Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure 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 of Rotating Liquid 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 of Rotating Liquid [ω_Liquid]			+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%
✖Radius at any given Point is defined as the radius of the point in liquid taken into consideration.ⓘ Radius at any given Point [r_p]			+10% -10%

✖Distance of Free Surface from Bottom of Container is defined as the distance between the top surface and bottom of container.ⓘ Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure [Z_s]

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

Formula

`"Z"_{"s"} = "h"_{"o"}-(("ω"_{"Liquid"}^2/(4*"[g]"))*("R"^2-(2*"r"_{"p"}^2)))`

Example

`"2.20998m"="2.24m"-((("1.6rad/s")^2/(4*"[g]"))*(("0.8m")^2-(2*("0.3m")^2)))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
Z_s = h_o-((ω_Liquid^2/(4*[g]))*(R^2-(2*r_p^2)))
This formula uses 1 Constants, 5 Variables

Constants Used

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

Variables Used

Distance of Free Surface from Bottom of Container - (Measured in Meter) - Distance of Free Surface from Bottom of Container is defined as the distance between the top surface and bottom of container.
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 of Rotating Liquid - (Measured in Radian per Second) - Angular Velocity of Rotating Liquid 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.
Radius at any given Point - (Measured in Meter) - Radius at any given Point is defined as the radius of the point in liquid taken into consideration.

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 of Rotating Liquid: 1.6 Radian per Second --> 1.6 Radian per Second No Conversion Required
Radius of Cylindrical Container: 0.8 Meter --> 0.8 Meter No Conversion Required
Radius at any given Point: 0.3 Meter --> 0.3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z_s = h_o-((ω_Liquid^2/(4*[g]))*(R^2-(2*r_p^2))) --> 2.24-((1.6^2/(4*[g]))*(0.8^2-(2*0.3^2)))

Evaluating ... ...

Z_s = 2.20997955468993

STEP 3: Convert Result to Output's Unit

2.20997955468993 Meter --> No Conversion Required

FINAL ANSWER

2.20997955468993 ≈ 2.20998 Meter <-- Distance of Free Surface from Bottom of Container

(Calculation completed in 00.020 seconds)

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Home » Engineering » Chemical Engineering » Fluid Dynamics » Hydrostatic Forces on Surfaces » Fluids in Rigid Body Motion » Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure

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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)

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

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

Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure calculator uses 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))) to calculate the Distance of Free Surface from Bottom of Container, The Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure formula is defined as the function of height of the free surface of liquid without rotation, angular velocity, gravitational acceleration, radius of container in which the liquid is kept and radius at nay given point in the liquid. 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. Distance of Free Surface from Bottom of Container is denoted by Z_s symbol.

How to calculate Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure using this online calculator? To use this online calculator for Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure, enter Height of Free Surface of Liquid without Rotation (h_o), Angular Velocity of Rotating Liquid (ω_Liquid), Radius of Cylindrical Container (R) & Radius at any given Point (r_p) and hit the calculate button. Here is how the Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure calculation can be explained with given input values -> 2.20998 = 2.24-((1.6^2/(4*[g]))*(0.8^2-(2*0.3^2))).

FAQ

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

The Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure formula is defined as the function of height of the free surface of liquid without rotation, angular velocity, gravitational acceleration, radius of container in which the liquid is kept and radius at nay given point in the liquid. 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 Z_s = h_o-((ω_Liquid^2/(4*[g]))*(R^2-(2*r_p^2))) or 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))). 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 of Rotating Liquid 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 & Radius at any given Point is defined as the radius of the point in liquid taken into consideration.

How to calculate Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure?

The Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure formula is defined as the function of height of the free surface of liquid without rotation, angular velocity, gravitational acceleration, radius of container in which the liquid is kept and radius at nay given point in the liquid. 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 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))). To calculate Equation for Free Surface of Liquid in Rotating Cylinder at Constant Pressure, you need Height of Free Surface of Liquid without Rotation (h_o), Angular Velocity of Rotating Liquid (ω_Liquid), Radius of Cylindrical Container (R) & Radius at any given Point (r_p). With our tool, you need to enter the respective value for Height of Free Surface of Liquid without Rotation, Angular Velocity of Rotating Liquid, Radius of Cylindrical Container & Radius at any given 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 Distance of Free Surface from Bottom of Container?

In this formula, Distance of Free Surface from Bottom of Container uses Height of Free Surface of Liquid without Rotation, Angular Velocity of Rotating Liquid, Radius of Cylindrical Container & Radius at any given Point. We can use 1 other way(s) to calculate the same, which is/are as follows -

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]))

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