Name: fluid pressure in an accelerating elevator
Uploaded: 2023-05-16T08:18:41.000Z
Duration: 1 min 17 s
Channel: JoVE

K12 Standards

Alabama Course of Study Science

9-12

Physics

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

9-12.P.1.4.d

Accelerating Fluids

위로 가속하는 엘리베이터에 설치된 비커를 생각해 보십시오. 비커에 극미한 단면적을 가진 높이 h의 얇은 실린더가 있다고 가정합니다.
이 극소 실린더에 포함된 액체에는 세 가지 수직 힘이 작용합니다.
그들은 바닥 표면 아래에 존재하는 액체로 인한 상향 힘, 상단 표면 위의 액체로 인한 하향 힘, 무게로 인한 하향 힘입니다.
액체가 가속하기 때문에 뉴턴의 제2법칙에서 관계를 얻습니다.
유체 요소의 질량을 밀도로 나타내면 방정식이 단순화되고 가속 유체에 대한 압력 차이에 대한 표현이 얻어집니다.
물체가 동일한 가속 액체 안에 잠겨 있다고 가정합니다. 그것은 부력과 그 무게로 인한 힘을 경험합니다.
단순화를 위해 몸은 동일한 액체의 동일한 부피로 대체됩니다. 이것은 비커 내부의 전체 액체를 동일한 가속도를 경험하는 균일한 질량으로 만듭니다.
뉴턴의 제2법칙에서 부력은 가속도로 표현됩니다.

유체 가속

유체가 등가속도 상태에 있을 때 압력과 부력 방정식이 수정됩니다. 일정한 가속도 a로 위로 가속되는 엘리베이터에 비커가 놓여 있다고 가정해 보겠습니다. 비이커 안에 단면적 ΔS이 무한대이고 높이가 h인 얇은 원통이 있다고 가정합니다.

이 극소 원통 내 액체의 움직임을 고려하여 압력차를 구합니다. 이 액체에는 세 가지 수직 힘이 작용합니다.

<ol>
	<li>원통 바닥 표면 아래에 존재하는 액체로 인해 위쪽으로 힘이 가해집니다.</li>
	<li>원통 상단 표면 위의 액체로 인한 하향 힘</li>
	<li>하향력은 원통형 요소의 무게로 인해 발생합니다.</li>
</ol>

이 세 가지 힘에 의해 액체는 위쪽으로 가속됩니다. 뉴턴의 제2법칙을 사용하면 다음과 같은 식이 얻어집니다.

<img alt="Equation1" src="/files/ftp_upload/14713/14713_Equation_1.svg" style="text-align: center; height: 16px;" />

유체 요소의 질량을 밀도(⍴)로 표현하면 방정식이 단순화되고 가속하는 유체에 대한 압력 차이에 대한 식이 얻어집니다.

<img alt="Equation2" src="/files/ftp_upload/14713/14713_Equation_2.svg" style="text-align: center; height: 18px;" />

부력을 얻기 위해 물체가 동일한 가속 액체 안에 담갔다고 가정합니다. 무게로 인해 부력과 힘을 경험합니다. 단순화를 위해 본체는 동일한 양의 동일한 액체로 대체됩니다. 뉴턴의 제2법칙으로부터 부력은 가속도로 표현되며 다음과 같은 식을 얻게 된다.

<img alt="Equation3" src="/files/ftp_upload/14713/14713_Equation_3.svg" style="text-align: center; height: 18px;" />

유체가 일정한 가속도 상태에 있으면 압력 및 부력 방정식이 수정됩니다. 비커가 엘리베이터에 배치되어 가속한다고 가정합니다.

/files/media/science-education/science-education-thumbs/14713.jpg

Education

교육

JoVE Core

물리학

Unit 1

제1단원

Fluid Mechanics

유체역학

KEY TERMS AND CONCEPTS

주요 용어 및 개념

fluid pressure in an accelerating elevator

Fluid pressure changes when a liquid accelerates inside a moving container. A beaker placed in an elevator that moves upward with constant acceleration is one example. In this setup, the pressure and buoyant force equations must be modified.

To find the pressure difference, the liquid is modeled as a thin vertical cylinder with height h and an infinitesimal cross-sectional area, ΔS. Three vertical forces act on this small fluid element. The liquid below the bottom surface pushes upward, the liquid above the top surface pushes downward, and the element’s weight also acts downward. Because the cylinder accelerates upward, Newton’s second law is used to relate these forces.

