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

✖Acceleration in X Direction is the net acceleration in x direction.ⓘ Acceleration in X Direction [a_x]			+10% -10%
✖Acceleration in Z Direction is the net acceleration in z direction.ⓘ Acceleration in Z Direction [a_z]			+10% -10%
✖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 2 from Origin in X Direction [x₂]			+10% -10%
✖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.ⓘ Location of Point 1 from Origin in X Direction [x₁]			+10% -10%

✖Change in Z Coordinate of Liquid's Free Surface is defined as the difference between the z coordinate at point 2 and 1.ⓘ Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction [ΔZ_s]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Chemical Engineering Formula PDF PDF Image

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)
ΔZ_s = -(a_x/([g]+a_z))*(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

ΔZ_s = -(a_x/([g]+a_z))*(x₂-x₁) --> -(1.36/([g]+1.23))*(0.85-0.25)

Evaluating ... ...

ΔZ_s = -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)

You are here -

Home » Engineering » Chemical Engineering » Fluid Dynamics » Hydrostatic Forces on Surfaces » Fluids in Rigid Body Motion » Vertical Rise or Drop of Free Surface given Acceleration in X and Z Direction

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

Prerana Bakli has verified this Calculator and 1600+ more calculators!

< Fluids in Rigid Body Motion Calculators

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

LaTeX 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)

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

LaTeX 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)

Free Surface Isobars in Incompressible Fluid with Constant Acceleration

LaTeX 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

Vertical Rise of Free Surface

LaTeX 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

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

LaTeX Go

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 ΔZ_s 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 (a_x), Acceleration in Z Direction (a_z), 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 ΔZ_s = -(a_x/([g]+a_z))*(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 (a_x), Acceleration in Z Direction (a_z), 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

Home

FREE PDFs

🔍 Search