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Thursday, April 23, 2020

FLUID STATICS - Fluid statics is the field of physics that involves the study of fluids at rest. Because these fluids are not in motion, that means they have achieved a stable equilibrium state, so fluid statics is largely about understanding these fluid equilibrium conditions. When focusing on incompressible fluids (such as liquids) as opposed to compressible fluids (such as most gases), it is sometimes referred to as hydrostatics. A fluid at rest does not undergo any sheer stress, and only experiences the influence of the normal force of the surrounding fluid (and walls, if in a container), which is the pressure. (More on this below.) This form of equilibrium condition of a fluid is said to be a hydrostatic condition. Fluids that are not in a hydrostatic condition or at rest, and are therefore in some sort of motion, fall under the other field of fluid mechanics, fluid dynamics. Consider a cross-sectional slice of a fluid. It is said to experience a sheer stress if it is experiencing a stress that is coplanar, or a stress that points in a direction within the plane. Such a sheer stress, in a liquid, will cause motion within the liquid. Normal stress, on the other hand, is a push into that cross-sectional area. If the area is against a wall, such as the side of a beaker, then the cross-sectional area of the liquid will exert a force against the wall (perpendicular to the cross section - therefore, not coplanar to it).

A beaker containing fluid with layers of different colors. The top layer is purple, the next layer is amber, then clear, then a whitish liquid. A hydrometer is sticking out of the beaker.

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Fluid Statics

By Andrew Zimmerman Jones

Fluid statics is the field of physics that involves the study of fluids at rest.

Because these fluids are not in motion, that means they have achieved a stable equilibrium state, so fluid statics is largely about understanding these fluid equilibrium conditions.

When focusing on incompressible fluids (such as liquids) as opposed to compressible fluids (such as most gases), it is sometimes referred to as hydrostatics.

A fluid at rest does not undergo any sheer stress, and only experiences the influence of the normal force of the surrounding fluid (and walls, if in a container), which is the pressure. (More on this below.) This form of equilibrium condition of a fluid is said to be a hydrostatic condition.

Fluids that are not in a hydrostatic condition or at rest, and are therefore in some sort of motion, fall under the other field of fluid mechanics, fluid dynamics.

Major Concepts of Fluid Statics

Sheer stress vs. Normal stress

Consider a cross-sectional slice of a fluid. It is said to experience a sheer stress if it is experiencing a stress that is coplanar, or a stress that points in a direction within the plane.

Such a sheer stress, in a liquid, will cause motion within the liquid. Normal stress, on the other hand, is a push into that cross-sectional area.

If the area is against a wall, such as the side of a beaker, then the cross-sectional area of the liquid will exert a force against the wall (perpendicular to the cross section - therefore, not coplanar to it).

The liquid exerts a force against the wall and the wall exerts a force back, so there is net force and therefore no change in motion.

The concept of a normal force may be familiar from early in studying physics, because it shows up a lot in working with and analyzing free-body diagrams.

When something is sitting still on the ground, it pushes down toward the ground with a force equal to its weight.

The ground, in turn, exerts a normal force back on the bottom of the object. It experiences the normal force, but the normal force doesn't result in any motion.

A sheer force would be if someone shoved on the object from the side, which would cause the object to move so long that it can overcome the resistance of friction.

A force coplanar within a liquid, though, isn't going to be subject to friction, because there isn't friction between molecules of a fluid. That's part of what makes it a fluid rather than two solids.

But, you say, wouldn't that mean that the cross section is being shoved back into the rest of the fluid? And wouldn't that mean that it moves?

This is an excellent point. That cross-sectional sliver of fluid is being pushed back into the rest of the liquid, but when it does so the rest of the fluid pushes back.

If the fluid is incompressible, then this pushing isn't going to move anything anywhere. The fluid is going to push back and everything will stay still.

(If compressible, there are other considerations, but let's keep it simple for now.)

Pressure

All of these tiny cross sections of liquid pushing against each other, and against the walls of the container, represent tiny bits of force, and all of this force results in another important physical property of the fluid: the pressure.

Instead of cross-sectional areas, consider the fluid divided up into tiny cubes.