The mass of the fluid element is written in terms of density, ρ, to simplify the result. This gives the pressure difference for an accelerating fluid. The same idea is then used to determine buoyant force.

For buoyancy, a body is placed in the same accelerating liquid. It experiences buoyant force and its own weight. To make the analysis easier, the body is replaced by an equal volume of the same liquid. Newton’s second law then gives the buoyant force in terms of the acceleration, leading to the final expression.

Fluid Pressure in an Accelerating Elevator

fluid-pressure-in-an-accelerating-elevator

characteristics of fluids

Fluid Behavior Under Force

Fluid behavior under force differs from the behavior of solids. When a force acts parallel to the top surface of a solid, the solid resists it because of internal friction between its layers. This is called shearing resistance. If the force is removed, the shearing forces help the solid return to its original shape. Other deformation forces can also change the shape of a solid for a short time, as long as the force stays below a threshold magnitude. Solids usually keep their shape, which makes...

/files/media/science-education/science-education-thumbs/14710.jpg

density

Density, Floating, and Specific Gravity

Density helps explain why objects sink or float in a fluid. It is also useful for identifying a substance and for learning about its phase and substructure. The SI unit of density is kg/m3, and the cgs unit is g/cm3. Liquids and solids usually have densities that are roughly comparable. That matches the fact that their atoms are in close contact. Gases have much lower densities than liquids and solids because their atoms are separated by large amounts of empty space. Density does not always...

pressure of fluids

Fluid Pressure in Everyday Life

Fluid pressure appears in many everyday situations, including blood pressure and weather systems. The same force can have a very different effect depending on the area it acts on. A force spread over 1 mm² creates 100 times more pressure than the same force spread over 1 cm². That is why a sharp needle can pierce skin with a small force, while the same force from a finger usually does not. Pressure is especially important when studying fluids. A fluid does not offer much resistance to a force...

variation of atmospheric pressure

Atmospheric Pressure and Altitude

Atmospheric pressure and altitude are closely linked. As height increases, atmospheric pressure decreases. This happens because the gravitational force per unit area becomes smaller as we move away from Earth’s surface. To describe this change, the atmosphere is treated with a constant air temperature at a given altitude. The ideal gas law of thermodynamics is also used as a good approximation for the air. Let p(y) be the atmospheric pressure at height y. The density ρ at y, the temperature T...

/files/media/science-education/science-education-thumbs/14711.jpg

pascal's law

Pascal’s Principle in Static Fluids

Pascal’s principle explains how pressure changes move through a fluid that is not flowing. A fluid at rest is in static equilibrium. If the fluid is water, it is in hydrostatic equilibrium. In this state, the net force on any part of the fluid must be zero, or the fluid will begin to flow. Blaise Pascal described this idea in 1653 in Treatise on the Equilibrium of Liquids. He showed that when pressure changes in an enclosed fluid, that change is transmitted without loss through the fluid and...

application of pascal's law

Hydraulic Force Transfer with Pascal's Law

Hydraulic force transfer uses Pascal's law to move pressure through an enclosed fluid. Pascal showed experimentally that a change in pressure applied to a confined fluid is transmitted undiminished throughout the fluid and to the walls of its container. That idea is the basis of hydraulics, a major part of modern mechanical technology. Hydraulic systems appear in automotive brakes, hydraulic jacks, and many other machines. A simple hydraulic system uses two pistons at the same height. Because...

pressure gauges

Gauge vs Absolute Pressure

Pressure gauges often show pressure relative to atmospheric pressure. Many gauges, including those on scuba tanks, are set to read zero at atmospheric pressure. That reading is called gauge pressure. When the pressure inside the tank is higher than atmospheric pressure, the gauge shows a positive value. Some gauges can also measure negative pressure. This is useful in a vacuum chamber, which is a rigid chamber where some air has been pumped out. Because the pressure inside the chamber is below...

