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

STEP 0: Pre-Calculation Summary
Formula Used
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)
ΔZs = -(ax/([g]+az))*(x2-x1)
This formula uses 1 Constants, 5 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
Variables Used
Change in Z Coordinate of Liquid's Free Surface - Change in Z Coordinate of Liquid's Free Surface is defined as the difference between the z coordinate at point 2 and 1.
Acceleration in X Direction - (Measured in Meter per Square Second) - Acceleration in X Direction is the net acceleration in x direction.
Acceleration in Z Direction - (Measured in Meter per Square Second) - Acceleration in Z Direction is the net acceleration in z direction.
Location of Point 2 from Origin in X Direction - Location of Point 2 from Origin in X Direction is defined as the length or distance of that point 2 from origin in x direction only.
Location of Point 1 from Origin in X Direction - Location of Point 1 from Origin in X Direction is defined as the length or distance of that point 2 from origin in x direction only.
STEP 1: Convert Input(s) to Base Unit
Acceleration in X Direction: 1.36 Meter per Square Second --> 1.36 Meter per Square Second No Conversion Required
Acceleration in Z Direction: 1.23 Meter per Square Second --> 1.23 Meter per Square Second No Conversion Required
Location of Point 2 from Origin in X Direction: 0.85 --> No Conversion Required
Location of Point 1 from Origin in X Direction: 0.25 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ΔZs = -(ax/([g]+az))*(x2-x1) --> -(1.36/([g]+1.23))*(0.85-0.25)
Evaluating ... ...
ΔZs = -0.0739354786099043
STEP 3: Convert Result to Output's Unit
-0.0739354786099043 --> No Conversion Required
FINAL ANSWER
-0.0739354786099043 -0.073935 <-- Change in Z Coordinate of Liquid's Free Surface
(Calculation completed in 00.004 seconds)

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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)

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

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)
ΔZs = -(ax/([g]+az))*(x2-x1)

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

Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction calculator uses 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) to calculate the Change in Z Coordinate of Liquid's Free Surface, The Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction formula is defined as the function of Acceleration on both x and z direction, gravitational acceleration and distance of the point from origin in x direction. 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. Change in Z Coordinate of Liquid's Free Surface is denoted by ΔZs symbol.

How to calculate Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction using this online calculator? To use this online calculator for Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction, enter Acceleration in X Direction (ax), Acceleration in Z Direction (az), Location of Point 2 from Origin in X Direction (x2) & Location of Point 1 from Origin in X Direction (x1) and hit the calculate button. Here is how the Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction calculation can be explained with given input values -> -0.073935 = -(1.36/([g]+1.23))*(0.85-0.25).

FAQ

What is Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction?
The Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction formula is defined as the function of Acceleration on both x and z direction, gravitational acceleration and distance of the point from origin in x direction. 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 ΔZs = -(ax/([g]+az))*(x2-x1) or 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). Acceleration in X Direction is the net acceleration in x direction, Acceleration in Z Direction is the net acceleration in z direction, Location of Point 2 from Origin in X Direction is defined as the length or distance of that point 2 from origin in x direction only & Location of Point 1 from Origin in X Direction is defined as the length or distance of that point 2 from origin in x direction only.
How to calculate Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction?
The Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction formula is defined as the function of Acceleration on both x and z direction, gravitational acceleration and distance of the point from origin in x direction. 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 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). To calculate Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction, you need Acceleration in X Direction (ax), Acceleration in Z Direction (az), Location of Point 2 from Origin in X Direction (x2) & Location of Point 1 from Origin in X Direction (x1). With our tool, you need to enter the respective value for Acceleration in X Direction, Acceleration in Z Direction, Location of Point 2 from Origin in X Direction & Location of Point 1 from Origin in X Direction 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 Change in Z Coordinate of Liquid's Free Surface?
In this formula, Change in Z Coordinate of Liquid's Free Surface uses Acceleration in X Direction, Acceleration in Z Direction, Location of Point 2 from Origin in X Direction & Location of Point 1 from Origin in X Direction. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • 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
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