Each side of the cube is being pushed on by the surrounding liquid (or the surface of the container, if along the edge) and all of these are normal stresses against those sides.

The incompressible fluid within the tiny cube cannot compress (that's what "incompressible" means, after all), so there is no change of pressure within these tiny cubes.

The force pressing on one of these tiny cubes will be normal forces that precisely cancel out the forces from the adjacent cube surfaces.

This cancellation of forces in various directions is of the key discoveries in relation to hydrostatic pressure, known as Pascal's Law after the brilliant French physicist and mathematician Blaise Pascal (1623-1662).

This means that the pressure at any point is the same in all horizontal directions, and therefore that the change in pressure between two points will be proportional to the difference in height.

Density

Another key concept in understanding fluid statics is the density of the fluid.

It figures into the Pascal's Law equation, and each fluid (as well as solids and gases) have densities that can be determined experimentally. Here are a handful of common densities.

Density is the mass per unit volume. Now think about various liquids, all split up into those tiny cubes I mentioned earlier.

If each tiny cube is the same size, then differences in density means that tiny cubes with different densities will have different amount of mass in them.

A higher-density tiny cube will have more "stuff" in it than a lower-density tiny cube.

The higher-density cube will be heavier than the lower-density tiny cube, and will therefore sink in comparison to the lower-density tiny cube.

So if you mix two fluids (or even non-fluids) together, the denser parts will sink that the less dense parts will rise.

This is also evident in the principle of buoyancy, that explains how displacement of liquid results in an upward force, if you remember your Archimedes.

If you pay attention to the mixing of two fluids while it's happening, such as when you mix oil and water, there'll be a lot of fluid motion, and that would covered by fluid dynamics.

But once the fluid reaches equilibrium, you'll have fluids of different densities that have settled into layers, with the highest density fluid forming the bottom layer, up until you reach the lowest density fluid on the top layer.

An example of this is shown on the graphic on this page, where fluids of different types have differentiated themselves into stratified layers based on their relative densities.

Andrew Zimmerman Jones

Math and Physics Expert

Education

M.S., Mathematics Education, Indiana University

B.A., Physics, Wabash College

Introduction

Academic researcher, educator, and writer with 23 years of experience in physical sciences

Works at Indiana Department of Education as senior assessment specialist in mathematics

Co-author of String Theory For Dummies

Member of the National Association of Science Writers

Experience

Andrew Zimmerman Jones is a former writer for ThoughtCo who contributed nearly 200 articles for more than 10 years. His topics ranged from the definition of energy to vector mathematics. Andrew is a dedicated educator; and he uses his background in the physical sciences, educational assessment, writing, and communications to advance that mission.

Andrew is co-author of String Theory For Dummies, which discusses the basic concepts of this controversial approach. String theory tries to explain certain phenomena that are not currently explainable under the standard quantum physics model.

Since 2018, Andrew has worked at the Indiana Department of Education as a senior assessment specialist in mathematics; prior to which he served as a senior assessment editor at CTB/McGraw Hill for 10 years. In addition, Andrew was a researcher at Indiana University's Cyclotron Facility. He is a member of the National Association of Science Writers.

Education

Andrew Zimmerman Jones received an M.S. in Mathematics Education from Indiana University–Purdue and a B.A. in Physics from Wabash College.

Awards and Publications

String Theory For Dummies (Wiley–For Dummies Series, 2009)

Harold Q. Fuller Prize in Physics (Wabash College, 1998)

ThoughtCo and Dotdash

ThoughtCo is a premier reference site focusing on expert-created education content. We are one of the top-10 information sites in the world as rated by comScore, a leading Internet measurement company. Every month, more than 13 million readers seek answers to their questions on ThoughtCo.