/files/media/science-education/science-education-thumbs/14712.jpg

archimedes' principle

Buoyant Force from Fluid Pressure

Archimedes' principle explains buoyant force in a fluid. An upward buoyant force acts on an object that is partially or fully immersed in a fluid. This force is equal to the weight of the fluid displaced by the object. To see why an object floats, imagine removing a submerged object from the fluid. The space it occupied would be filled by fluid with weight w_fl. That weight is supported by the surrounding fluid, so the buoyant force must match the weight of the displaced fluid. The principle...

density and archimedes' principle

How Buoyancy Depends on Density

Buoyancy and density explain why some objects float and others sink. A lump of clay sinks in water, but the same clay can float when it is shaped like a boat. The change in shape lets it displace more water, which increases the buoyant force even though its mass stays the same. The same idea applies to steel ships. An object with an average density lower than the surrounding fluid will float. The fluid has more mass in the same volume, so it has more weight. The buoyant force equals the weight...

accelerating fluids

Fluid pressure changes when a liquid accelerates inside a moving container. A beaker placed in an elevator that moves upward with constant acceleration is one example. In this setup, the pressure and buoyant force equations must be modified. To find the pressure difference, the liquid is modeled as a thin vertical cylinder with height h and an infinitesimal cross-sectional area, ΔS. Three vertical forces act on this small fluid element. The liquid below the bottom surface pushes upward, the...

surface tension and surface energy

Why Liquids Form Drops and Float

Surface tension and surface energy explain why liquids behave the way they do at their surface. A paint brush moves freely in water, but its bristles stick together after it is taken out. That change is caused by surface tension. Inside a liquid, bulk molecules feel attractive forces from nearby molecules in all directions. At the surface, molecules feel a net downward pull from the molecules below them. Because of this imbalance, the liquid surface acts like a stretched membrane and tries to...

/files/media/science-education/science-education-thumbs/14714.jpg

excess pressure inside a drop and a bubble

excess-pressure-inside-a-drop-and-a-bubble

Surface Tension in Drops and Bubbles

Surface tension sets the pressure difference in small drops and bubbles. For a tiny liquid drop, gravity can be neglected, so the drop is treated as spherical. It can also be viewed as two equal hemispherical drops joined together by surface tension. The forces on the drop come from three sources. The liquid inside pushes outward, the air outside pushes inward, and surface tension acts along the diameter between the two hemispheres. Since surface tension is force per unit length, it creates a...

/files/media/science-education/science-education-thumbs/14715.jpg

buoyancy

Buoyant Force in Sinking and Floating

Buoyant force explains why objects float, sink, or stay suspended in a fluid. A fluid can be a liquid or a gas, and every object placed in it experiences this upward force. A metal ball sinks, while a rubber ball floats. A submarine also changes its buoyancy to move up or down. The force comes from pressure changes in the fluid. Fluid pressure increases with depth because the weight of the fluid above also increases. That means the bottom of an object feels more pressure than the top. This...

contact angle

Wetting and Surface Curvature

Wetting and surface curvature describe how a liquid behaves where it meets a solid. When a solid is dipped into a liquid, the liquid surface can bend near the contact line. In some cases, the liquid rises along the solid. In others, the surface becomes convex or depressed near the solid. This behavior comes from cohesive and adhesive forces. Adhesive force is the attraction between molecules of different materials, such as a solid and a liquid. Cohesive force is the attraction between...

/files/media/science-education/science-education-thumbs/14737.jpg

rise of liquid in a capillary tube

Capillary Action in Thin Tubes

Capillary action explains why liquid can rise or fall in a very thin tube compared with the liquid around it. A capillary is a narrow cylindrical tube, and the effect becomes noticeable when it is dipped into a liquid. The movement happens because two forces act in opposite directions. Cohesive forces make liquid molecules stick to each other, so the liquid tends to hold together and form a rounded shape. Adhesive forces pull the liquid toward the walls of the container. In a narrow glass...

/files/media/science-education/science-education-thumbs/14738.jpg

laminar and turbulent flow

Fluid Motion Patterns in Air and Water

Fluid dynamics studies fluids in motion. Scientists often use velocity vectors to show fluid motion in places like meteorology. For example, wind in the atmosphere can be mapped with vectors that show the speed and direction of the wind at each point. Another way to show fluid motion is with a streamline. A streamline shows the path of a small volume of fluid as it flows. When the flow changes with time, the streamlines do not match the flow lines. The fluid velocity is always tangential to...

equation of continuity

Fluid Flow in Narrowing Pipes

Fluid flow in a pipe is described by flow rate and average speed. Flow rate, or volume flow rate, is the amount of fluid that passes a point through an area in a given time. It depends on both how fast the fluid moves and the size and shape of the conduit. For a river or pipe, a greater speed usually means a greater flow rate. A larger cross-sectional area also increases flow rate. That is why the same fluid can move differently through conduits of different sizes. The relationship becomes...

