of Container given Radius and Angular Velocity of Container, you need Height of Free Surface of Liquid without Rotation (h_o), Angular Velocity (ω) & Radius of Cylindrical Container (R). With our tool, you need to enter the respective value for Height of Free Surface of Liquid without Rotation, Angular Velocity & Radius of Cylindrical Container 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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