For more than 20 years, Dotdash brands have been helping people find answers, solve problems, and get inspired. We are one of the top-20 largest content publishers on the Internet according to comScore, and reach more than 30% of the U.S. population monthly. Our brands collectively have won more than 20 industry awards in the last year alone, and recently Dotdash was named Publisher of the Year by Digiday, a leading industry publication.

https://www.thoughtco.com/fluid-statics-4039368

Sunday, January 14, 2018

FLUID DYNAMICS - Fluid dynamics is one of two branches of fluid mechanics, which is the study of fluids and how forces affect them. Fluid dynamics provides methods for studying the evolution of stars, ocean currents, weather patterns, plate tectonics and even blood circulation. Some important technological applications of fluid dynamics include rocket engines, wind turbines, oil pipelines and air conditioning systems systems.

Fluid Dynamics

What Is Fluid Dynamics?

By Jim Lucas, Live Science Contributor

Fluid dynamics is "the branch of applied science that is concerned with the movement of liquids and gases," according to the American Heritage Dictionary.

Fluid dynamics is one of two branches of fluid mechanics, which is the study of fluids and how forces affect them.

(The other branch is fluid statics, which deals with fluids at rest.)

Scientists across several fields study fluid dynamics.

Fluid dynamics provides methods for studying the evolution of stars, ocean currents, , weather patterns, plate tectonics and even blood circulation.

Some important technological applications of fluid dynamics include rocket engines, wind turbines, oil pipelines and air conditioning systems systems.

What is flow?

The movement of liquids and gases is generally referred to as "flow," a concept that describes how fluids behave and how they interact with their surrounding environment — for example, water moving through a channel or pipe, or over a surface.

Flow can be either steady or unsteady.

In his lecture notes, "Lectures in Elementary Fluid Dynamics" (University of Kentucky, 2009) J. M. McDonough, a professor of engineering at the University of Kentucky, writes, "If all properties of a flow are independent of time, then the flow is steady; otherwise, it is unsteady."

That is, steady flows do not change over time.

An example of steady flow would be water flowing through a pipe at a constant rate.

On the other hand, a flood or water pouring from an old-fashioned hand pump are examples of unsteady flow.

Flow can also be either laminar or turbulent.

Laminar flows are smoother, while turbulent flows are more chaotic.

One important factor in determining the state of a fluid’s flow is its viscosity, or thickness, where higher viscosity increases the tendency of the flow to be laminar.

Patrick McMurtry, an engineering professor at the University of Utah, describes the difference in his online class notes, "Observations About Turbulent Flows" (University of Utah, 2000), stating, "By laminar flow we are generally referring to a smooth, steady fluid motion, in which any induced perturbations are damped out due to the relatively strong viscous forces. In turbulent flows, other forces may be acting the counteract the action of viscosity."

Laminar flow is desirable in many situations, such as in drainage systems or airplane wings, because it is more efficient and less energy is lost.

Turbulent flow can be useful for causing different fluids to mix together or for equalizing temperature.

According to McDonough, most flows of interest are turbulent; however, such flows can be very difficult to predict in detail, and distinguishing between these two types of flow is largely intuitive.

An important factor in fluid flow is the fluid's Reynolds number (Re), which is named after 19th century scientist Osborne Reynolds, although it was first described in 1851 by physicist George Gabriel Stokes.

McDonough gives the definition of Re as, "the ratio of inertial to viscous forces."

The inertial force is the fluid's resistance to change of motion, and the viscous force is the amount of friction due to the viscosity or thickness of the fluid.

Note that Re is not only a property of the fluid; it also includes the conditions of its flow such as its speed and the size and shape of the conduit or any obstructions.

At low Re, the flow tends to be smooth, or laminar, while at high Re, the flow tends to be turbulent, forming eddies and vortices.

Re can be used to predict how a gas or liquid will flow around an obstacle in a stream, such as water around a bridge piling or wind over an aircraft wing.

The number can also be used to predict the speed at which flow transitions from laminar to turbulent.

Liquid flow

The study of liquid flow is called hydrodynamics.

While liquids include all sorts of substances, such as oil and chemical solutions, by far the most common liquid is water, and most applications for hydrodynamics involve managing the flow of this liquid.

That includes flood control, operation of city water and sewer systems, and management of navigable waterways.

Hydrodynamics deals primarily with the flow of water in pipes or open channels.