bernoulli's equation

Fluid Pressure and Speed in Motion

Bernoulli's equation connects fluid pressure with fluid speed. It helps explain why moving fluids can create pressure changes in everyday situations. One example is when two trains pass each other quickly and seem to pull inward. The same effect can happen when two cars pass each other at high speed. As the air between the trains or cars speeds up, its pressure drops. The air on the outside stays at atmospheric pressure. That pressure difference creates a net inward force on the vehicles.

bernoulli's principle

Fluid Pressure and Speed Changes

Bernoulli's equation links fluid pressure and fluid speed in a static, incompressible fluid. For horizontal flow, where gravitational energy density stays constant, the equation is especially useful. In that setting, the result is known as Bernoulli's principle. Bernoulli's principle says that fluid pressure drops when speed increases, and pressure rises when speed decreases. This pressure-speed relationship helps explain how moving fluids behave in simple flow situations. It also provides a...

bernoulli's principle: applications

Bernoulli's Principle in Fluid Devices

Bernoulli's principle helps explain how many fluid devices work when the fluid moves at a constant height. It is useful for devices that use fast flow to create low pressure and for devices that measure fluid speed. Some devices use this pressure change to pull one fluid into another. These are called entrainment devices. A Bunsen burner uses an adjustable gas nozzle to entrain air for proper combustion. An atomizer uses a squeeze bulb to make a jet of air that pulls perfume drops into the...

/files/media/science-education/science-education-thumbs/14739.jpg

energy conservation and bernoulli's equation

energy-conservation-and-bernoulli-s-equation

Bernoulli’s Equation in Streamlined Flow

Bernoulli’s equation describes energy in a moving fluid. It comes from the conservation of energy principle, or the work-energy theorem, applied to an incompressible, inviscid fluid in laminar, steady, irrotational flow. The equation says that pressure energy, potential energy, and kinetic energy per unit volume stay constant along a streamline. Each term has the units of energy per unit volume. The kinetic energy per unit volume is called kinetic energy density, and the potential energy per...

/files/media/science-education/science-education-thumbs/14753.jpg

viscosity

Viscosity and How Fluids Flow

Viscosity describes how easily a fluid flows. Water moves quickly, while honey and maple syrup flow slowly and stick to a surface. That difference comes from fluid friction between liquid layers and between a fluid and the material around it. In this example, water has a lower viscosity than honey and maple syrup. Viscosity is measured in newton-second per meter squared (N·s/m2) or pascal-second (Pa·s). It also changes with temperature and can differ from one fluid to another by several orders...

poiseuille's law and reynolds number

Fluid Resistance, Viscosity, and Flow Regime

Fluid resistance, viscosity, and flow regime shape how liquid moves through a horizontal tube. Fluid flows from high pressure to low pressure. The flow rate, Q, is the ratio of the pressure difference to the resistance in the tube. A larger pressure difference gives a higher flow rate. Poiseuille's law describes laminar flow of an incompressible fluid in a tube. In this relation, the factors that affect flow rate except pressure are grouped into resistance. Resistance depends on the tube size...

stokes' law

Terminal Velocity in a Viscous Fluid

Viscous forces act like friction in a liquid. They resist the relative motion of molecules and pull back on a solid body moving through the fluid. The size of this force depends on the body’s shape and size, its speed, and the liquid’s viscosity, density, and temperature. For a spherical solid object, the force in a fluid is described by Stokes’ law. This law applies only at low Reynolds number, when the flow is laminar and not turbulent. Experiments show that the force is proportional to the...

/files/media/science-education/science-education-thumbs/14736.jpg

key terms and concepts

See how constant acceleration changes fluid pressure and buoyant force in an elevator example. Learn the force balance and Newton’s second law result.

Fluid Pressure in an Accelerating Elevator | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

Introduction to Scalars

Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, &#34;a class period lasts ...

Introduction to Vectors

To define some physical quantities, there is a need to specify both magnitude as well as direction. For example, when the U.S. Coast Guard dispatches a ...

Position and Displacement

The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary ...

Average Velocity

To calculate the other physical quantities in kinematics, we must introduce the time variable. The time variable allows us not only to state the position ...

Instantaneous Velocity - I

The average velocity during a time interval cannot tell us how fast or in what direction a particle is moving at any given time during the interval. To ...

Instantaneous Velocity - II

Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity of an object ...

Average Acceleration

The importance of understanding acceleration spans our day-to-day experiences, as well as the vast reaches of outer space and the tiny world of subatomic ...

