Slope of Isobar given Inclination Angle of Free Surface Calculator

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)

Variables Used

Slope of Isobar - Slope of Isobar is defined as the slope of the Free surface i.e. dZisobar/dx.
Inclination Angle of Free Surface - (Measured in Radian) - Inclination Angle of Free Surface is defined as the angle that the free surface makes with the horizontal.

STEP 1: Convert Input(s) to Base Unit

Inclination Angle of Free Surface: 5 Degree --> 0.0872664625997001 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S = -tan(θ) --> -tan(0.0872664625997001)

Evaluating ... ...

S = -0.0874886635259075

STEP 3: Convert Result to Output's Unit

-0.0874886635259075 --> No Conversion Required

FINAL ANSWER

-0.0874886635259075 ≈ -0.087489 <-- Slope of Isobar

(Calculation completed in 00.004 seconds)

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Credits

Created by Ayush gupta

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

Ayush gupta has created this Calculator and 300+ more calculators!

Verified by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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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)

Slope of Isobar given Inclination Angle of Free Surface Formula

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

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 Slope of Isobar given Inclination Angle of Free Surface?

Slope of Isobar given Inclination Angle of Free Surface calculator uses Slope of Isobar = -tan(Inclination Angle of Free Surface) to calculate the Slope of Isobar, The Slope of Isobar given Inclination Angle of Free Surface formula is defined as the function of inclination angle. Thus we conclude that the isobars (including the free surface) in an incompressible fluid with constant acceleration in linear motion are parallel surfaces whose slope is in the xz-plane. The free surface of such a fluid is a plane surface, and it is inclined unless ax = 0 (the acceleration is in the vertical direction only). Also, conservation of mass, together with the assumption of incompressibility (𝜌 = constant), requires that the volume of the fluid remain constant before and during acceleration. Therefore, the rise of fluid level on one side must be balanced by a drop of fluid level on the other side. This is true regardless of the shape of the container, provided that the liquid is continuous throughout the container. Slope of Isobar is denoted by S symbol.

How to calculate Slope of Isobar given Inclination Angle of Free Surface using this online calculator? To use this online calculator for Slope of Isobar given Inclination Angle of Free Surface, enter Inclination Angle of Free Surface (θ) and hit the calculate button. Here is how the Slope of Isobar given Inclination Angle of Free Surface calculation can be explained with given input values -> -0.087489 = -tan(0.0872664625997001).

FAQ

What is Slope of Isobar given Inclination Angle of Free Surface?

The Slope of Isobar given Inclination Angle of Free Surface formula is defined as the function of inclination angle. Thus we conclude that the isobars (including the free surface) in an incompressible fluid with constant acceleration in linear motion are parallel surfaces whose slope is in the xz-plane. The free surface of such a fluid is a plane surface, and it is inclined unless ax = 0 (the acceleration is in the vertical direction only). Also, conservation of mass, together with the assumption of incompressibility (𝜌 = constant), requires that the volume of the fluid remain constant before and during acceleration. Therefore, the rise of fluid level on one side must be balanced by a drop of fluid level on the other side. This is true regardless of the shape of the container, provided that the liquid is continuous throughout the container and is represented as S = -tan(θ) or Slope of Isobar = -tan(Inclination Angle of Free Surface). Inclination Angle of Free Surface is defined as the angle that the free surface makes with the horizontal.

How to calculate Slope of Isobar given Inclination Angle of Free Surface?

The Slope of Isobar given Inclination Angle of Free Surface formula is defined as the function of inclination angle. Thus we conclude that the isobars (including the free surface) in an incompressible fluid with constant acceleration in linear motion are parallel surfaces whose slope is in the xz-plane. The free surface of such a fluid is a plane surface, and it is inclined unless ax = 0 (the acceleration is in the vertical direction only). Also, conservation of mass, together with the assumption of incompressibility (𝜌 = constant), requires that the volume of the fluid remain constant before and during acceleration. Therefore, the rise of fluid level on one side must be balanced by a drop of fluid level on the other side. This is true regardless of the shape of the container, provided that the liquid is continuous throughout the container is calculated using Slope of Isobar = -tan(Inclination Angle of Free Surface). To calculate Slope of Isobar given Inclination Angle of Free Surface, you need Inclination Angle of Free Surface (θ). With our tool, you need to enter the respective value for Inclination Angle of Free Surface 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 Slope of Isobar?

In this formula, Slope of Isobar uses Inclination Angle of Free Surface. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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