Geology professor John Southard's lecture notes from an online course, "Introduction to Fluid Motions " (Massachusetts Institute of Technology, 2006), outline the main difference between pipe flow and open-channel flow: "flows in closed conduits or channels, like pipes or air ducts, are entirely in contact with rigid boundaries," while "open-channel flows, on the other hand, are those whose boundaries are not entirely a solid and rigid material."

He states, "important open-channel flows are rivers, tidal currents, irrigation canals, or sheets of water running across the ground surface after a rain."

Due to the differences in those boundaries, different forces affect the two types of flows.

According to Scott Post in his book, "Applied and Computationsl Fluid Mechanics," (Jones & Bartlett, 2009), "While flows in a closed pipe may be driven either by pressure or gravity, flows in open channels are driven by gravity alone."

The pressure is determined primarily by the height of the fluid above the point of measurement.

For instance, most city water systems use water towers to maintain constant pressure in the system.

This difference in elevation is called the hydrodynamic head.

Liquid in a pipe can also be made to flow faster or with greater pressure using mechanical pumps.

Gas flow

The flow of gas has many similarities to the flow of liquid, but it also has some important differences.

First, gas is compressible, whereas liquids are generally considered to be incompressible.

In "Fundamentals of Compressible Fluid Dynamics" (Prentice-Hall, 2006), author P. Balachandran describes compressible fluid, stating, "If the density of the fluid changes appreciably throughout the flow field, the flow may be treated as a compressible flow."

Otherwise, the fluid is considered to be incompressible.

Second, gas flow is hardly affected by gravity.

The gas most commonly encountered in everyday life is air; therefore, scientists have paid much attention to its flow conditions.

Wind causes air to move around buildings and other structures, and it can also be made to move by pumps and fans.

One area of particular interest is the movement of objects through the atmosphere.

This branch of fluid dynamics is called aerodynamics, which is "the dynamics of bodies moving relative to gases, especially the interaction of moving objects with the atmosphere," according to the American Heritage Dictionary.

Problems in this field involve reducing drag on automobile bodies, designing more efficient aircraft and wind turbines, and studying how birds and insects fly.

Bernoulli's principle

Generally, fluid moving at a higher speed has lower pressure than fluid moving at a lower speed.

This phenomenon was first described by Daniel Bernoulli in 1738 in his book "Hydrodynamics," and is commonly known as Bernoulli's principle.

It can be applied to measure the speed of a liquid or gas moving in a pipe or channel or over a surface.

This principle is also responsible for lift in an aircraft wing, which is why airplanes can fly.

Because the wing is flat on the bottom and curved on the top, the air has to travel a greater distance along the top surface than along the bottom.

To do this, it must go faster over the top, causing its pressure to decrease. This makes the higher-pressure air on the bottom lift up on the wing.

Problems in fluid dynamics

Scientists often try to visualize flow using figures called streamlines, streaklines and pathlines.

McDonough defines a streamline as "a continuous line within a fluid such that the tangent at each point is the direction of the velocity vector at that point."

In other words, a streamline shows the direction of the flow at any particular point in the flow.

A streakline, according to McDonough, is "the locus [location] of all fluid elements that have previously passed through a given point."

A pathline (or particle path), he writes, is "the trajectory of an individual element of fluid."

If the flow does not change over time, the pathline will be the same as the streamline.

However, in the case of turbulent or unsteady flow, these lines can be quite different.

Most problems in fluid dynamics are too complex to be solved by direct calculation.

In these cases, problems must be solved by numeric methods using computer simulations.

This area of study is called numerical or computational fluid dynamics (CFD), which Southard defines as "a branch of computer-based science that provides numerical predictions of fluid flows."

However, because turbulent flow tends to be nonlinear and chaotic, particular care must be taken in setting up the rules and initial conditions for these simulations.

Small changes at the beginning can result in large differences in the results.

The accuracy of simulations can be improved by dividing the volume into smaller regions and using smaller time steps, but this increases computing time.

For this reason, CFD should advance as computing power increases.

Jim Lucas is a freelance writer and editor specializing in physics, astronomy and engineering. He is general manager of Lucas Technologies.

https://www.livescience.com/47446-fluid-dynamics.html

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