Instantaneous Acceleration

Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration ...

Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position ...

average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity Vectors

To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an object ...

Acceleration Vectors

In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, &#916;v, therefore the ...

Direction of Acceleration Vectors

Acceleration occurs when velocity changes in magnitude (an increase or decrease in speed), direction, or both. Although acceleration is in the direction ...

1. Obtain, evaluate, and communicate ideas about kinematics, including scalar quantities (distance and speed) and vector quantities (position, displacement, velocity, and acceleration).

9-12.P.1.1

velocity-and-position-by-graphical-method

Velocity and Position by Graphical Method

Velocity and position can be calculated from the known function of acceleration as a function of time. The total area under the acceleration-time graph ...

a. Analyze data to create and interpret graphs of position, velocity, and acceleration versus time for one-dimensional motion.

9-12.P.1.1.a

Kinematic Equations - I

When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of ...

Kinematic Equations - II

The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant ...

Kinematic Equations - III

The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity ...

Kinematic Equations: Problem Solving

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the ...

Free-falling Bodies: Introduction

All objects, neglecting air resistance, fall with the same acceleration towards the Earth&#39;s center due to the force exerted by the Earth&#39;s ...

Free-falling Bodies: Example

An object falling without any air resistance under the influence of gravitational force is said to be in free-fall. For free-falling bodies, the ...

b. Analyze free fall motion using one-dimensional kinematics to determine the acceleration due to gravity (g).

9-12.P.1.1.b

Projectile Motion

An object thrown in the air follows a parabolic path under the influence of Earth&#39;s gravitational force. The motion of such an object is called ...

/files/media/science-education/science-education-thumbs/12634.jpg

Projectile Motion: Equations

Projectile motion is commonly observed in our day-to-day life. For example, a basketball thrown by a player, an arrow shot from a bow, and kids jumping ...

Projectile Motion: Example

The theory of projectile motion is very useful for players of several sports to improve their performance. For example, a javelin thrower needs to throw ...

c. Analyze and interpret data to explain changes in the vector quantities of position, velocity, and acceleration in two-dimensional projectile motion, including projectiles launched horizontally and at an angle.

9-12.P.1.1.c

d. Use mathematics and computational thinking to solve problems, using kinematics equations in both one- and two-dimensional motion.

9-12.P.1.1.d

Newton's First Law: Introduction

Motion draws our attention. Motion itself can be beautiful, causing us to marvel at the forces needed to create spectacular sights, such as that of a ...

Newton's First Law: Application

Experience suggests that an object at rest remains at rest if left alone, and that an object in motion tends to slow down and stop unless some effort is ...

Internal and External Forces

Newton&#39;s first law states that a net external force causes a change in motion. External forces act on an object or system, originating outside of the ...

Newton's Second Law

Newton&#39;s second law is closely related to his first law of motion. It mathematically gives the cause-and-effect relationship between force and changes ...

Mass and Weight

Mass and weight are often used interchangeably in everyday conversation. For example,&#160; medical records often show our weight in kilograms, but never ...

Weightlessness

When an object is dropped, it accelerates toward the center of the Earth. If the net external force on the object is its weight, it is said to be in free ...

Apparent Weight

True weight is the measure of the gravitational force acting on an object. However, if the object accelerates, its measured weight is different from its ...

/files/media/science-education/science-education-thumbs/14695.jpg

Newton's Third Law: Introduction

Whenever one body exerts a force on a second body, the first body experiences a force equal in magnitude and opposite in direction, to the force that it ...

Newton's Third Law: Examples

Newton&#39;s third law states that every action has an equal and opposite reaction. Consider a swimmer pushing off the side of a pool. They push against ...

2. Construct explanations of dynamics from evidence, using Newton's laws of motion.

9-12.P.1.2

Force

Forces affect every moment of our life. Our bodies are held to the Earth by force, and they are held together by the forces of charged particles. When we ...

Types of Forces

In most situations, forces can be grouped into two categories: contact forces and field forces.&#160; Contact forces occur as a result of direct physical ...

first-law-particles-in-one-dimensional-equilibrium

First Law: Particles in One-dimensional Equilibrium

Newton&#39;s first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a ...

a. Evaluate the effects of balanced and unbalanced forces on an object's motion.

9-12.P.1.2.a

Fluid Pressure in an Accelerating Elevator

Description

Transcript

Tags

More videos by Standards